Journal of Alloys and Compounds 582 (2014) 703–707

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Journal of Alloys and Compounds

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Microstructural dependence on middle eigenvalue in Ti–Ni–Au

0925-8388/$ - see front matter � 2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.jallcom.2013.08.132

⇑ Corresponding author. Tel.: +32 484180298.E-mail address: shihui851001@gmail.com (H. Shi).

H. Shi a,⇑, R. Delville a,c, V. Srivastava b,d, R.D. James b, D. Schryvers a

a EMAT, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerp, Belgiumb Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN 55455, USAc SCK-CEN, Boeretang 200, B-2400 Mol, Belgiumd GE Global Research, 1 Research Cir, Schenectady, NY 12309, USA

a r t i c l e i n f o

Article history:Received 4 June 2013Received in revised form 19 August 2013Accepted 19 August 2013Available online 29 August 2013

Keywords:Shape memory alloys (SMAs)Transmission electron microscopy (TEM)MartensiteAusteniteHysteresisTwinning

a b s t r a c t

The microstructure of various compounds of the Ti–Ni–Au alloy system is investigated by transmissionelectron microscopy in relation with changing lattice parameters improving the compatibility conditionsbetween austenite and martensite expressed by the k2 = 1 equation based on the Geometrically NonLin-ear Theory of Martensite (GNLTM). Although local differences in microstructure are observed, whenincreasing the gold content compound twins are replaced by Type I twins, while twinned lamellar struc-tures are replaced by untwinned plates and self-accommodating structures when k2 = 1 is approached, allconfirming the predictions of the GNLTM.

� 2013 Elsevier B.V. All rights reserved.

1. Introduction

TiNi-based shape memory alloys (SMAs) have been widelystudied for their unique thermo-mechanical properties arisingfrom the energy-dissipating martensitic transformation. The appli-cation of certain shape memory devices, such as actuators, sensorsand other cycling parts, is, however, often limited by a relativelylarge hysteresis, which can lead to poor fatigue properties. It alsodecreases their resistance to fracture since the work dissipatedduring the hysteresis causes the creation of defects, which can be-come sites of crack initiation [1]. Therefore, reducing hysteresis is aparticularly important aspect in the process of alloy improvementfor many SMA applications. In order to minimize the thermo-mechanical hysteresis by increasing the austenite–martensite lat-tice compatibility, extensive research has been carried out to finda suitable ternary element for the TiNiX system. It was found thatadding certain noble elements such as Pd, Pt and Au can dramati-cally decrease the SMAs’ hysteresis at certain precise concentra-tions [1–4].

Some years ago, a new application of the Geometrically NonLin-ear Theory of Martensite (GNLTM) concerning hysteresis reductionwas proposed by James and Zhang [5,6]. It was found that for a par-ticular combination of austenite and martensite lattice parametersthe hysteresis can be greatly reduced as a result of a perfect match

between parent and product phases, which lowers the energy bar-rier resulting from the mismatch strain existing between austeniteand classically twinned martensite [2]. In particular, the middleeigenvalue k2 of the transformation strain matrix is an indicatorof this compatibility, so when k2 equals 1 a low hysteresis is ex-pected. Tuning this eigenvalue k2 can be done by adding ternaryand quaternary elements to the binary Ni–Ti alloy. Cui et al. havealready experimentally confirmed this theory by investigatingthe lattice parameters and the thermal hysteresis of composition-spread Ti–Ni–Cu and Ti–Ni–Pd thin-films [1]. They observed inall cases a sharp drop of the hysteresis for alloys when k2 ap-proaches 1. This was further confirmed by Zhang et al., who foundthe same correlation for bulk alloys of Ti–Ni–Au, Ti–Ni–Pt and Ti–Ni–Pd [2] and by Zarnetta et al. for the quaternary Ti–Ni–Cu–Pdsystem in which an increased fatigue life was observed [7]. Alsoother systems such as the Ni45Co5Mn40Sn10 Heusler alloy revealparticular features such as minimal thermal hysteresis, high mag-netization, low magnetic anisotropy and relatively high transfor-mation temperature when approaching the k2 = 1 condition [8].

