On the crystal structure of TiNi-Cu martensite

Scripta mater. 44 (2001) 1–7 www.elsevier.com/locate/scriptamat

ON THE CRYSTAL STRUCTURE OF TiNi-Cu MARTENSITE P.L. Potapov, A.V. Shelyakov* and D. Schryvers Electron Microscopy for Materials Research (EMAT), University of Antwerp, RUCA, Groenenborgerlaan 171, B-2020 Antwerp, Belgium *Moscow Engineering Physics Institute, Kashirskoe Shosse 31, 115409, Moscow, Russia (Received June 7, 2000) (Accepted July 28, 2000) Keywords: TiNi; TiNi-Cu; Martensitic transformation; Martensite; X-ray diffraction; Crystal structure Introduction TiNi-based shape memory alloys attract much attention for their unique properties associated with the reversible martensitic transformation. For a comprehensive understanding of the mechanism of the transformation and its related macroscopic behaviour, it is important to know the crystal structure of the phases involved. In binary TiNi, the transformation is known to proceed from the parent B2 structure to the martensitic B19⬘ structure. The latter has been interpreted as a monoclinic distortion of the B19 orthorhombic structure. After Otsuka and Ren [1], the lattice changes during the B2-B19⬘ transformation can be described as follows (Fig. 1a). A straining of the B2 structure along [001]B2, [110]B2 and [11៮ 0]B2 directions plus a (110)[11៮ 0]B2 shuffle produce the B19 orthorhombic structure. In the present paper, the magnitude of the shuffle is denoted as ␦, as indicated in Fig. 1a. This shuffle can be also described as a transverse (110)[11៮ 0]B2 wave with a [110]B2 wave vector, wavelength equal to 2d(110)B2 and an amplitude of 1/2␦. Then, a (001)[11៮ 0]B2, i.e. (100)[001៮ ]B19, homogeneous shear drives the B19 into the monoclinic B19⬘. The positions of atoms in the B19⬘ structure are, however, not fully consistent with the scheme described in Fig. 1a. Careful experimental examinations [2,3] have revealed that Ni atoms in (010)B19⬘ basal planes are shifted from the central positions such that the plane looses its centre of symmetry (Fig. 1b: (010)B19⬘ layer). In binary TiNi, the presence of the orthorphombic structure as the intermediate step of the B23 B19⬘ transformation is only imaginative. In compositions with Ni partially substituted by Cu, the transformation can indeed be separated in two distinguishable steps: from parent to the orthorhombic structure and from the orthorhombic structure to the monoclinic B19⬘ [4,5]. In alloys with high Cu concentration, the transformation is even frozen at the first step and never comes to the monoclinic B19⬘ [6,7]. However, the question remains whether the intermediate orthorhombic structure is really B19 as suggested by the previous studies of TiNi-Cu alloys. The B19 structural type, determined in TiPt, TiPd, MgCd and TiAu [8], is known to belong to the Pmmb space group. Identification of TiNi-Cu martensite as the B19 structure is based mainly on geometrical considerations as in Fig. 1a, which dictate the Pmmb group for the resulting orthorhombic structure. However, this group is not limited to the given B19 structure type. As shown in Fig. 1b, the B19 structure implies a centre of symmetry in the (010)ORT atomic layers while the Pmmb group generally allows a shift of Ni atoms from the central position in the [001]ORT or [001៮ ]ORT direction. To keep the Pmmb symmetry group, this shift should alternate its direction in each subsequent (010)ORT layer. To distinguish with the B19 type, the resulted structure will 1359-6462/01/$–see front matter. © 2001 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved. PII: S1359-6462(00)00555-8

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Figure 1. Schematic of (a) the structural transformation from B2 to B19⬘ after Otsuka and Ren [1] and (b) the atomic configuration of (010) layers in B19⬘, B19 and the general Pmmb space group denoted by the ‘ORT’ index.

