Advanced TEM Investigations on Ni-Ti Shape Memory Material: Strain and Concentration Gradients Surrounding Ni 4 Ti 3 Precipitates

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1 Mater. Res. Soc. Symp. Proc. Vol Materials Research Society S3.6.1 Advanced TEM Investigations on Ni-Ti Shape Memory Material: Strain and Concentration Gradients Surrounding Ni 4 Ti 3 Precipitates Dominique Schryvers, Wim Tirry and Zhiqing Yang Electron Microscopy for Materials Science (EMAT), University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerpen, Belgium ABSTRACT Lattice deformations and concentration gradients surrounding Ni 4 Ti 3 precipitates grown by appropriate annealing in a Ni 51 Ti 49 B2 austenite matrix are determined by a combination of TEM techniques. Quantitative Fourier analysis of HRTEM images reveals a deformed nanoscale region with lattice deformations up to 2% while EELS and EDX indicate a Ni depleted zone up to 150 nm away from the matrix-precipitate interface. INTRODUCTION NiTi alloys with near-equiatomic composition can exhibit shape memory and superelastic properties resulting from a temperature or stress induced austenite-martensite phase transformation. The behaviour and characteristics of this transformation are strongly influenced by the presence of Ni 4 Ti 3 precipitates in the B2 austenite matrix and which can be obtained by appropriate annealing procedures. The atomic structure and morphology of these precipitates have been investigated before [1,2,3]. Due to the anisotropic change of the unit cell dimensions and lattice parameters the precipitates form with a lens shape inside the cubic matrix. Their influence on the transformation temperatures and the occurrence of multiple step transformations was mainly investigated by differential scanning calorimetry (DSC) measurements and conventional transmission electron microscopy (TEM) [4-7]. Small precipitates with a diameter of the central disc up to 300 nm remain coherent or semi-coherent and can act as nucleation centers for the formation of the so-called R-phase [4,6], a rhombohedral distortion preceding the martensitic transformation. Larger precipitates lose their coherency with the matrix and the stress field is partially relaxed by the introduction of interface dislocations [9,10], though they can still act as nucleation centers [4]. This behaviour is explained by the fact that the lattice mismatch between precipitate and matrix induces a stress field in the surrounding matrix favouring particular variants of the product phases. Also the change of Ni concentration in the matrix, due to the higher Ni content in the precipitates, can be expected to have an influence on the local transformation temperatures as is the case for concentration changes at the bulk level [4,8]. However, up till now no quantitative experimental measurements of the strain or concentration gradients exists. In the present work high resolution transmission electron microscopy (HRTEM) is used to measure the actual lattice deformations in the matrix around the Ni 4 Ti 3 precipitates. Relative differences in interplanar spacings are determined by Fast Fourier techniques applied to the HRTEM images. To determine the presence of a possible variation in Ni concentration in close proximity of a precipitate nanoprobe electron energy loss spectroscopy (EELS), Energy Filtered TEM (EFTEM) and energy dispersive X-ray (EDX) analysis are used.

2 S3.6.2 The cubic B2 structure of the matrix has a lattice parameter of a = nm [11], while for the precipitate the hexagonal description will be used with lattice parameters a = b = 1.124nm and c = nm [12]. As a result of the decrease in symmetry, eight precipitate variants are possible, with a conventional orientation relationship [1,12]: (1 1 1) B2 // (0 0 1) H ; [3-2 -1] B2 // [1 0 0] H In this case the [111] B2 direction corresponds to the normal to the central plane of the lens shaped precipitate. In this direction there is a 2.9% contraction in the precipitate with respect to the matrix. TEM images indeed reveal this lens shape and conventional two-beam TEM contrast indicates the presence of a strain field [4]. Figure 1(a)(b) shows schematic top and side views of a precipitate while in figure 1(c) a two-beam bright field (BF) TEM image reveals the stress fields as strong contrast changes in the matrix surrounding the precipitates. EXPERIMENTAL TECHNIQUES Two batches of Ni 51 Ti 49 samples were prepared; samples A contain precipitates with a diameter between 100 nm and 500 nm, the precipitates in samples B have a diameter smaller than 100 nm. The A and B samples were prepared from the same basic material but received a different heat treatment in vacuum. Both were first annealed at 950 C for 1 hour followed by water quenching and then aged for 4 hours at 500 C (A samples) and 450 C (B samples). TEM specimens were prepared by mechanical grinding followed by twin-jet electropolishing with a solution of 93% acetic acid and 7% perchloric acid at 6 C. High resolution images are obtained with a top-entry JEOL 4000EX electron microscope equipped with a LaB 6 filament and operating at 400kV. Standard photographic plates were used in order to obtain as large regions as possible on a single image. Lattice deformations or strain are determined by measuring and comparing interplanar spacings by Fast Fourier Transformation (FFT) of different locations in the HR image. In practice, the pixel distance between the central Figure 1. Schematic drawing of the lens shaped Ni 4 Ti 3 precipitate in the two zones used for observation: a) the [10-1] B2 and b) the [11-1] B2. c) typical BF image of Ni 4 Ti 3 precipitates with surrounding strain contrast.