According to the same theory, the perfect match of austeniteand martensite structures at the habit plane translates intothe occurrence of large plates of single martensite variants forthe product phase instead of the classic multiply twinned martens-ite plates. Under general conditions, Ti–Ni martensite plates con-sist of lamellar twinning with the tapering tips of two variantsforming an intermediate layer close to the habit plane [9] whereask2 = 1 systems form single variant martensite–austenite interfaces

704 H. Shi et al. / Journal of Alloys and Compounds 582 (2014) 703–707

[10]. The type of twinning also follows from the GNLTM theory andis found to be Type I or II for k2 > 1 and compound for k2 < 1. Thesestructural predictions have led to a transmission electron micros-copy (TEM) microstructural investigation of the Ti–Ni–Pd systemaround the composition where the hysteresis is greatly reduced.It was confirmed that the decrease of hysteresis is indeed accom-panied by significant changes in the microstructure [3,4,10]. In or-der to prove the universality of these findings, we have extendedthese investigations to other systems, such as Ti–Ni–Au or Ti–Ni–Pt. The addition of Pt in the latter, however, greatly reduces thequality of electropolished samples which are necessary for a studylooking for large scale effects, so the focus of the present TEM workis on the microstructure of the Ti50Ni50�xAux system where x is sys-temically tuned to approach and cross the k2 = 1 condition. The setof alloys originates from the samples used by Zhang et al. [2,11].

2. Experimental

The Ti50Ni50�xAux (x = 10, 13, 15 and 18) bulk alloys used in this study were pre-pared by arc melting pure elements (99.98 mass% Ti, 99.995 mass% Ni, 99.95 mass%Au) in an argon atmosphere. The ingots were cut into slabs of about 1 mm in thick-ness by EDM (Electrical Discharge Machining) subsequently followed by homogeni-zation at 900 �C during 20 ks followed by water quenching. TEM samples of 3 mmdisks in diameter were spark-cut from the slabs, mechanically polished to a 150–200 lm thickness and finally electropolished to perforation in a Tenupol 3 systemwith an electrolyte of 80% CH3OH and 20% H2SO4 operating at15 V, 0.12 A,�20 �C. Extra care had to be taken to minimize Au nanoparticle redeposition onthe thin foil by reducing the starting thickness of the sample and tuning the pumpflow rate, the voltage and current of the instrument. TEM observations were carriedout in a Philips CM20 microscope operated at 200 kV using a side-entry type dou-ble-tilt specimen holder with angular ranges of +45� to �45�.

Precise average lattice parameters of both martensite and austenite at the tran-sition temperature were measured with a Scintag X-ray diffractometer (XRD)equipped with a temperature-controlled stage on polycrystalline slabs chemicallyetched using an electrolyte of 85% CH3COOH and 15% HClO4 [2]. Local lattice param-eters of austenite were measured by SAED using gold nanoparticles (remnants fromthe electropolishing) as internal reference. Differential scanning calorimetry (DSC)was performed on a TA Instruments Q1000 using 100 lm thick slabs, etched bythe same method. Transformation temperatures were measured from these DSCcurves and compared with the more precise determination using in situ XRD.

3. Results and discussion

The Ti50Ni50�xAux system undergoes a martensitic transforma-tion from a cubic (B2) to an orthorhombic (B19) lattice except forcompositions with a small amount of Au (x 6 10) in which casethe monoclinic B190 is formed, as in binary Ti–Ni. Table 1 showsaveraged XRD lattice parameters of both B2 austenite (a0)and B19 martensite (a, b, c) for four different compositions ofTi50Ni50�xAux along with the corresponding k2 and H, the thermalhysteresis defined as ((As + Af) � (Ms + Mf))/2 (with A/Ms/f therespective start/finish temperatures or the austenite/martensitetransformations). Fig. 1(a) and (b) shows the DSC curves ofTi50Ni37Au13 and Ti50Ni35Au15, respectively. The crossovers fromthe tangent lines from the peaks and the extrapolated backgroundprovide values for these transformation temperatures. Althoughslightly varying absolute values from such measures can be ob-tained depending on the actual procedure used or when differ-ences in, e.g., peak broadening exist, it is clear that Ti50Ni37Au13

Table 1XRD lattice parameters of austenite B2 phase (a0) and martensite B19 phase (a, b, c)(Å). k2 and H denote the middle eigenvalue of the transformation matrix and thethermal hysteresis (degrees), the latter determined from DSC.

