Origin of zero and negative thermal expansion in severely-deformed superelastic NiTi alloy

Acta Materialia 124 (2017) 79e92

Contents lists available at ScienceDirect

Acta Materialia journal homepage: www.elsevier.com/locate/actamat

Full length article

Origin of zero and negative thermal expansion in severely-deformed superelastic NiTi alloy A. Ahadi a, b, *, Y. Matsushita c, T. Sawaguchi c, Q.P. Sun d, K. Tsuchiya c a

International Center for Young Scientists, National Institute for Materials Science (NIMS), 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan State Key Lab of Water Resources and Hydropower Engineering and School of Civil Engineering, Wuhan University, China c National Institute for Materials Science (NIMS), 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan d Department of Mechanical and Aerospace Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 16 September 2016 Received in revised form 19 October 2016 Accepted 21 October 2016

We have investigated the physical origin of anomalous in-plane thermal expansion (TE) anisotropy leading to invar-like behavior and negative TE in nanostructured NiTi sheets manufactured via severe cold-rolling. The roles of grain size (GS), crystallographic texture, thermally-induced phase transformation, and intrinsic (lattice level) TE of austenite (B2) and martensite (B190 ) phases on the macroscopic TE behavior are addressed. It is shown that by controlling the cold-rolling thickness reduction and heat-treatment temperature the coefficient of thermal expansion (CTE) can be controlled in a wide range from positive (a ~ 2.1  105 K1) to negative (a ~ 1.1  105 K1) via in-plane anisotropy of TE. A very small CTE of a ~ 5.3  107 K1 (invar-like behavior) in a wide temperature window of 230 K (353 e123 K) is obtained at an angle of 33.5 to the rolling direction (RD) of the severely cold-rolled sheet. TEM and XRD studies show that the microstructure underlying such anomalous TE behavior consists of a mixture of B2 nano-grains and retained/residual deformation-induced martensite and that the observed anomalous TE anisotropy is due to the intrinsic anisotropic TE of residual martensite. The invar-like behavior is the result of the cancellation of the positive TE of austenite phase with the negative TE of residual martensite along 33.5 to the RD. A simple rule of mixture model incorporating the intrinsic TE of B2 and B190 lattices and the texture coefficients of the sample is proposed which successfully captures the anomalous in-plane TE anisotropy. The discovery of high dimensional stability over a wide temperature window along with temperature insensitive non-hysteretic linear superelasticity of the severely-deformed NiTi opens up a new route for designing stable SMAs for applications in ragged environments. © 2016 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Severe plastic deformation Shape memory alloys Nanocrystalline microstructure In situ transmission electron microscopy (TEM) Zero and negative thermal expansion

1. Introduction The temperature-dependence of dimensions, usually referred to as thermal expansion (TE), is an intrinsic feature of metallic materials that arises from atomic bonding considerations [1]. Such temperature-dependence of dimensions, especially in the presence of large temperature variations or temperature gradients, limits the application of metallic materials to narrow temperature windows. For example, the difference in coefficient of TE (CTE) between

* Corresponding author. International Center for Young Scientists, National Institute for Materials Science (NIMS), 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan. E-mail address: [email protected] (A. Ahadi). http://dx.doi.org/10.1016/j.actamat.2016.10.054 1359-6454/© 2016 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

substrate and thin films creates internal stress that affects the physical, electrical and thermal properties of the thin films [2e4]. In bridges, railroad tracks, and pipelines the TE has to be compensated by expansion joints. In high-precision instruments such as standard rulers and clocks where high dimensional stability of the components is required, materials with low TE (LTE) or even zero TE (ZTE) are employed. In recent years, there has been a significant growth of interest in developing materials showing Negative TE (NTE), LTE, and ZTE from both practical and theoretical points of view [5]. Several material systems showing NTE, LTE, and ZTE (tailorable TE) have been developed in which the value of CTE can be tailored to a specific value by chemical composition modification [6e12]. Shape memory alloys (SMAs) undergoing a thermoelastic firstorder martensitic phase transformation (PT) are well-known in

80

A. Ahadi et al. / Acta Materialia 124 (2017) 79e92

medical, aeronautical, and MEMS applications [13,14]. Recently, it has been reported that SMAs can exhibit tailorable TE via manipulating their microstructure. Kainuma et al. first reported that moderately cold-rolled Cu-Zn-Al SMA shows CTE varying from 0 to 15  106 K1 [15,16]. Later, the tailorable TE was reported in Ti23Nb-0.7Ta-2Zr-O (TNTZ) Gum metal alloy after moderate coldrolling reductions [17,18]. Kim et al. investigated the effect of nanodomains on the LTE/ZTE of as-rolled Gum metal with chemical composition of Ti-23Nb-0.7Ta-2Zr-1.2O (at%) [19] and attributed the LTE/ZTE to compensation of vibrational lattice strain via growth of nanodomains during cooling [20]. However, others have attributed the LTE of Gum metal to the strain glass mechanism [21]. Monroe et al. proposed a universal mechanism leading to existence of NTE/ZTE in materials undergoing thermoelastic martensitic PT [22]. Using NiTiPd, CoNiGa, and TiNb as model alloys they argued that the TE anisotropy is directly linked to the crystallographic relationship between the austenite and martensite lattices [22]. Recently, Hao et al. reported tailorable TE in Ti‒15Nb‒2.5Zr‒4Sn alloy due to nano-scale concentration modulation via phase separation [23]. Hence, it is noted that the mechanism of tailorable TE (LTE/ZTE/PTE) in SMAs is scattering and different scenarios have been proposed. For NiTi SMAs with the most widespread applications, there is no systematic work available on the existence of tailorable TE and its relationship with the microstructure remains unexplored. In this study, we investigate the in-plane TE anisotropy of NiTi sheets (Ti-50.6 at.% Ni) manufactured via severe cold-rolling and controlled heat treatment. We report the existence of tailorable TE via in-plane anisotropy in the as-rolled and moderately heattreated sheets. We show that the value of linear CTE is controllable between a ¼ þ21  106 K1 and a ¼ 11  106 K1 and a near ZTE (a ¼ 0.53  106 K1) can be achieved along 33.5 to the rolling direction (RD). The intrinsic TE behavior of B2 and B190 structures and the corresponding TE matrices in the temperature range from 50 to 400 K are measured. The physical origin of the obtained tailorable TE is investigated using in-situ cooling TEM and in-situ XRD and a simple model of TE anisotropy is proposed that satisfactorily captures the observed NTE/ZTE/PTE behavior. The results suggest that the superelastic NiTi can be employed as a tailorable TE material without the need to modify its chemical composition. The combination of temperature-insensitive nonhysteretic superelasticity [24] along with high dimensional stability offers the severely-deformed superelastic NiTi alloy as suitable candidate for applications in ragged environments.

[26,27]. 2.2. Thermal expansion (TE) measurements The role of microstructure on TE behavior was studied by a highresolution thermal mechanical analyzer (TMA 402 F1/F3 Hyperion) from NETZSCH Company. Rectangular bars with dimensions of 18  2.84  0.60 mm3 were cut along different angles to the RD (0 , 22.5 ,33.5 ,45 ,67.5 and 90 ) as shown in Fig. 1a. The specimens were heated up to 353 K with a heating rate of 10 K/min, held for 10 min for temperature uniformity, and then cooled down to 123 K using a cooling rate of 2 K/min with LN2 cooling system. The macroscopic thermal strain was calculated as l(T)l0/l0 where l is the length at each temperature and l0 is the length at 353 K. Note that for clear illustration of PTE/ZTE/NTE response l0 is chosen at 353 K. 2.3. Texture measurements The texture of the as-rolled and heat treated sheets was studied by measuring the incomplete (110), (200), and (211) pole figures (PFs) of the parent austenite phase (B2) using a Rigaku XRD machine with Co Ka radiation source equipped with a 2-axis goniometer. The PFs were measured in the 15o < a < 90o and 0o < b < 360o with an incident slit of 5 mm, a step of 1.5 , and b speed of 63 deg/s. In the as-rolled sheets the background was measured sufficiently away from the diffraction profiles due to broadened diffraction peaks. The defocusing was corrected using a plasma-atomized NiTi powder [28]. The Orientation Distribution Function (ODF) and transformation texture calculations were performed with MTEX package [29]. 2.4. In-situ cooling TEM A JIB-4000 Focused Ion Beam (FIB) was used to fabricate thin foils with thickness of less than 80 nm for in-situ TEM observations.