3 S3.6.3 spot and the spot belonging to the crystallographic plane under consideration is measured with subpixel accuracy by fitting a sinc² function to each spot. The measured interplanar spacing of the corresponding plane in the precipitate is chosen as reference distance. Differences d in interplanar spacing are given as percentage in accordance to this reference distance: for example, a d of 3% means that the measured interplanar spacing is 3% larger than the corresponding spacing in the precipitate. The accuracy of the method is 0.6% with a spatial resolution of 5 nm, the size of the Fourier window. This error was estimated by applying the technique to the image of an undistorted matrix and taking the standard deviation of the determined interplanar spacings. A second technique used to reveal the presence of strain fields is the geometrical phase image method developed by Hÿtch et al [13,14]. This method is based upon calculating the local Fourier components of the digitized high resolution image. After choosing a reference area in the image the local phase (i.e., the complex part of the Fourier components) is calculated for one specific g vector in the FFT of the image. The phase field that is received in this way is equivalent to the displacement field [13]. The strain components εxx, εyy, εxy, εyx as well as the rotation can be deduced from this data by calculating the gradient of the displacement field. The spatial resolution for this method is 2 nm and the error on the strain is 0.5% [15]. Distortions in the image due to the projector lens or introduced by digitizing the image are compensated by using the same reference images as used to determine the error in the first method. It will be shown that both methods give the same result taking into account the respective precisions. EELS and EFTEM experiments are carried out on a Phillips CM30 field emission TEM equipped with a GIF2000 post column energy filter. When acquiring EELS spectra and EFTEM images, a zone orientation slightly off-axis from [10-1] B2 is chosen in order to reduce diffraction effects and to have a minimal overlap between the lens shaped precipitate and the matrix. EELS spectra are collected in diffraction mode with a camera length of 195 mm and an entrance aperture to the GIF system of 2 mm, which corresponds to a collection semi-angle of 3.35 mrad (much larger than the estimated convergence angle 1.2 mrad). EFTEM images are acquired using the standard three-window method. The post-edge window was positioned right at the threshold of the L 3,2 edges of Ni and Ti. Energy window widths of 20 ev and 25 ev were chosen for Ti and Ni, respectively, to cover the white lines of each element. Relative drift between successive images was corrected by a cross-correlation technique when computing the elemental intensity map. Energy dispersive X-ray (EDX) analysis is carried out using a Phillips CM20 transmission electron microscope equipped with a Si(Li) Oxford EDX detector. RESULTS AND DISCUSSION Part I: Lattice strain measurements Based on the known lattice parameters and crystallographic relations between the matrix and precipitates, the [10-1] B2 and [11-1] B2 zones are considered to be the most interesting ones since these will reveal the largest deformations. Moreover, in the [10-1] B2 zone the (111) B2 central plane is observed edge-on and thus a major part of the interface between the matrix and precipitate can also be considered to be viewed edge-on., however, this plane makes an angle of with the incident beam, which results in an area of overlap between matrix and precipitate. On the other hand, the HRTEM images of the [11-1] B2 zone are typically of a better quality due to overall larger lattice spacings.