Alloys a0 a b c k2 H

Ti50Ni40Au10 3.0660 2.8971 4.3089 4.6073 0.9938 4Ti50Ni37Au13 3.0743 2.8901 4.3466 4.6200 0.9997 3.5Ti50Ni35Au15 3.0803 2.8820 4.3642 4.6231 1.0018 6.5Ti50Ni32Au18 3.0872 2.8886 4.4005 4.6323 1.0079 12

has a smaller thermal hysteresis than Ti50Ni35Au15. Moreover,these measured temperatures were compared with those obtainedfrom the in situ XRD data with the high and low temperature spec-tra used as references for the austenite, resp. martensite structures[2,11]. When the intensity in the XRD patterns decreases 2% fromthe reference patterns, the temperature is defined as the respectivestart temperature (As or Ms). When the intensity in the XRD pat-terns increases to 98% of the reference patterns, this temperatureis defined as the finish temperature (Af or Mf). It was found thatfor all samples the hysteresis calculated from the in situ XRD datawas about double that of the DSC measure. In relative terms, ofcourse, the Au13 sample still has the smallest hysteresis.

Twin parameters calculated by GNLTM and based on the XRDlattice parameters shown in Table 1 are listed in Table 2. Allparameters are calculated based on the transformation from B2to B19. The twin plane and shear direction are denoted by K1 andg1, respectively. Three twinning modes, {111} Type I, h211i TypeII and {001} compound twin can exist in the system. It is con-firmed from the twin width ratio k(=w1/(w1 + w2), with w1 andw2 are twin widths of the two martensite variants forming the twinlamella, w1 < w2,) calculated with GNLTM that Type I/II twins arenot expected for k2 < 1 and conversely compound twins shouldnot appear when k2 > 1.

3.1. Ti50Ni40Au10

Fig. 2(a) shows B190 martensite with compound twins with{001}B190 twin plane and h100iB190 shear direction observed inTi50Ni40Au10. Fig. 2(b) and (c) are selected area electron diffraction(SAED) [1 �10] patterns corresponding to the encircled zones 1 and2 in Fig. 2(a), revealing twinned and untwinned martensite, respec-tively. The h angle indicated in Fig. 2(c) equals 84.3�, which con-firms the monoclinic structure of B190 which is only observed inTi50Ni40Au10 and not in the investigated alloys with higher Au con-tent. The existence of twinned and non-twinned B190 areas couldbe due to local concentration differences and their influence onthe lattice parameters or to local strain fields.

Some samples of Ti50Ni40Au10 also contain the orthorhombicB19 martensite with compound twins, which, in view of the resultswith the higher Au content samples, may again indicate small andlocal concentration differences in the alloy. Fig. 2(d) shows a brightfield (BF) TEM micrograph of lamella of such twins with the corre-sponding diffraction patterns obtained from the encircled region intwo different zone axes [�311] and [01 �1], as shown in Fig. 2(e) and(f), respectively. The black dots visible on Fig 2(d) (and also some-what in Fig. 2(a)) are due to Au nano-deposition in the process ofsample preparation by electropolishing, although thinning condi-tions have been adjusted to minimize this deposition. As a compar-ison with Fig. 2(c), the b angle indicated in Fig. 2(f) is 90�, whichconfirms the orthorhombic B19.

3.2. Ti50Ni37Au13

A large B19 martensite plate of several microns wide but with-out twins is observed in Ti50Ni37Au13, as seen from Fig. 3(a). In or-der to ensure no twins exist in this plate, diffraction patterns takenfrom the region inside the circle in the BF image and along differentzone axes [100], [2 �10] and [3 �10] are presented in Fig. 3(b), (c) and(d), respectively. The arrows point at a self-accommodating trian-gle formed by different B19 variants [12,13]. Even when phasecompatibility is achieved in the Ti50Ni37Au13 due to the k2 � 1,there still exists shape change and volume change between theaustenite and martensite. In order to accommodate this shape/vol-ume change, self-accommodation of martensite plates is necessaryand plays an important role in the final morphology of the micro-structure. Fig. 3(e) shows a typical triangle self-accommodating

Fig. 1. DSC curves of (a) Ti50Ni37Au13 and (b) Ti50Ni35Au15. The transformation temperatures As, Af, Ms, and Mf and thermal hysteresis H(H=((As + Af) � (Ms + Mf))/2) aremeasured by crossover from the tangent line of the peak and the extrapolated background. The lower hysteresis for the Au13 sample as well as the difference in peak widthbetween both samples is clear.

Table 2Twinning modes and twin ratios for Ti50Ni50�xAux, x = 10, 13, 15, 18 calculated using GNLTM. K1 is the twinning plane and g1 the shear direction. The twin width ratio k is alsogiven.