2. Materials and experiments 2.1. Materials Polycrystalline superelastic NiTi sheets with chemical composition of Ti-50.6 at.% Ni and initial thickness of 1.524 mm were purchased from Johnson Matthey Company. The as-received sheets were annealed at a temperature of 1073 K (800  C) for 1 h and quenched in water. Sheets with dimensions of 30  1.524  100 mm3 were sandwiched in stainless steel sheets and cold-rolled in a 4hi cold-rolling mill set (YoshidaKinen Company) to thickness reductions of 42%, 50%, and 60%. The 50% rolled sheets were heat treated at temperatures of 1073 K for 30 min (referred to as 1073-30 sheet hereafter), 973 K for 5 min (973-5), and 623 K for 20 min (623-20). The 42% rolled sheet was annealed at 523 K for 60 min (523-60). The above heat treatments result in a range of microstructures with different features such as GS [24], defect density, texture [25], and different volume fraction of residual martensite as well as different superelastic properties

Fig. 1. (a) Schematic of the rectangular bars cut along different angles to the RD (4) of the sheets for TE anisotropy measurements by TMA and (b) a typical SEM image of the thin foils fabricated by FIB for in-situ TEM observations.

A. Ahadi et al. / Acta Materialia 124 (2017) 79e92

The thin foils were mounted on copper thin foils. The surface of the samples were coated by carbon before thinning to protect the surface from Ga damage. A Gatan 636 holder with liquid nitrogen cooling capability was used for in-situ observation of thermallyinduced microstructural changes from 300 down 103 K in a JEM2100F1 transmission electron microscopy (TEM). 2.5. In-situ low temperature XRD In order to measure the temperature-dependent lattice constants of B2 and B190 crystal structures required for calculation of the TE matrix, in-situ XRD measurements were performed on NiTi powders prepared by gas-atomizing (GA) and plasma-atomizing (PA) techniques. The PA powder has a slightly Ni-rich composition (Ti-50.9 at.%Ni), similar to the composition of bulk material used in our study, and the GA powder has a Ti-rich composition with Ti-49.2 at.% Ni. In order to remove the processing inhomogeneity, the GA powder was annealed at 1073 K for 30 min. The DSC curves of the powders are provided in Fig. F1 of Supplemental Data. The XRD patterns were recorded in the temperature range from 400 down to 50 K at temperature intervals of 15 K using a Rigaku SmartLab (9 kW XRD) equipped with a CuKa1 radiation source and 1D-type semiconductor (D'teX Ultra 250) with l ¼ 0.154056 nm. A customized Helium cooling cryogenic system was used in order to cool the powders. The samples were cooled down to 50K and kept in that temperature for 12 h for temperature uniformity before recording the XRD patterns. XRD patterns were recorded in the 10 < 2q < 100 using a step size of 0.02 deg/step and scan speed of 0.8 deg/sec. The B190 diffracting planes were indexed according to a ¼ 2.889 Å, b ¼ 4.120 Å, c ¼ 4.622 Å, and b ¼ 96.8 from Otsuka et al. [30]. 3. Results and discussion 3.1. Texture of austenite phase (B2 parent phase) In Fig. 2aef the texture of the austenite phase in the as-rolled and heat treated sheets is represented as 42 sections in Euler space where an orientation is identified by three angles 41, f, and 42. The (110), (200), and (211) pole figures used for calculation of ODF are shown in Fig. F2 of Supplemental Data. It is seen that the 973-5 and 623-20 sheets (Fig. 2bec) have very similar texture components; along the RD they possess a dominant component near {111}〈110〉 and {332}〈110〉 fibers (a-fibers) with a spread towards {110}〈110〉. In the ND the dominant texture component is close to {111}〈110〉 g-fiber. These texture components are commonly observed in recrystallization annealed NiTi and NiTiFe alloys [31,32]. Comparing Fig. 2b and c it is noted that with a maximum texture index (TI) of 7.4 the 973-5 sheet has the stronger texture than the 623-20 sheet with TI ¼ 5 indicating that with increasing annealing temperature from 623 K to 973 K the texture becomes stronger. With further increase of annealing temperature to 1073 K however, the overall texture becomes weaker and more random as seen in Fig. 2a. From Fig. 2def the main texture of the 523-60 and CR42% sheets is approximated as completeg-fiber {111} 〈uvw〉 in the ND direction. In these sheets a relatively weak a-fiber {331}〈110〉 texture component in the RD direction is observed which is in accordance with the pervious texture studies of coldrolled NiTi sheets [33e35]. 3.2. TE of coarse-grained and nano-grained NiTi Fig. 3aec shows the room temperature (RT) microstructures, DSC curves, and anisotropic TE behavior of the 1073-30, 973-5, and

81

623-20 sheets. As it is seen from the TEM images and DSC curves, all the three specimens have a fully austenitic microstructure at RT and that the average GS is decreased from about 10 mm in the 1073-30 sheet (Fig. 2a1) to ~ 60 nm in the 973-5 sheet (Fig. 2a2). The microstructure of the 623-20 sheet consists of a relatively high density of defects and the average GS (measured with XRD) is about 16 nm. The DSC curve of the 1073-30 sheet (Fig. 3b1) shows that during cooling the sample undergoes a thermally-induced PT (see also Fig. 4 for in-situ TEM observations) with Ms ¼ 278 K, Mf ¼ 255 K, and a thermal hysteresis Ap-Mp ¼ 15 K. In a clear one-to-one correspondence with the DSC curve, the TE behavior of the 1073-30 sheet (Fig. 3c1) shows three distinct stages of expansion/contraction as commonly observed in conventional coarse-grained and single-crystalline SMAs [36e38]. Upon cooling in the austenitic regime (T > Ms), the sample contracts with CTE of aB2 ¼ 12.1  106 K1. In this regime (T > Ms), no TE anisotropy is observed between the TD 45o RD, 45 , and TD directions (aRD B2  aB2  aB2 ). Once the Ms is reached, the specimen length starts to increase in the RD direction (see inset in Fig. 3c1) due to phase transformation Dε ¼ 0.034% (see Fig. 3c1 and c2). In this regime (Mf < T < Ms), TE anisotropy is observed as expansion along RD and TD directions while along 45 to the RD the sample contracts. The anisotropy in this regime originates from the dependence of transformation strain to texture [31]. In the fully martensitic regime (T < Mf), the specimen's length during cooling uniformly 6 1 TD 45o decreases in all directions, i.e. aRD K B190  aB190  aB190 ~ 8.9  10 (no TE anisotropy). The isotropy of TE in this regime, however, is unexpected since the monoclinic crystal structure exhibits significant TE anisotropy (see Figs. 11 and 12) [39,40]. This is due to the fact that the martensite forms with random orientations through the self-accommodating morphology of martensite [41e44] as shown in the in-situ TEM micrograph at 103 K in Fig. 4 (see also section 3.7 for quantitative discussion). During heating, reverse PT occurs, the length is recovered after a hysteresis loop [27,45] and a small residual strain of ~ 0.064% is left behind [46]. The PT in 973-5 sheet, due to a much reduced GS to the nanocrystalline regime, occurs in a two-stage manner (A/R and R/M) as seen in the DSC curve (Fig. 3b2). The TE behavior of this specimen shows that in the austenitic regime (T > Rs), 6 TD 45o aRD K1 (no TE anisotropy). The B2  aB2  aB2 ¼ 12.8  10 isotropic TE behavior in this regime, despite the strong texturing of austenite phase (see Fig. 2b), is due to the intrinsic (lattice level) isotropic TE of austenite phase (see Fig. 12). In the transformation regime (Mf < T < Rs), the RD direction expands in a two-stage manner in accordance with the transformation sequence observed from DSC. Compared with the 1073-30 sheet, the expansion due to phase transformation is an order of magnitude larger (εtr ¼ 0.37%) in the 973-5 sheet. In the martensitic regime 6 1 TD 45o (T < Mf)aRD K meaning no in-plane B190 zaB190 zaB190 ¼ 5.1  10 TE anisotropy which is due to random formation of martensite. The random formation of martensite variants can be deduced from the appearance of sporadic B190 diffraction spots in the reciprocal space as shown in the SAED pattern recorded in-situ at 103 K in Fig. 4 (see also Fig. F3 of Supplemental data for enlarged figure). For the 623-20 sheet the heat flow signal shows a broadened Rphase transformation with Rs ~ 327 K while a very weak peak (Mp) is observed at around 180 K (see inset in Fig. 3b3). Similar to the 1073-30 and 973-5 sheets there is no TE anisotropy in the fully 6 1 TD 45o austenitic regime (T > Rs), aRD K . With B2  aB2  aB2 ¼ 11.3  10 cooling below Rs the length continuously decreases (nonlinearly) in all directions (Fig. 3c3). Indeed the difference in the amount of