4 S3.6.4 In samples A precipitates with a diameter between 200 nm and 300 nm are selected for coherency reasons, as explained above. In a [11-1] B2 orientation two of the three edge-on {011} B2 families of planes ((101) B2 and (011) B2 ) have a theoretical difference of 2.01% between the interplanar spacings of the precipitate and the unstrained matrix. The difference in interplanar spacing is measured along the [101] B2 direction for the (101) B2 planes. A typical image is shown in figure 2(a) and the graph in figure 2(b) corresponds with the strain field measured in the direction of the arrow. At a distance of 50 nm away from the centre of the precipitate d reaches a maximum of about 4%, which thus implies an expansive strain of about 2% with respect to the unstrained matrix. However, it is unclear from this image whether this value represents a true maximum or whether the expansive strain reaches even higher values when moving further away from the precipitate. Close to the interface the measured d is about 2%, i.e. unstrained matrix, and it increases linearly up to the maximum of 4%. On the other hand, at the tip of the precipitate the (101) B2 interplanar spacing is found to be smaller than the corresponding value for the matrix thus implying a compression. The interplanar spacing of the third {011} B2 family of planes, (1-10) B2 which lies perpendicular to the central axis of the precipitate in the present crystallographic zone, has a theoretical mismatch of only 0.38% which is confirmed by the fact that no difference between these interplanar spacings was measured. For samples B precipitates with a diameter around 50 nm were examined. In this case more precipitates are present and two of the same variant can even be examined in a single micrograph. In the example shown in figure 3 two parallel precipitates are found about 40 nm apart. To obtain a two dimensional image of the strain field with a better spatial resolution of 2 nm instead of 5 nm, the geometrical phase image method is applied. This method allows to determine the strain in any chosen direction. A reference area is taken in the same image at a position where no strain due to the precipitates is expected (dashed rectangle in figure 3(a)). The contour plot in figure 3(a) visualizes εxx, the strain in the x-direction, which is chosen parallel with the [101] B2 direction. The plot in figure 3(b) shows the εxx profile of the strain field along the [101] B2 direction at the arrow in figure 3(a). This profile can directly be compared with the measurements of differences in interplanar spacing for the (101) planes since εxx = d (101). The graph of the d measurements is given elsewhere [16], and reveals the same result within the Figure 2. a) High Resolution image of a precipitate and surrounding matrix in [11-1] B2 orientation. The arrow indicates the [101] B2 direction along which d is measured, as given in (b).

5 S3.6.5 precision of 0.5%. As the strain is now measured with respect to the unstrained matrix (dashed rectangle), the precipitates show a strain of -2%, the eigenstrain for the present direction. The maximum strain in the matrix is 2% and is found at a distance between 5 and 10 nm of the interface between the matrix and the nearby precipitate. When moving further away from the precipitate, d decreases sharply. In between both precipitates a region of approximately 20 nm of unstrained matrix is seen indicating that there is no interaction between the strain fields (and related stress fields) arising from these close by precipitates. Black and dark gray areas in the contour plot indicate a negative strain, which means that at the tip of the precipitate the matrix is slightly compressed, as was also the case for the larger precipitates. As already mentioned above there is an area of matrix-precipitate overlap when looking in the [11-1] B2 zone which implies that the information close to what appears to be the interface might be difficult to interpret. Image simulations (made with Mactempas) indicate that the lattice images observed in the present zone can be expected for samples between 10 and 15 nm in thickness, which corresponds with an area of overlap of 5.3 nm, i.e. certainly closer to the precipitate then the maximum strain location at 50 nm in samples A and only interfering with the first part of the increment towards the maximum in samples B. Moreover, although the image from these areas might be distorted because the two structures give an interfering image, image simulations show that the observed interplanar spacing for lattice images clearly revealing the matrix can never be larger than the real one, as expected. The maximum for the observed d, even in the case of the small precipitates, is therefore real and not an artefact. This maximum is reached at a distance d from the precipitate depending on the size of the latter. Similar results can be obtained when viewing the matrix in the [10-1] B2 zone. In this orientation the interface plane is viewed edge-on and so the region close to the interface can be used in good confidence since there is no region of overlap. Unfortunately, in most cases only line resolution of the (101) planes could be recorded in this zone. Again for samples A it was found that a compression appears at the tips of the precipitates and that the strain is increasing when moving away from the interface. The experimental results of the strain fields are compared with a theoretical calculation based on the Eshelby approach. The complete solution for the stress field surrounding an elliptical inclusion is found in [17]. An algorithm provided by K. Gall was adapted and used to Figure 3. The plot shows the contour lines of the εxx strain component (x-axis is chosen parallel to [101] B2 ). The graph corresponds with the profile along the arrow.