Type of twins X K1 g1 Twin ratio k k2

{111} Type I 10 {111} h1�0.13�0.87i ø 0.993813 h1�0.20�0.80i ø 0.999715 h1�0.23�0.77i 0.0735 1.001818 h1�0.27�0.73i 0.2079 1.0079

h211i Type II 10 {0.54�0.08�1} h211i ø 0.993813 {0.58�0.16�1} ø 0.999715 {0.61�0.21�1} 0.0898 1.001818 {0.64�0.28�1} 0.2313 1.0079

{011} Compound 10 {011} h01�1i 0.094 0.993813 0.004 0.999715 ø 1.001818 ø 1.0079

Fig. 2. Illustration of B190 and B19 martensite with compound twins in Ti50Ni40Au10. (a) BF image of twinned and untwinned B190 martensite, (b) and (c) are SAED from theencircled regions 1 and 2 in (a) along [�110], respectively. (d) BF image of twinned B19 martensite, (e) and (f) SAED from the encircled region in (a) along [31 �1] and [01 �1]zones, respectively, the former confirming the twinning, the second the orthorhombic character.

H. Shi et al. / Journal of Alloys and Compounds 582 (2014) 703–707 705

group (SAG) in Ti50Ni37Au13. Unlike the traditional SAG in NiTi asseen in Fig. 3 of [13], internal twins are not observed in the presentSAG. This is another consequence of the phase compatibility.According to the three-dimensional model of the self-accommo-dating variants [12] as represented in the inset of Fig. 3(e), thethree martensite plates can be labeled as variants 2, 4 and 6 ofthe model. Fig. 3(f), (g) and (h) are corresponding SAED patterns

from variants 2, 4 and 6. Experimentally, variants 4 and 6 are ob-served to meet along a (111) Type I twin interface in [01 �1] zoneorientation with the electron beam slightly tilted from the above[100]2 direction.

In order to check the assumption of local concentration varia-tions affecting the observed structural features through thechanges in lattice parameter, precise lattice parameters of 4 differ-

Fig. 3. (a) Illustration of twinless B19 martensite with diffraction patterns of different zone axes in Ti50Ni37Au13; (b) [001], (c) [2 �10] and (d) [3 �10]. (e) BF image of SAG withinset of illustration of three variants and corresponding model [11], (f), (g) and (h) are SAED patterns of encircled 2, 4 and 6 in (e), respectively.

Fig. 4. (a) Illustration of pockets of {111} Type I twins of B19 martensite inside anuntwinned martensite plate in Ti50Ni35Au15 with corresponding diffraction patternin (b).

706 H. Shi et al. / Journal of Alloys and Compounds 582 (2014) 703–707

ent austenite regions in this sample were measured by SAED, usingthe 111 diffraction ring of the omnipresent Au particles as aninternal reference. Taking into account the dependence of the lat-tice parameter on the size of the particles [14], here between 5and 20 nm, the austenite lattice parameters found in 3 of the 4 re-gions equals 3.08 ± 0.01 Å (which corresponds with the averagedXRD result of this sample), while one region yields a lattice param-eter of 3.05 ± 0.01 Å. This confirms local variations in latticeparameter, which appear to be unavoidable in these types of sys-tems and can lead to local differences in transformation tempera-tures and martensite microstructures, such as the observation ofType I twins in this Ti50Ni37Au13 sample. In other words, in the re-gion showing the Type I twins, the gold content is expected to beslightly higher than 13 at.%. Although the presented TEM imagesand SAED measures should not be considered to provide properstatistical data on the concentration variations, such a composi-tional inhomogeneity could be one of the reasons for the (slight)width of the DSC peaks as seen in Fig. 1. Unfortunately, the accu-racy and precision of any spectroscopic tool available is not suffi-cient to detect these extremely small differences.

3.3. Ti50Ni35Au15

In Ti50Ni35Au15 pockets of lamellar twins inside a larger untwin-ned plate of B19 martensite are observed as shown in Fig. 4(a). Thecorresponding diffraction pattern with zone axis [01 �1] in Fig. 4(b)clearly reveals the (111) Type I twinning. The observation of (111)Type I twins in Ti50Ni35Au15 is consistent with the theory by Jameset al. when following the lattice parameter data in Table 1 showingk2 > 1 for this compound. The variation between twinned anduntwinned areas can again be related to local variations in concen-tration. As the DSC curves in Fig. 1 illustrate, the width of the trans-formation peaks in Ti50Ni35Au15 is larger than in Ti50Ni37Au13,which could indicate a higher degree of compositional inhomoge-neity in the former.