82

A. Ahadi et al. / Acta Materialia 124 (2017) 79e92

Fig. 2. Representation of austenite texture through f2 sections of ODF for (a) 1073-30, (b) 973-5, (c) 623-20, (d) 523-60, (e) CR42%, and (f) CR60% sheets.

length change between RD, 45 , and TD directions evidences the occurrence of structural PT (most likely R-phase transformation) during cooling. With further cooling to below Mp (see Fig. 3b3) the length starts to increase (continuously) in the RD direction and keeps decreasing in TD direction, i.e. the TE behavior is anisotropic. Obviously, the observation of hysteresis area and TE anisotropy below Mp indicates the occurrence of martensitic PT in this sample below 180 K. The occurrence of martensitic PT is further confirmed by the appearance of B190 diffraction spots in SAED patterns recorded in-situ at 103 K as shown in Fig. 4 (see also Fig. F4 of Supplemental data). 3.3. Anomalous NTE, ZTE, and invar-like behavior in severelydeformed NiTi Fig. 5aec shows the RT microstructures, DSC curves, and anisotropic TE behavior of the 523-60, CR42%, and CR60% sheets. The TEM images in Fig. 5a1-a3 clearly show that the sheets have high density of defects and the average GS (measured with XRD) ranges from 21 nm in the 523-60 sheet down to 5 nm in the CR60% sheet [47e51]. Local amorphous bands were observed in the CR60% sheet. Consequently, the DSC curves (Fig. 5b) show broadened and weak signals due to high density of defects and nano GS [52,53]. In stark contrast with the TE behavior of 1073-30, 973-5, and 623-20 sheets whereas distinct stages of expansion/contraction and hysteresis were observed, the TE of 523-60, CR42%, and CR60%

sheets exhibit continuous expansion or contraction depending on the orientation to the RD and that the thermal hysteresis becomes very small and finally vanishes in the CR60% sheet. Along the RD direction these sheets show anomalous continuous expansion during cooling, i.e. they exhibit NTE response while along the TD direction they undergo continuous contraction, i.e. they exhibit PTE response. It is also very interesting to note that in the CR60% sheet the temperature dependence of thermal strain along each orientation becomes almost linear and thus the CTE is almost a constant. In all the 523-60, CR42%, and CR60% sheets the transition from NTE in the RD direction to PTE in the TD direction is continuous/gradual. For example, in the CR60% sheet, the CTE at 250 K gradually increases from aRD ¼ 8.1  106 K1 in the RD to aTD ¼ 14.9 106 K1 in the TD direction as shown in Fig. 6. From Fig. 6 it is also 6 1 seen that the CR42% sheet has larger NTE (a250K K ) RD ¼-9.5 10 6 1 than CR60% (a250K K ) while the 523-60 sheet has RD ¼ 8.1 10

¼ 2.8 106. As will be shown in section the lowest NTE of a250K RD 3.7, such difference in the CTE value in the RD direction is mainly due to a difference in the volume fraction of retained/residual DI martensite in these sheets. Moreover, a very unique property in the CR60% sheet is that a very low TE is achievable along the 33.5 to the RD direction (see blue curve in Fig. 5c3). In this orientation, the value of CTE is very small and changes slightly with temperature (from a33:5o ¼ 0.53 106 K1 at 350 K to a33:5o ¼ 1.03 106 K1 at 123 K). Such low value of CTE (smaller than CTE of invar

A. Ahadi et al. / Acta Materialia 124 (2017) 79e92

83

Fig. 3. TEM images of the initial microstructure 1073-30 (a1), 973-5 (a2), and 623-20 (a3) sheets. DSC thermograms of the 1073-30 (b1), 973-5 (b2), and 623-20 (b3) sheets. Evolution of macroscopic strain with temperature along RD, 4 ¼ 45 , and TD directions for 1073-30 (c1) 973-5 (c2), and 623-20 (c3) sheets.

with a ¼ 1.5 106 K1) along with its weak temperature sensitivity over a wide temperature window (DT ¼ 232 K) is a highly appealing property for applications whereas high dimensional stability over a wide temperature range are required. 3.4. In-situ TEM and XRD analysis on the anomalous TE behavior While in-situ TEM provides direct real-time picture of very local microstructural changes during cooling, in-situ XRD can provide more quantitative results on the global changes of microstructure as well as evolution of lattice strains due to thermal lattice vibration mechanism. Fig. 7 shows in-situ TEM images taken from the same area of thin foil at three different temperatures; 103 K, 173 K, and 300 K for the 523-60 and CR60% sheets. The TEM images and the corresponding SAED patterns reveal that the microstructure of the CR60% sheet remain almost unchanged during cooling down to 103 K, i.e. thermally-induced martensitic PT is suppressed due to extremely fine GS and high density of defects introduced during severe cold-rolling [26,43,53]. It is worth noting that our in-situ observations even at higher magnifications also revealed no discernible microstructural activity during cooling in the CR60% sheet. In the 523-60 sheet however, continuous local changes of the microstructure are observed as evidenced from the change in contrast in the green dashed areas. Indeed the observation of nonlinear length change and temperature hysteresis in the TE behavior of 523-60 sheet (Fig. 5c1) indicates that such contrast changes are due to a martensitic PT.

Fig. 8a and b shows the in-situ XRD profiles from 350 down to 50 K. At 350 K the XRD profiles of all sheets consists of a broad and asymmetric peak at 2q ~ 42.5 corresponding to 110B2 and a peak located at 2q ~ 38.4 assigned to 110B190 . The XRD profiles show that with cooling the intensity of the 110B2 peak continuously decreases and that of the 110B190 increases indicating a continuous martensitic PT [27]. This is however, in contradiction with the in-situ TEM observations of the CR60% whereas no change in the average microstructure with cooling was observed which is most likely due to the inhomogeneity of the microstructure in the CR60% sheet. However, a more precise analysis of the XRD profiles show that with cooling from 350 to 300 K the diffracted intensities does not change, i.e. no PT occurs in this temperature range. On the other hand, by referring to the TE curves (Fig. 5c1ec3), it is clearly noted that all the sheets exhibit anomalous TE anisotropy (NTE, PTE, and ZTE) between 350 and 300 K. Therefore, a continuous martensitic PT is indeed not the physical origin of such anomalous TE in the CR60% and CR42% sheets. Fig. 8c shows the evolution of lattice strain of the 110B2 with temperature. A PTE behavior is observed with heating from 4 to 400 K for all the three sheets. This indicates that the high density of point defects, existence of partial amorphous phase, and extreme grain refinement does not introduce any NTE or ZTE effect in the austenite phase. Lastly, in Fig. 8a and b there exists asymmetric shift of the 110B2 peak with cooling as shown in the red insets. As will be shown in sections 3.5 and 3.6 all these anomalous features are due to the existence of residual/retained DI B190 martensite and its inherently anisotropic TE behavior.