6 S3.6.6 perform the computation of the strain field. Figure 4 shows a contour plot of ε[101] for a precipitate with approximately the same size (50 nm) and dimensions of those in Figure 3. This plot confirms the experimental observations on a qualitative level: the matrix is again slightly compressed at the tip of the precipitate and that the maximum of the strain is not localised at the interface but away from it. An important difference, however, is the magnitude of strain. A maximum strain of around 1.5% is measured whereas in the computation this is 0.12%, which is more than a factor of ten different. A reason for this might be the assumption of an equal stiffness for precipitate and matrix. Since the elasticity modulus of Ni 4 Ti 3 has not yet been measured, this discrepancy between theoretical and experimental values might be an indication that this modulus of the precipitate is not equal to that of the matrix. Interactions between elasticity moduli and shape and orientation of precipitates in a matrix are indeed known [18,19]. Also, the real shape of the precipitates deviates from the ideal ellipsoid although one would only expect some visible differences around the tips. Other features that could affect the calculation of the strain are the actual orientation of the precipitate in the thinned foil in view of the direction of maximum strain and the use of a continuum model for phenomena at the nanoscale. The computation of the strain fields in such a case is more complex and the solution is not considered here. Part II: Analytical TEM analysis The formation of Ni 4 Ti 3 precipitates not only introduces a coherent strain field in the surrounding matrix, it also affects the composition of the retained matrix since the precipitates are enriched in Ni with respect to the original material with a nominal composition of Ni 51 Ti 49. The following EELS and EDX results reveal the effect on the composition in the retained matrix surrounding the Ni 4 Ti 3 precipitates in samples A, i.e. those with relatively large precipitates. Figure 4. Computed strain field of the ε[101] component for a precipitate with a diameter of 50 nm.

7 S3.6.7 The local concentration N A for an element A in the material can be calculated from the EELS spectra by [20], IA( β, ) NA = (1) I ( β, ) σ ( β, ) low where I A (β, ) is the measured ionization edge intensity integrated within an energy range and inside a collection semi-angle β (after background subtraction and plural scattering removal by deconvolution with the Fourier-ratio method), I low (β, ) is the intensity of a window of equal β and containing the zero loss, and σ A (β, ) is the partial ionization cross-section. The equation (1) can also be used in EFTEM analysis. The effect of plural scattering cannot be removed from the EFTEM intensity map; nevertheless the effect of diffraction contrast and thickness variation can be corrected by dividing the ionization map by the corresponding low loss image and thickness map. In the case of the binary NiTi the Ni/Ti atomic ratio is thus determined as A N N A B IA( β, A) σb( β, B) E IA( β, A) = = kab (2) I ( β, ) σ ( β, ) I ( β, ) B B A A B B E where k AB =σ B (β, B )/σ A (β, A ) is the so-called k-factor. The stoichiometric proportion for the precipitate in the sample is considered as N Ni /N Ti = 4/3, and can be used as a reference standard. The k-factor can thus be determined from the precipitates in the samples and the elemental concentration for each element in the matrix can then be deduced from the measured Ni/Ti atomic ratio. This approach has the advantage that diffraction and thickness variation effects are largely eliminated as all references and measurements are obtained from regions close to one another. Figure 5 shows a TEM image (a) and the corresponding EELS analysis results (b) on a precipitate and the neighboring matrix. The dark spots on the TEM image are contamination cones because of prolonged nanoprobe electron illumination and can be used as markers for the measured positions. Judging from the TEM image, there is no bending nor significant thickness variation within the investigated region. Further EELS analysis indicates that the thickness is in the range of times of the inelastic scattering mean free path, which is suitable for EELS analysis. The reported data in figure 5(b) are averaged per single distance from the precipitate-matrix interface, thus each time containing three measurements. The calculated Ni/Ti atomic ratio, with a minimum value of 0.95, reveals a region depleted in Ni within a range of about 150 nm from the precipitate-matrix interface and which should be compared with the nominal value of 1.04 for the original Ni 51 Ti 49 matrix. The standard deviation for the measurements inside the precipitate is about 1.0%, (although an absolute accuracy for one measurement generally could be considerably worse than 1.0% in an absolute quantification by equation (1)). Additionally, the Ni and Ti concentration is calculated and shown in figure 5(b).