be referred as ‘orthorhombic’ with an index ‘ORT’. Such an atomic shift can be described as a transverse wave of the Ni sublattice with a wave vector [110]B2, a shift direction [1៮ 10]B2 and an amplitude ␯, where the ␯-value is depicted in Fig. 1b. Note that two distinguished directions of a ␯ shift are possible: in phase or antiphase with respect to the shuffle direction of␦. The former will be denoted as positive and the latter as negative ␯. The possibility of such a shift was never considered in TiPt, TiAu, MgCd alloys with the reported B19 structure, because the maximal symmetry of (010)ORT layers was always assumed [8]. Such an assumption, however, does not appear straightforward for TiNi-Cu, as an asymmetric configuration of the (010)B19⬘ layers has already been discovered in the B19⬘ structure of binary TiNi [2,3]. Additionally, a small shift of atoms from the central-symmetric positions has been observed in the (010)ORT layers of the orthorhombic AuCd [9], which was previously considered as having the B19 type [8]. This paper presents a closer look at the crystal structure of TiNi-Cu martensite. Detailed X-ray examinations reveal that the structure differs from the standard B19 type and demonstrate a shift of atoms inside the (010)ORT layers similar to that observed in the B19⬘ structure. Finally, some changes in the conventional description of the B23 B19⬘ transformation are suggested, based on the new evidence. Experimental Amorphous ribbons containing 50 at.% Ti, 25at.%Ni and 25at.%Cu, were manufactured by the single-roller melt-spinning technique under argon atmosphere. The spinning yields a cooling rate of about 5 ⫻ 105 K/s. Afterwards, the ribbons were subjected to a heat treatment at 500°C for 5 min to promote crystallisation of the cubic structure. Such a procedure results in a fine grain microstructure suitable for quantitative X-ray analysis. On subsequent cooling to room temperature, the cubic parent structure transforms into the orthorhombic martensite. The conventional TEM studies were performed on a Philips CM-20 twin microscope operating at 200kV. X-ray diffraction studies were performed in the Bragg-Brentano geometry using a powder Philips PW1830 diffractometer with monochromated Cu K␣ radiation. Measurements were done at room temperature with step intervals of 0.025 degree. The obtained scans were subjected to background subtraction and profile fitting procedures incorporated in the PC-APD Philips software. Alternatively,

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Figure 2. (a) Typical microstructure of a TiNi-Cu ribbon with a SAED pattern of (b) orthorhombic martensite and (c) untransformed cubic structure.

the raw X-ray scans were treated by the Rietveld-refinement program RIETAN-98 developed by F.Izumi (NIRIM, Tsukuba, Japan). The background was approximated by a finite sum of Legendre polynomials [10]. The peaks were assumed to have a symmetric shape and their profiles were fitted by the modified pseudo-Voigt function [11,12]. The thermal atomic displacement factor was taken as isotropic and equal for all types of atoms. The preferred orientation was described by the Marsh-Dollase function [13,14] with the adjustable parameter r, which should be less than 1 when preferred orientations exist. Results and Discussion Fig. 2a shows the microstructure of a TiNi-Cu ribbon with grains of 0.5–1␮m in size. Almost all grains are transformed to martensite and demonstrate the fine internal twinning typical for martensitic phases. Fig. 2b shows a SAED pattern, which can be indexed as the 101 zone of the orthorhombic structure. Occasionally, few untransformed grains with the cubic structure are found. The SAED pattern of the cubic structure along the 110 zone shows the B2 type ordering with 001 superstructural reflections (Fig. 2c). No additional reflections at positions corresponding to L21 or DO3 types of ordering were detected. Thus, Cu atoms seem to be randomly distributed in the Ni-sublattice retaining the B2 type order as in binary TiNi. Fig. 3 shows the X-ray diffraction scan of the annealed TiNi-Cu. All observed peaks can be successfully indexed in terms of the orthorhombic lattice. No 0n0 reflections, where n is an odd integer, were observed, supporting the Pmmb space group. Also, no visible peaks from the parent B2 structure

Figure 3. X-ray scan of a TiNi-Cu ribbon revealing the single diffraction pattern from the orthorhombic structure.