84

A. Ahadi et al. / Acta Materialia 124 (2017) 79e92

Fig. 4. In-situ TEM images and SAED patterns captured at RT and 103 K showing a typical thermally-induced martensitic PT in 1073-30 and 973-5 sheets. The SAED of 623-20 sheet at 103 K shows very weak diffraction rings belonging to martensite.

3.5. Retained/residual deformation-induced B190 martensite and its thermal stability The microstructure of severely-deformed NiTi has been the subject of several studies [43,47,48,51,53e55]. Besides the welladdressed extreme grain refinement and amorphisation, local residual/retained deformation-induced martensite has been frequently observed in deformed NiTi [55,56]. Chi-scan XRD measurements of the CR42%, CR60%, and 523-60 sheets are shown in Fig. F5 of Supplemental data. The residual martensite is clearly observed as evolving B190 diffraction peaks with increasing Chi rotation. Stronger intensities of B190 diffraction peaks in the CR42% sheet indicates higher volume fraction of residual martensite compared to CR60% sheet while the 523-60 has the lowest volume fraction of residual martensite. The lower volume fraction of residual martensite in the CR60% sheet compared to the CR42% sheet is in line with recent studies [57] which shows that the volume

fraction of residual martensite decreases when the cold-rolling height reduction is above a certain level. A selective TEM micrograph, HRTEM image, and a set of SAED patterns taken from different areas of thin foil in the CR42% sheet are shown in Fig. 9aeg. In the HRTEM images twin lamellae with nano-width were frequently observed as shown in Fig. 9b. In the corresponding SAED patterns the residual martensite is manifested as streaks between B2 diffraction spots (Fig. 9cee). In ring-type diffraction patterns (Fig. 9f and g) they appear as rings with relatively lower diffraction intensities compared with B2 diffraction rings [55,56]. Fig. 9h shows the stability of residual martensite with annealing temperature. It is seen that the intensity of the residual deformation-induced 110B190 peak decreases with increasing annealing temperature indicating a reduction of volume fraction of residual martensite while the FWHM of the 110B2 decreases due to grain growth and annihilation of defects. At about 600 K (327  C) the residual martensite peak 110B190 vanishes.

A. Ahadi et al. / Acta Materialia 124 (2017) 79e92

85

Fig. 5. TEM images of the initial microstructure of 523-60 (a1), CR42% (a2), and CR60% (a3) sheets. DSC thermograms of 523-60 (b1), CR42% (b2), and CR60% (b3) sheets. Evolution of macroscopic strain with temperature along RD, 4 ¼ 22.5 , 33.5 , 45 , 67.5 and TD directions for 523-60 (c1) CR42% (c2), and CR60% (c3) sheets.

Fig. 6. In-plane variation of coefficient of TE (CTE) at 250 K with angle to the RD (4) showing a gradual transition from NTE in the RD to PTE in the TD in the cold-rolled and recovery-annealed sheets.

3.6. Intrinsic TE of B2 and B190 crystal structures from 50 to 400 K Fig. 10a and b shows in-situ XRD profiles of the gas-atomized (GA) and plasma-atomized (PA) powders at three typical temperatures from 50 to 300 K. For the GA powder (Fig. 11a), at 50 K, the peaks located at 38.24 , 38.9 , 41.06 , 43.96 , and 44.94 are unambiguously assigned to 110B190 , 002B190 , 111B190 , 020B190 , and 111B190 diffracting planes of monoclinic martensite, respectively. A precise analysis of the peak profiles at different temperatures reveals that the GA powder contains trigonal R-phase. For example, at 275 K, the R-phase is clearly noted as two sharp humps/shoulders located at right side (112R) and left side (030R) of the 110B2 peak as

shown in the inset. In the XRD profile of the PA powder (Fig. 10b) the main diffraction peaks belong to the monoclinic martensite as indexed by blue color. However, a precise analysis of the XRD profiles at different temperatures reveal that even with cooling down to 50 K, the PA powder contains residual austenite as evidenced from the peak located at 42.52 . The same observation was made in the GA powder after annealing at 1073 K. Thus, in the PA and GA-annealed powders we have been able to measure the temperature-dependent lattice spacings of both B190 and B2 (residual/untransformed B2) down to 50 K (well below the transformation temperatures), see Fig. F1 of Supplemental data for transformation temperatures. Furthermore, the insets in Fig. 10a and b shows that during cooling the 110B190 , 020B190 , and 111B190 peaks move towards higher 2q angles (lower d-spacings) while 002B190 and 111B190 peaks move in opposite direction i.e. lower 2q angles (higher d-spacings), indicating the intrinsic TE anisotropy of B190 lattice planes. Moreover, it is also noted that the magnitude of peak shift also depends on the peak. For the GA-annealed powder, the 110B190 peak is continuously displaced from 38.28 at 50 K to 38.12 at 275 K (D2q ¼ 0.16 ) while the 111B190 peak is much less displaced from 41.22 at 50 K to 41.23 at 275 K (D2q ¼ 0.01 ). The evolution of thermal lattice strain (see Appendix A for definition) with temperature is represented in the first row of Fig. 11 for all the powders tested. The markers are experimental points and the solid lines are second-order polynomial fits to the experimental data (see also Table 1). It is clearly seen that in contrast to the B2 structure where all the diffracting planes isotropically expand during heating, i.e. they exhibit PTE response, the 020B190 , 110B190 , 111B190 , and 022B190

86

A. Ahadi et al. / Acta Materialia 124 (2017) 79e92

Fig. 7. In-situ TEM images and SAED patterns of the 523-60 and CR60% sheets captured at RT and 103 K.

Fig. 8. In-situ XRD profiles from 50 to 350 K for the CR60% (a) and 523-60 (b). The evolution of thermal lattice strain with temperature in the B2 phase (c).

planes undergo PTE while 111B190 , 002B190 , and 112B190 planes exhibit NTE. In the GA powder, the 020B190 plane possess the maximum PTE (a200K 020

B190

 26:1  106 K1) and the 112B190 plane

possesses the maximum NTE (a200K

112B190

¼ 23:5  106 K1) while

the 111B190 plane has the lowest CTE of a200K

111B190

¼ 4:3  106 K1.

In Fig. 11 the three dimensional representation of the TE matrix

(also known as quadric) for the B2 and B190 crystal structures at a selective temperature of 150 K are shown. It is seen that the TE matrix of the B2 crystal structure is in the form of a sphere indicating the isotropy of CTE in all crystallographic directions. The TE quadric of the B190 crystal structure is in the form of a dumbbelllike hyperbole (blue color), representing a set of crystallographic directions with negative CTE, and a red torus representing a set of

A. Ahadi et al. / Acta Materialia 124 (2017) 79e92

87

Fig. 9. (a) TEM micrograph of the CR42% sheet, (b) a HRTEM image of the red inset showing nanoscale twin lamellae, (c) SAED pattern of the area numbered 1, (d) SAED pattern of the area numbered 2, (e) SAED pattern of the area numbered 3, (f) SAED pattern of the blue circle numbered 4, (g) a representative SAED pattern of the CR60% sheet and (h) in-situ heating XRD diffractogram of the CR42% showing the stability of residual martensite with annealing temperature. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

crystallographic directions with positive CTE. Note that by convention the Y axis is chosen so as to lie along the b of monoclinic (diad axis), Z along the c and X is along the a* ¼ b c axis [39]. It is common practice to represent the quadric in its principal axes by rotation of the coordinates along the b axis counter clockwise for 4¼0.5tan1(2ja31j/a33a11), e.g. 21.32 for the GA powder as it is shown in Fig. 12. The principal X, Y, and Z directions for monoclinic crystal lie along [305], [010] and [601], respectively. The [601] is the maximum PTE direction with a250K ¼ 9:3  106 K1 and the [305] ½601