3.4. Ti50Ni32Au18

As shown in Fig. 5(a), B19 martensite is found in Ti50Ni32Au18

(circle 2) together with some retained austenite (circle 1), as seenfrom the corresponding SAED patterns in Fig. 5(c) and (b), respec-tively. The fact that austenite is observed although Mf is aboveroom temperature is possibly due to a thin foil effect, locally reduc-ing the transformation temperature, although again compositioninhomogeneities can play an enforcing role. {111}B19 Type I twinsare shown in Fig. 5(d). Fig. 5(e), (f) and (g) are SAED patterns fromthe encircled zones 1, 2 and 3, respectively. Region 2 represents

one of the three variants of B19 martensite, while regions 1 and3 are the {111}B19 Type I twins.

The changes in microstructure with composition of theTi50Ni50�xPdx system are shown in Fig. 1 of Ref. [3]. Twinless mar-tensite plates exist in Ti50Ni39Pd11, with k2 = 1.0001 while lamellartwins-within-twins appear when Pd increases up to 25 at.% and k2

becomes 1.0070. As shown in Fig. 5, the Ti–Ni–Au system does notshow lamellar Type I twins in Ti50Ni32Au18 where k2 = 1.0079.However, lamellar twins were reported in this ternary system fora Au content of 40 at.% [15]. In other words, a much larger contentof Au than Pd is needed to provide the lamellar Type I twins forTi50Ni50�xAux. Since Pd atoms are larger than Au ones, with thesame content of ternary additions to binary NiTi, the change oflattice parameters for Ti50Ni50�xPdx system is larger thanTi50Ni50�xAux. This may possibly explain the observation that themicrostructures in the Ti50Ni50�xPdx system vary more drasticallythan in the Ti50Ni50�xAux system along with changing k2 valueand opens the possibility to easier fine tuning of the microstructureand thermo-mechanical behaviour.

As for the composition inhomogeneities, similar microstruc-tural variations were also observed in the Ti50Ni50�xPdx system[16] and are related with the fact that these structures are not line

Fig. 5. (a) Illustration of B19 martensite (circle 2) and residual austenite (circle 1) plate in Ti50Ni35Au18 with corresponding SAED patterns in (c) and (b). (d) Illustration of B19martensite {111}B19 Type I twins in Ti50Ni35Au18: (f) single variant, (e) and (g) opposite twin configurations.

H. Shi et al. / Journal of Alloys and Compounds 582 (2014) 703–707 707

compounds but cover relatively large stability regions in therespective phase diagrams, allowing for small local deviations ofthe nominal composition without much difference in free energy.The differences in concentration are inferred based on the observa-tion of local changes in lattice parameter of the austenite by com-parison with the internal reference of the Au particles. The latter isessential, since even convergent beam ED could not resolve thesmall differences in lattice parameter in the Ti50Ni50�xPdx system[16]. Although this approach is appropriate, the expected differ-ences in Au content are relatively small and could not be confirmedby spectroscopic means, due to the limited accuracy and precisionof such techniques for individual local measurements. Moreover,the present TEM observations provide only a very limited viewon the entire bulk sample, so extrapolations to the bulk levelshould be handled with care. Nevertheless, the respective peakbroadenings in the different DSC curves could give some indicationof the concentration spread in each of the samples.

4. Conclusions

The microstructural predictions of the GNLTM are confirmed bythe observation of large twinless B19 martensite plates and SAGs inTi50Ni37Au13 when k2 is close to 1. Also the change from compoundto Type I twins when increasing the Au content and shifting k2

from smaller to larger than 1 confirms the predictions of theGNLTM. Although the above trends are clear, local microstructurechanges may arise from local concentration inhomogeneities inthe sample, which is suggested from the local lattice parameterdeviations as measured through the Au particles remaining fromthe electropolishing and used as reference. Such concentration

inhomogeneities could further induce some peak broadening inthe DSC curves.

Acknowledgements

H.S. thanks the CONNEC ‘‘Connecting Europe and China throughInteruniversity Exchange’’, an Erasmus Mundus project, and theFWO research project G.0576.09N for supporting this work.

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