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TABLE 1 Results of Rietveld refinement of atomic positions in the orthorhombic TiNi-Cu martensite Refined parameters

Assumption of ␯ shift NO YES YES YES

Preferred orientation vector NO NO 011 010

Rp

Preferred orientation parameter r

Shuffle ␦

Shift ␯

Degree or order

Thermal atomic displacement

4.33% 3.98% 3.80% 3.10%

— — 0.89 0.89

5.0% 5.1% 4.9% 5.1%

— ⫺2.6% ⫺2.8% ⫺2.4%

0.96 0.98 0.95 0.99

0.46 0.35 0.46 0.44

were found probably due to the small number of untransformed grains. From the positions of twelve peaks situated in the range 2␪ ⫽ 55 . . . 95deg, the lattice parameters of the orthorhombic structure were calculated as a ⫽ 0.29177(6), b ⫽ 0.42900(8), c ⫽ 0.45039(8) nm. Strongly overlapping peaks, e.g. 202, 032 and 220, were excluded from the analysis as those were subjected to significant errors. The observed values are in good agreement with the previous studies of martensite in TiNi-Cu alloys [7]. Table 1 lists the results of the Rietveld refinement of atomic positions with several hypotheses. Additionally, the degree of order and the thermal displacement factor were varied although they show only a small influence on the reliability factor. Assumption of a ␯-shift in the (010)ORT layers as depicted in Fig. 1b, improves the R factor noticeably. The best match with experiment is obtained at a shift value of about 2.6% of the c parameter. Further improvement can be obtained by taking the probable preferred orientation of grains into account. Table 1 lists two types of texture, 011 and 010, which were found to improve the R factor. Assumption of the 010 texture yields the best results. Fig. 4 shows the final result of the Rietveld refinement with an obtained R factor of 3.10%. However, despite of the good R number, the Rietveld method has the intrinsic problem with the correct accounting of the preferred orientation in martensitic polycrystals. As known from the crystallography of the cubic3orthorhombic martensitic transformation, each single orientation of the parent phase transforms into at least 12 orientation variants of the orthorhombic phase [15]. Even taking in consideration that some of these variants are crystallographically equivalent, the simply textured B2 must cause several preferred orientations in the product orthorhombic phase with complicated relations among them. That is probably the reason why different assumptions for the texture in Table 1 improve the R factor. To avoid unpredictable influence of the preferred orientations, we performed a selective analysis of couples of reflections located along the same crystallographic directions. The intensity ratio between 100/200, 001/002 and 011/022 peaks was measured as 0.083⫾0.045, 0.117⫾0.021 and 0.080⫾0.023,

Figure 4. Results of Rietveld refinement of atomic positions in the orthorhombic TiNi-Cu martensite. The refined parameters are ␦ ⫽ 5.1,␯ ⫽ ⫺2.4% and the final R factor is 3.10%.

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Figure 5. Lines in the 2D ␦-␯ space satisfying the experimental intensity ratios between 001/002 and 011/022 peak couples. Each line is presented including the borders showing the actual experimental precision. The cross-section of the 001/002 and 011/022 lines yields the solution with ␦ ⫽ 11.4%, ␯ ⫽ ⫺1.8%. The solution with ␯⬎0 is rejected as explained in the text.