6 K1. direction is the principal NTE direction a250K ½205 ¼ 7:36  10

The asymptote between the positive and negative hyperbolae (dashed lines) is a ZTE direction in monoclinic crystal. At 350 K the ZTE direction is [10 0 11] and with decreasing temperature it rotates leading to slight change of CTE, e.g. at 350 K a350K ¼ 0:0018   106 K1 and it decreases to a150K 

½10 0 11

and a50K 

½10 0 11

½10 0 11

¼ 0:04  106 K1 at 150 K 

¼ 0:1  106 K1 at 50 K. In other words, [10 0100 ]

direction of B190 crystal structure in NiTi remains a low TE (LTE) direction over a wide temperature range. The above lattice level picture of TE in NiTi clarifies, qualitatively, several features of TE behavior observed in the severely coldrolled and recovery annealed sheets (Figs. 3 and 5). For example, the lack of TE anisotropy in the fully austenitic regime, T > Ms or T > Rs (see Fig. 3b1 and b2), is due to the intrinsic isotropic TE of B2 crystal structure, despite significant texturing of austenite grains (see Fig. 2). The anomalous NTE, PTE, and ZTE of CR60%, CR42%, and 523-60 sheets is linked to the intrinsic anisotropic TE of residual/ retained B190 phase. Fig. 10. In-situ XRD profiles of the (a) GA and (b) PA powders in the temperature window of 50e300 K. The peaks assigned to B190 peaks are indexed by blue color and those of the B2 peaks are indexed by red color. The insets show the dependence of peak shift to temperature indicating the intrinsic anisotropic TE of B190 lattice planes. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

3.7. Analytical model of TE anisotropy Here we shall describe a simplified theoretical approach to capture the anomalous TE anisotropy of the severely-deformed and

88

A. Ahadi et al. / Acta Materialia 124 (2017) 79e92

Fig. 11. Evolution of lattice strain with temperature and 3-dimensional representation of TE matrix (quadric) for (a) B2 crystal structure and (bed) B190 crystal structure.

Table 1 The temperature-dependence of thermal expansion coefficient (CTE) of austenite (B2) and martensite (B190 ) lattice planes. (hkl)

B19′ 110 002 111 020 111 112 022 B2 110 200 211

Sample

a (hkl)(T) (106K1)

a (hkl)(T) (106K1)

a (hkl)(T) (106K1)

Plasma-atomized powder (Ti-50.9 at.% Ni)

Gas-atomized powder (Ti-49.2 at.% Ni)

Gas-atomized powder annealed at 1073 K

(50e245 K) 0.515 þ 12.426  102 T 0.917  7.436  102T 1.618  2.544  102 T

(50e275 K) 2.597 þ 11.44  102 T 0.210  6.009  102 T 0.858  2.580  102 T

(50e275 K) 3.947 þ 14.323  102 T 5.65  0.28  102 T -1.714þ0.372102T

1.768 þ 14.342  102 T 5.870 þ 12.44  102 T 1.624  12.068  102 T

8.946 þ 17.544  102 T 1.141 þ 6.547  102 T 4.220  9.671  102 T

0.24 þ 9.78  102 T 1.16þ6.22102T 1.879  12.21  102 T

0.438 þ 4.074  102 T (0e400 K) 4.861þ4.0154102T þ3.115þ4.879102T 4.201þ5.155102T

1.463 þ 2.555  102 T (0e400 K) N/A N/A N/A

1.27 þ 4.24  102 T (0e400 K) 5.023 þ 4.256  102 T þ3.797 þ 5.224  102 T 4.222 þ 5.302  102 T

Fig. 12. (a) 3-dimensional representation of TE quadric at different temperatures for B190 crystal structure in principal axes [010], [601], and [305]. Planar TE of B190 crystal structure. The dashed line shows the ZTE direction at a specific temperature. Note that the ZTE direction only slightly rotates with heating/cooling.

recovery-annealed superelastic NiTi sheets. In doing so, we ignore the occurrence of forward/reverse PT during the course of cooling/ heating. Hence, the TE of the sheets only originates from pure TE of B2 and residual B190 martensite phases. Indeed this assumption is best justified for the CR60% and CR42% sheets where thermallyinduced PT is almost fully suppressed. TE matrix is a second-rank tensor type physical property (see Appendix A), hence, it can be represented as a quadric in its principal axes:

aðhÞ ¼ aP11 h211 þ aP22 h222 þ aP33 h233

(1)

where aP11, aP22, and aP33 are the eigenvalues of TE matrix and h11, h22, and h33 are the orthonormal crystal directions. Using spherical polar coordinates conversion Eq. (1) may be written in terms of specimen coordinates f andg as:

A. Ahadi et al. / Acta Materialia 124 (2017) 79e92

1 3 i 2 h þ pffiffiffiffiffiffi ð2aP33  aP11  aP22 ÞC211 þ 53ðaP11  aP22 ÞC221 P 2 ðfÞ 15 10 i 2 2 h þ pffiffiffi ð2aP33  aP11  aP22 ÞC212 þ 53ðaP11  aP22 ÞC222 P 2 ðfÞcosð2gÞ 15 5

89

aðf; gÞ ¼ ðaP11 þ aP22 þ aP33 Þ

In Eq. (2) C211 , C221 , C212 , and C222 are the second-order coefficients of spherical harmonics series expansion characterizing an ODF 2

andP 2 ðfÞ and P 2 ðfÞ are the normalized generalizations of the second-order Legendre functions [58]. The average CTE at a specific temperature is modeled analogous to the TE of reinforced composites whereas the matrix is austenite (B2) and variants of residual B190 martensite (V1,2,…,12) are modeled as reinforcing particles as shown schematically in Fig. 13. The average TE of such microstructure may be written using rule of mixture (ROM) as:

〈a〉Voigt ¼

M X

Vm a ¼ VB2 aB2 þ

m¼1

12 X

Vi aB190

(3)

i¼1

Here VB2 is the volume fraction of austenite, Vi is the volume fraction of residual martensite variants, aB2 is the volume average of B2 TE matrix over all the existing B2 orientations in the sample, and aB190 is the volume average of B190 TE matrix over all the existing orientations of the martensite variants in the sample. a is written as:

aB2 ¼

Z

aB190 ¼

aB2 ðgÞfB2 ðgÞdg Z

aB190 ðgÞfB190 ðgi Þdgi

(4)

(5)

where fB2(g) is the measured (see Fig. 2) ODF of austenite grains and fB19'(gi) is the ODF of residual martensite variants calculated from the known orientation relationships between austenite and martensite [59]. From Eq. (2) it is readily deduced that for a fully austenitic sample, no matter how the austenite grains are oriented, the TE

(2)

behavior is isotopic in all directions (see Fig. 3 for T > Ms/Rs) since the eigenvalues of TE matrix are equal aP11~aP22~aP33 and Eq. (2) reduces to aB2 ðf; gÞ ¼ const ¼ aP11 > 0. Another implication of Eq. (2) is that for a fully martensitic sample with randomly oriented martensite variants (random martensite texture) the C211 , C221 , C212 , and C222 are very small (close to zero) and thus Eq. (1) is reduced to

aB190 ðf; gÞ ¼ 13 ðaP11 þ aP22 þ aP33 Þ > 0. This is the case for the 107330 and 973-5 sheets in the T < Mf regime (see Fig. 3c1-c2) whereas due to random formation of martensite variants during stress-free cooling the sample shows isotropic PTE behavior. In other words, for a fully martensite NiTi sample one has to align the martensite variants to a certain direction of the specimen by applying an external mechanical field or permeant deformation to tailor the CTE towards a specific value. The theoretical predictions of TE anisotropy using Eq. (3) are compared with the experimental results in Fig. 14. The theoretical line is calculated assuming the same texture coefficients for all the sheets and volume fraction of residual martensite being the only varying parameter. It is seen that the developed model successfully captures the gradual transition from NTE in the RD to PTE in the TD. The ROM model also show that the lower NTE value in the RD direction in the CR42% compared with CR60% (see Fig. 6) is due to higher volume fraction of residual martensite in the CR42% specimen. It is important to note that for improved theoretical predictions of TE anisotropy not only the exact volume fraction of residual martensite and amorphous phase are required but also an accurate knowledge of variants present in the severely-cold rolled sheet is needed in order to accurately predict the texture coefficients. 4. Summary and conclusions We have investigated the effects of severe plastic deformation

Fig. 13. Schematic of microstructural changes during cold-rolling showing the existence of two variants of residual martensite inside nano grains.

90

A. Ahadi et al. / Acta Materialia 124 (2017) 79e92

Fig. 14. Comparison between the theoretical predictions of TE anisotropy according to Eq. (3) and experimental results for different volume fraction of residual martensite (vm).

on the thermal expansion (TE) behavior of superelastic NiTi sheets. In particular, the physical origin of anomalous invar-like behavior (ZTE), positive thermal expansion (PTE), and negative TE (NTE) observed in severely-deformed sheets are investigated. The roles of grain size (GS), texture, thermally-induced phase transformation (PT), volume fraction of residual/retained martensite, and intrinsic (lattice level) TE on the anomalous TE behavior are elucidated. The main conclusions of this study are summarized as follow: 1 The TE behavior of coarse-grained NiTi (with GS in the micron range) and nano-grained NiTi (with average GS larger than ~ 60 nm) sheets is realized by three distinct stages during cooling/ heating; PTE behavior with isotropic contraction/expansion of austenite phase (above transformation temperatures), anisotropic and hysteretic expansion/contraction due to thermallyinduced PT (in the transformation regime), and PTE behavior with isotropic expansion/contraction of martensite (below transformation temperatures). 2 The TE behavior of the severely cold-rolled and recoveryannealed sheets show an anomalous in-plane anisotropy. The coefficient of TE (CTE) gradually changes from a~21106 K1 in the TD direction of the sheets (PTE) to a~11106 K1 in the RD direction of the sheets (negative TE) and a very small CTE of a~0.53106 K1 (invar-like behavior) is obtained at a specific angle to the rolling direction (RD). 3 By controlling the degree of cold-rolling thickness reduction and recovery annealing temperature one can not only tailor the value of CTE, but also control the temperature dependence of length change from the linear dependence in severely deformed sheets (due to suppression of thermally-induced PT) to strong nonlinear dependence in recovery annealed sheets (due to occurrence of continuous PT). 4 Post-mortem TEM observations and Chi-scan XRD studies show that the microstructure of sheets showing such anomalous TE anisotropy consists a mixture of nanoscale residual martensite and austenite nanograins. In-situ TEM and XRD studies under cooling show that the microstructure of severely cold-rolled sheets remain unchanged/untransformed with cooling down to 103 K, i.e. thermally-induced martensitic PT does not occur hence excluding the thermally-induced PT as the physical origin of such anomalous TE behavior. 5 The TE matrix of B190 monoclinic crystal structure is measured using powder XRD from 50 to 400 K. It is found that The TE of B190 crystal structure is highly anisotropic with crystallographic directions having PTE, NTE, and ZTE. Using a rule of mixture it is shown that the anomalous anisotropic TE of severely-deformed NiTi sheets originates from the anisotropic TE of residual B190 martensite. The volume fraction and crystallographic orientation of residual martensite determine the average CTE of the

sheet along different directions. As such, by controlling the volume fraction of residual martensite through controlled severe cold-rolling, one can tailor the value of CTE gradually from PTE to NTE along different directions within the ND plane.

Acknowledgments This work is financially supported by International Center for Young Scientists (ICYS) under grant number C1052. We would like to thank Dr. Sasan Dadbakhsh for providing the NiTi Powders and Mr. Kono and Ms. Kinoshita from the ICYS office for the continued assistance with TMA experiments. The fruitful comments of Dr. Jeremy Schaffer from Fort Wayne Metals is highly appreciated. We are also grateful to the partial financial support of this work by the Hong Kong Research Grant Council (project No. N-HKUST617/14).

Appendix A. Calculation of TE matrix The TE of a crystal structure is a second-rank tensor type property a with components aij. For cubic crystals such as B2 structure in NiTi the temperature-dependent a(T) is written as:

2

a11

aðTÞ ¼ 4 0 0

0

a11 0

3 0 0 5

a11

(A.1)

For monoclinic crystals such as B190 in NiTi a(T) may be written as:

2

a11

0

a13

3

aðTÞ ¼ 4 0 a22 0 5 a31 0 a33

(A.2)

The components of TE matrix aij are commonly determined from diffraction techniques by measuring the evolution of lattice strains of different crystallographic planes [60]. In this study, powder XRD in the temperature range of 50e400 K is used. The CTE of a hkl lattice plane at a specific temperature aThkl is written as:

aThkl

  v dThkl  dT¼50k vεThkl 1 hkl ¼ T¼50k ¼ vT vT dhkl

(A.3)

where εThkl is the temperature-dependent thermal lattice strain, dThkl is the experimentally-measured lattice spacing of hkl plane at temperature T, and dT¼50K is the lattice spacings of hkl plane at a hkl chosen reference temperature such as 50 K in this study. In cubic crystals, the TE of a lattice plane in its normal direction Al is given by:

A. Ahadi et al. / Acta Materialia 124 (2017) 79e92

0 Al ¼ ð h

k

a11

k Þ@ 0 0

0

a11 0

10 1 0 h 0 A@ k A a11 l

(A.4)

Although measurement of a single diffracting plane is sufficient to determine a11, in this study a11 is calculated as an arithmetic mean of three different B2 planes as:

a11 ¼ 1=3ða110 þ a200 þ a211 Þ

(A.5)

For a monoclinic crystal we have:

0 Al ¼ ð h

k

a11

k Þ@ 0

a31

0

a22 0

10 1 h 0 A@ k A a33 l

a13

(A.6)

If expansion/contraction of several lattice planes An are measured the whole set of measurements may be written as:

1 0 2 A1 h1 B A2 C B h22 B C¼B @ « A B @ « An h2n 0

k21 k22 « k2n

1 l21 2h1 l1 0 C a11 l22 2h2 l2 C C@ 0 « A « a31 l2n 2hn ln

0

a13

0

a33

a22

1

0 A

(A.7)

The best value of aij can be determined using a least-square method by solving the following equation [61]:

a ¼ ðQt QÞ1 Qt A

(A.8)

where

0

h2 B 12 B h2 Q¼B @ « h2n

k21 k22 « k2n

1 l21 2h1 l1 C l22 2h2 l2 C C « A « 2 2h l n n ln

(A.9)