respectively and these ratios should not be sensitive to the texture of the sample. The 100/200 ratio depends only on the order between Ti and Ni sublattices and the measured value of 0.083 yields a degree of order of 0.90⫾0.12. The 001/002 and 011/022 ratios are strongly sensitive to the z-positions of both Ti and Ni atoms. Fig. 5 plots the lines in the 2D ␦-␯ space, which satisfy the experimental 001/002 and 011/022 values including the actual experimental precision. Note that two different lines with positive and negative ␯ both satisfy the measured 001/002 value of 0.117. The crossing of the 001/002 and 011/022 lines yields two possible (␦,␯) solutions matching the experimental 001/002 and 011/022 ratios. The solution with ␦ ⫽ 3.5% and ␯ ⫽ ⫹3.9% is rejected, because it results in non-consistent intensities of 112, 121, 103, 113 and other peaks with higher 2␪, even accounting for texture. For instance, the calculated intensity of the 103 peak is almost zero, while this peak is clearly seen in Fig. 3. The second solution with ␦ ⫽ 11.4% and ␯ ⫽ ⫺1.8%, gives realistic intensities for peaks with higher 2␪ . So, both the standard Rietveld refinement and selective intensity analysis yield a ␯ value of about ⫺2%. The ␦ values obtained by both methods differ noticeably (5.1% and 11.4%) which is probably explained by the lower sensitivity of the peak intensities to the ␦ parameter. The value of 11.4% for ␦ is retained as the selective intensity analysis is not sensitive to the preferred orientation in the sample. The present experimental work reveals a shift of atoms inside the (010) layers of the orthorhombic TiNi-Cu martensite, although the reason for appearance of such a shift is not quite clear. It is unlikely that this shift is related with the ternary composition of TiNi-Cu alloy, as Cu and Ni atoms seem to be randomly mixed in the Ni-sublattice. Note that the B19⬘structure in binary TiNi also exhibits atomic shifts from the centro-symmetric positions (Fig. 1b) despite of its simple equiatomic composition. Taking into account that the orthorhombic structure in TiNi-based alloys can be considered as an intermediate step in the transformation from B2 to B19⬘, the atomic configuration of both structures should be analysed in relation with each other. Fig. 6 shows the orthorhombic structure in TiNi-Cu and the monoclinic one in TiNi viewed along the [010] directions. The former is drawn using the present experimental data while the latter is based on the data of Kudoh et al. [3]. In the orthorhombic structure (Fig. 6a), the characteristic tetraheder Ti1-Ti2-Ni1-Ni2 is outlined, which consists of the typical interatomic bonds. The minimisation of the Ni1-Ni2 bond causes a slight shift of the Ni2 atom in the [001]ORT and the Ni1 atom in the [001៮ ]ORT direction. Although such an atomic resettlement breaks the centre of symmetry of the (010)ORT layers, all Ni atoms remain in positions allowed by the Pmmb group. The same Ti1-Ti2-Ni1-Ni2 tetraheder can be found in the monoclinic B19⬘ structure (Fig. 6b). Moreover, the plane normal to the Ti1-Ti2 bond remains approximately the mirror plane for this tetraheder, which means that there is no monoclinic

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Figure 6. View at (a) the orthorhombic structure in TiNi-Cu and (b) monoclinic one in TiNi along the [010] direction. In both structures, the similar Ti1-Ti2-Ni1-Ni2 tetraheders are outlined, where minimisation of Ni1-Ni2 bonds induces the ␯-distortion of the (010) layers. Additionally, every second (001) layer in Fig. 6b is monoclinically distorted causing an overall monoclinicity of the unit cell.

distortion in the considered (001)B19⬘ layer. Similar to the orthorhombic structure in TiNi-Cu, the positions of Ni1 and Ni2 atoms in B19⬘can be described in terms of a ␯-shift along the normal to the (001)B19⬘ plane with a shift value of 4.1%. At the same time, compared to Fig. 6a, Ti1-Ti3-Ni3-Ni4 tetraheders in the subsequent (001) layer are strongly monoclinically distorted, which causes an overall monoclinicity of the B19⬘ structure. So, the following two corrections in the conventional transformation path [1] are suggested. 1) Firstly, B2 transforms into the orthorhombic structure with Pmmb symmetry where Ni atoms are resettled by a ␯–shift. 2) Then, each second atomic (001)ORT layer is subjected to a (001)[1៮ 00]ORT shear producing the monoclinic unit cell, which is different from the previously suggested homogeneous shear (100)[001៮ ]ORT. Such transformation description looks more consistent with the experimental atomic positions in structures of both orthorhombic and monoclinic martensite in TiNi-based alloys. Conclusions 1. X-ray investigation reveals a shift of atoms from the centro-symmetric positions in the (010)ORT layers of the orthorhombic TiNi-Cu martensite. Thus, the structure differs from the standard B19 type suggested previously. 2. The B23 B19⬘ transformation in TiNi based alloys involves the transition from the cubic into the orthorhombic structure with internal atomic shifts inside the (010)ORT layers and a monoclinic distortion of each second (001)ORT layer. Acknowledgments Pavel Potapov likes to thank the Federal government of Belgium for financial support in the form of a DWTC grant and the University of Antwerp, RUCA for a RAFO guest professorship. Authors acknowledge the help of Dr. N.Khasanova in handling the RIETAN-98 program. References 1. 2. 3. 4.

K. G. Y. H.

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