Appendix B. Supplementary data Supplementary data related to this article can be found at http:// dx.doi.org/10.1016/j.actamat.2016.10.054. References [1] C. Kittel, Introduction to Solid State Physics, eighth ed., Wiley, 2004. [2] R.J. Arsenault, N. Shi, Dislocation generation due to differences between the coefficients of thermal expansion, Mater. Sci. Eng. 81 (1986) 175e187, http:// dx.doi.org/10.1016/0025-5416(86)90261-2. [3] W. Fang, C.-Y. Lo, On the thermal expansion coefficients of thin films, Sens. Actuators. A 84 (2000) 310e314, http://dx.doi.org/10.1016/S0924-4247(00) 00311-3. [4] G. Qian, T. Nakamura, C.C. Berndt, Effects of thermal gradient and residual stresses on thermal barrier coating fracture, Mech. Mater. 27 (1998) 91e110, http://dx.doi.org/10.1016/S0167-6636(97)00042-2. [5] R. Roy, D.K. Agrawal, H.A. McKinstry, Very low thermal expansion coefficient materials, Ann. Rev. Mater. Res. 19 (1989) 59e81, http://dx.doi.org/10.1146/ annurev.ms.19.080189.000423. [6] X. Song, Z. Sun, Q. Huang, M. Rettenmayr, X. Liu, M. Seyring, et al., Adjustable zero thermal expansion in antiperovskite manganese nitride, Adv. Mater. 23 (2011) 4690e4694, http://dx.doi.org/10.1002/adma.201102552. [7] J. Chen, L. Hu, J. Deng, X. Xing, Negative thermal expansion in functional materials : controllable thermal expansion by chemical modifications, Chem. Soc. Rev. 44 (2015) 3522e3567, http://dx.doi.org/10.1039/c4cs00461b. [8] L. Wang, C. Wang, Y. Sun, K. Shi, S. Deng, H. Lu, et al., Metal fluorides, a new family of negative thermal expansion materials, J. Mater. 1 (2015) 106e112, http://dx.doi.org/10.1016/j.jmat.2015.02.001. [9] C. Lind, Two decades of negative thermal expansion Research. Where do we stand? Materials 5 (2012) 1125e1154, http://dx.doi.org/10.3390/ma5061125. [10] M. Van Schilfgaarde, I.A. Abrikosov, B. Johansson, Origin of the Invar effect of iron-nickel alloys, Nature 400 (1999) 1e4, http://dx.doi.org/10.1038/21848. [11] A.L. Goodwin, C.J. Kepert, Negative thermal expansion and low-frequency modes in cyanide-bridged framework materials, Phys. Rev. B 71 (2005) 1e4,

91

http://dx.doi.org/10.1103/PhysRevB.71.140301. [12] B. Laboratories, L. Technologies, M. Hill, Pressure-induced amorphization and negative thermal expansion in ZrW2O8, Science 280 (2015) 886e888. [13] Y. Fu, H. Du, W. Huang, S. Zhang, M. Hu, TiNi-based thin films in MEMS applications: a review, Sens. Actuators. A 112 (2004) 395e408, http://dx.doi.org/ 10.1016/j.sna.2004.02.019. €ckel, An overview of nitinol medical applications, [14] T. Duerig, A. Pelton, D. Sto Mater. Sci. Eng. A 273 (1999) 149e160, http://dx.doi.org/10.1016/S09215093(99)00294-4. [15] R. Kainuma, J.J. Wang, T. Omori, Y. Sutou, K. Ishida, Invar-type effect induced by cold-rolling deformation in shape memory alloys, Appl. Phys. Let. 80 (2002) 4348e4350, http://dx.doi.org/10.1063/1.1485118. [16] Y. Sutou, T. Omori, J.J. Wang, R. Kainuma, K. Ishida, Characteristics of Cu e Al e Mn-based shape memory alloys and their applications, Mater. Sci. Eng. A 378 (2004) 278e282, http://dx.doi.org/10.1016/j.msea.2003.12.048. [17] M. Nakai, M. Niinomi, T. Akahori, H. Tsutsumi, X. Feng, M. Ogawa, Anomalous thermal expansion of cold-rolled Ti-Nb-Ta-Zr alloy, Mater. Trans. 50 (2009) 423e426, http://dx.doi.org/10.2320/matertrans.MRP2008380. [18] T. Saito, T. Furuta, J.-H. Hwang, S. Kuramoto, K. Nishino, N. Suzuki, et al., Multifunctional alloys obtained via a dislocation-free plastic deformation mechanism. Science 300 (2003) 464e467, http://dx.doi.org/10.1126/ science.1081957. [19] H.Y. Kim, L. Wei, S. Kobayashi, M. Tahara, S. Miyazaki, Nanodomain structure and its effect on abnormal thermal expansion behavior of a Tie23Nbe2Zre0.7Tae1.2O alloy, Acta Mater. 61 (2013) 4874e4886, http:// dx.doi.org/10.1016/j.actamat.2013.04.060. [20] L.S. Wei, H.Y. Kim, S. Miyazaki, Effects of oxygen concentration and phase stability on nano-domain structure and thermal expansion behavior of TieNbeZreTaeO alloys, Acta Mater. 100 (2015) 313e322, http://dx.doi.org/ 10.1016/j.actamat.2015.08.054. [21] Y. Wang, J. Gao, H. Wu, S. Yang, X. Ding, D. Wang, et al., Strain glass transition in a multifunctional b-type Ti alloy. Sci. Rep. 4 (2014) 3995, http://dx.doi.org/ 10.1038/srep03995. [22] J.A. Monroe, D. Gehring, I. Karaman, R. Arroyave, D.W. Brown, B. Clausen, Tailored thermal expansion alloys, Acta Mater. 102 (2016) 333e341, http:// dx.doi.org/10.1016/j.actamat.2015.09.012. [23] Y.L. Hao, H.L. Wang, T. Li, J.M. Cairney, A.V. Ceguerra, Y.D. Wang, et al., Superelasticity and tunable thermal expansion across a wide temperature range, J. Mater. Sci. Technol. 32 (2016) 705e709, http://dx.doi.org/10.1016/ j.jmst.2016.06.017. [24] A. Ahadi, Q.P. Sun, Stress hysteresis and temperature dependence of phase transition stress in nanostructured NiTidEffects of grain size, Appl. Phys. Let. 103 (2013) 21902, http://dx.doi.org/10.1063/1.4812643. [25] A. Ahadi, Q.P. Sun, Effects of grain size on the rate-dependent thermomechanical responses of nanostructured superelastic NiTi, Acta Mater. 76 (2014) 186e197, http://dx.doi.org/10.1016/j.actamat.2014.05.007. [26] Q.P. Sun, A. Ahadi, M. Li, M. Chen, Effects of grain size on phase transition behavior of nanocrystalline shape memory alloys, Sci. China Technol. Sci. 57 (2014) 671e679, http://dx.doi.org/10.1007/s11431-014-5505-5. [27] A. Ahadi, Q.P. Sun, Stress-induced nanoscale phase transition in superelastic NiTi by in situ X-ray diffraction, Acta Mater. 90 (2015) 272e281, http:// dx.doi.org/10.1016/j.actamat.2015.02.024. [28] S. Dadbakhsh, M. Speirs, J.P. Kruth, J. Schrooten, J. Luyten, J. Van Humbeeck, Effect of SLM parameters on transformation temperatures of shape memory nickel titanium parts, Adv. Eng. Mater. 16 (2014) 1140e1146, http:// dx.doi.org/10.1002/adem.201300558. [29] F. Bachmann, R. Hielscher, H. Schaeben, Texture analysis with MTEX e free and open source software toolbox, Solid State Phenom. 160 (2010) 63e68, http://dx.doi.org/10.4028/www.scientific.net/SSP.160.63. [30] K. Otsuka, T. Sawamura, K. Shimizu, Crystal structure and internal defects of equiatomie TiNi martensite, Phys. Status Solidi A 5 (1971) 457e470, http:// dx.doi.org/10.1002/pssa.2210050220. [31] G. Murasawa, K. Kitamura, S. Yoneyama, S. Miyazaki, K. Miyata, A. Nishioka, et al., Macroscopic stress-strain curve, local strain band behavior and the texture of NiTi thin sheets, Smart Mater. Struct. 18 (2009), http://dx.doi.org/10.1088/ 0964-1726/18/5/055003. [32] S. Miyazaki, V.H. No, K. Kitamura, A. Khantachawana, H. Hosoda, Texture of TiNi rolled thin plates and sputter-deposited thin films, Int. J. Plast. 16 (2000) 4e8, http://dx.doi.org/10.1016/S0749-6419(00)00004-8. [33] Y. Kaneno, A. Takahashi, T. Takasugi, Cold rolling texture of Ni-Based L12 ordered intermetallic alloys, Mater. Trans. 47 (2006) 1485e1491, http:// dx.doi.org/10.2320/matertrans.47.1485. [34] H. Inoue, N. Miwa, N. Inakazu, Texture and shape memory strain in TiNi alloy sheets, Acta Met. 44 (1996), http://dx.doi.org/10.1016/S1359-6454(96)001206. [35] S.H. Chang, S.K. Wu, Textures in cold-rolled and annealed Ti50Ni50 shape memory alloy, Scr. Mater. 50 (2004) 937e941, http://dx.doi.org/10.1016/ j.scriptamat.2004.01.009. [36] S. Qiu, V.B. Krishnan, S. a Padula, R.D. Noebe, D.W. Brown, B. Clausen, et al., Measurement of the lattice plane strain and phase fraction evolution during heating and cooling in shape memory NiTi, Appl. Phys. Let. 95 (2009) 141906, http://dx.doi.org/10.1063/1.3245308. [37] J. Uchil, K.P. Mohanchandra, K. Ganesh Kumara, K.K. Mahesh, T.P. Murali, Thermal expansion in various phases of Nitinol using TMA, Phys. B 270 (1999) 289e297, http://dx.doi.org/10.1016/S0921-4526(99)00186-6.

92

A. Ahadi et al. / Acta Materialia 124 (2017) 79e92

[38] D.A. Miller, D.C. Lagoudas, Thermomechanical characterization of NiTiCu and NiTi SMA actuators: influence of plastic strains, Smart Mater. Struct. 9 (2000) 640e652, http://dx.doi.org/10.1088/0964-1726/9/5/308. [39] K. Wang, J. Zhang, J. Wang, H. Zhang, Z. Wang, W. Yu, et al., Anisotropic thermal expansion of monoclinic potassium lutetium tungstate single crystals, J. Appl. Phys. 98 (2005) 4e9, http://dx.doi.org/10.1063/1.1991974. [40] R.P. Haggerty, P. Sarin, Z.D. Apostolov, P.E. Driemeyer, W.M. Kriven, Thermal expansion of HfO 2 and ZrO 2, J. Am. Ceram. Soc. 97 (2014) 2213e2222, http:// dx.doi.org/10.1111/jace.12975. [41] X. Jiang, M. Hida, Y. Takemoto, A. Sakakibara, H. Yasuda, H. Mori, In situ observation of stress-induced martensitic transformation and plastic deformation in TiNi alloy, Mater. Sci. Eng. A 238 (1997) 303e308, http://dx.doi.org/ 10.1016/S0921-5093(97)00422-X. [42] W. Tirry, D. Schryvers, In situ transmission electron microscopy of stressinduced martensite with focus on martensite twinning, Mater. Sci. Eng. A 481e482 (2008) 420e425, http://dx.doi.org/10.1016/j.msea.2006.12.214. [43] T. Waitz, V. Kazykhanov, H.P. Karnthaler, Martensitic phase transformations in nanocrystalline NiTi studied by TEM, Acta Mater. 52 (2004) 137e147, http:// dx.doi.org/10.1016/j.actamat.2003.08.036. €ger, C. Somsen, A. Dlouhy, G. Eggeler, In-situ TEM cooling/ [44] T. Simon, A. Kro heating experiments on deformed NiTi shape memory single crystals, in: ESOMAT 2009-8th Eur. Symp. Martensitic Transform, vol. 2030, 2009, pp. 1e7, http://dx.doi.org/10.1051/esomat/200902030. [45] J. Ortin, L. Delaey, Hysteresis in shape-memory alloys, Int. J. Non Linear Mech. 37 (2002) 1275e1281, http://dx.doi.org/10.1016/S0020-7462(02)00027-6. [46] R. Delville, B. Malard, J. Pilch, P. Sittner, D. Schryvers, Transmission electron microscopy investigation of dislocation slip during superelastic cycling of NieTi wires, Int. J. Plast. 27 (2011) 282e297, http://dx.doi.org/10.1016/ j.ijplas.2010.05.005. [47] K. Tsuchiya, M. Inuzuka, D. Tomus, A. Hosokawa, H. Nakayama, K. Morii, et al., Martensitic transformation in nanostructured TiNi shape memory alloy formed via severe plastic deformation, Mater. Sci. Eng. A 438e440 (2006) 643e648, http://dx.doi.org/10.1016/j.msea.2006.01.110. [48] Y. Kim, G. Cho, S. Hur, S. Jeong, T. Nam, Nanocrystallization of a Tie50.0Ni(at.%) alloy by cold working and stress/strain behavior, Mater. Sci. Eng. A 438e440 (2006) 531e535, http://dx.doi.org/10.1016/j.msea.2006.02.061. [49] T. Waitz, K. Tsuchiya, T. Antretter, F.D. Fischer, Phase transformations of nanocrystalline martensitic materials, MRS Bull. 34 (2009) 814e821, http:// dx.doi.org/10.1557/mrs2009.231.

[50] R. Delville, S. Kasinathan, Z. Zhang, J. Van Humbeeck, R.D. James, D. Schryvers, Transmission electron microscopy study of phase compatibility in low hysteresis shape memory alloys, Philos. Mag. 90 (2010) 177e195, http:// dx.doi.org/10.1080/14786430903074755. [51] K. Tsuchiya, Y. Hada, T. Koyano, K. Nakajima, M. Ohnuma, T. Koike, et al., Production of TiNi amorphous/nanocrystalline wires with high strength and elastic modulus by severe cold drawing, Scr. Mater. 60 (2009) 749e752, http://dx.doi.org/10.1016/j.scriptamat.2008.12.058. [52] M. Peterlechner, T. Waitz, H.P. Karnthaler, Nanocrystallization of NiTi shape memory alloys made amorphous by high-pressure torsion, Scr. Mater. 59 (2008) 566e569, http://dx.doi.org/10.1016/j.scriptamat.2008.05.004. [53] H. Nakayama, K. Tsuchiya, M. Umemoto, Crystal refinement and amorphisation by cold rolling in NiTi shape memory alloys, Scr. Mater. 44 (2001) 1781e1785, http://dx.doi.org/10.1016/S1359-6462(01)00740-0. [54] C. Yu, B. Aoun, L. Cui, Y. Liu, H. Yang, X. Jiang, et al., Synchrotron high energy X-ray diffraction study of microstructure evolution of severely cold drawn NiTi wire during annealing, Acta Mater. 115 (2016) 35e44, http://dx.doi.org/ 10.1016/j.actamat.2016.05.039. [55] R. Delville, B. Malard, J. Pilch, P. Sittner, D. Schryvers, Microstructure changes during non-conventional heat treatment of thin NieTi wires by pulsed electric current studied by transmission electron microscopy, Acta Mater. 58 (2010) 4503e4515, http://dx.doi.org/10.1016/j.actamat.2010.04.046. [56] S. Prokoshkin, V. Brailovski, S. Dubinskiy, K. Inaekyan, A. Kreitcberg, Gradation of nanostructures in cold-rolled and annealed TieNi shape memory alloys, Shape Mem. Superelast. (2016), http://dx.doi.org/10.1007/s40830-016-00561. [57] Y. Li, J.Y. Li, M. Liu, Y.Y. Ren, F. Chen, G.C. Yao, et al., Evolution of microstructure and property of NiTi alloy induced by cold rolling, J. Alloys Compd. 653 (2015) 156e161, http://dx.doi.org/10.1016/j.jallcom.2015.09.056. [58] O. Engler, V. Randle, Introduction to Texture Analysis, second ed., CRC Press, 2009. [59] V.M. Gundyrev, V.I. Zel’dovich, Determining orientation relationships for the B2 / B190 transformation in single crystal titanium nickelide according to the texture of B190 martensite, Bull. Russ. Acad. Sci. Phys. 74 (2010) 1501e1508, http://dx.doi.org/10.3103/S1062873810110043. [60] M.L. Dunn, H. Ledbetter, Thermal expansion of textured polycrystalline aggregates, J. Appl. Mech. 78 (1995) 1583e1588, http://dx.doi.org/10.1063/ 1.360734. [61] F.J. Nye, Physical Properties of Crystals, Oxford University Press, Bristol, 1957.