8 S3.6.8 Figure 5. (a) TEM image, (b) EELS results showing the Ni/Ti atomic ratio, Ni and Ti concentrations. The standard error for the measurements in the adjacent matrix is more than three times larger than in the case of the precipitate, which indicates a certain composition variation among the three averaged positions. Still, the measured depletion of Ni in the matrix can be considered real. Figure 6 shows a TEM image with four smaller precipitates (1-4) meeting at their tips together with the map and profiles for two rectangular regions. A statistical analysis on the atomic ratio map yields a Ni/Ti ratio of 1.33 ± 0.03 for the precipitates. Profile analysis (c) of region A indicates that there are Ni-depleted regions on both sides of precipitate 3. The right side (with a mean Ni/Ti atomic ratio of 0.96 in a region stretching out over 40 nm) is more depleted in Ni than the left side (with a mean Ni/Ti atomic ratio of 1.00 over a region of 20 nm). Profile analysis (d) on the matrix above precipitate 2 shows a similar result as the left side of precipitate 3. This can be understood by the fact that the measured region on the right side of precipitate 3 could be depleted by the formation of precipitate 3 as well as 2. Figure 6. (a) TEM image, (b) Ni/Ti atomic ratio map, (c) and (d) profiles for regions A and B. The dashed lines show the atomic ratio for Ni51Ti49.

9 S3.6.9 Precise composition results were obtained using the standard Cliff-Lorimer method for EDX quantification [21]. The relative elemental concentration (C Ni and C Ti ) is related to the measured X-ray intensities (I Ni and I Ti ) by an equation similar to equation (2). The value of the k-factor for the EDX quantification was again determined from the Ni 4 Ti 3 phase in the samples. The measured concentration for Ni and Ti in the matrix was then calculated based on the results from the precipitates. Since the atomic numbers for Ni and Ti are close to one another, a thickness calibration of absorption of X-rays generated by Ni and Ti was not performed, i.e., any effect of thickness variation was neglected in the present EDX quantification. Figure 7 shows the results of an EDX analysis at a region with most of the Ni 4 Ti 3 precipitates lying parallel to each other and at distances of around 200 nm. A Ni concentration of less than 51 at% was detected for most measured positions in the matrix. The averaged Ni concentration in the matrix is ± From these local analytical measurements it can be concluded that a small but significant Ni depleted region surrounding a Ni 4 Ti 3 precipitate can effectively be measured. From the nanoprobe EELS data it is seen that the depletion exists in an area up to 150 nm away from the precipitate-matrix interface. This area perfectly fits with the average value of the depletion when calculating the excess of Ni in the precipitate, i.e. all Ni needed to form the Ni 4 Ti 3 structure is obtained from the 150 nm matrix region surrounding it. This immediately implies that the precipitates in the EDX study all lie within one another s range of depletion, explaining the lower mean concentration of Ni as measured in the matrix. Figure 7. TEM image of a region investigated by EDX. Small circles and numbers show the measured position and the Ni concentration in at%.

10 S CONCLUSIONS The present work shows that the Ni 4 Ti 3 precipitates influence the lattice parameters as well as the concentration in nanoscale regions of the surrounding matrix. For small precipitates the influence region extends to about 20 nm into the matrix for both strain and concentration whereas for large precipitates the concentration gradient can extend over 150 nm while the strain does not yet reach a maximum 50 nm away from the interface. In all cases these regions perfectly compensate for the lattice mismatch and Ni depletion induced by the precipitate which leads to matrix strains of 2% and local concentration changes up to 8%. It should also be noted that no R-phase or martensite was observed surrounding the investigated precipitates. ACKNOWLEDGMENTS Z. Yang is supported by the GOA project Characterisation of nanostructures by means of advanced EELS and EFTEM of the University of Antwerp. The authors like to thank Martin Hÿtch for providing the necessary software for the geometrical phase image method. Part of this work was supported by the Marie Curie Research Training Network Multi-scale modelling and characterisation for phase transformations in advanced materials (MC FP ). REFERENCES 1. T. Tadaki, Y. Nakata, K. Shimizu, K. Otsuka, Trans JIM 27, 731 (1986) 2. M. Nishida, C.M. Wayman, Mater. Sci. Eng. 93, 191 (1987) 3. M. Nishida, C.M. Wayman and T.Honma, Metal. Trans. A 17, 1505 (1986) 4. L. Bataillard, J.-E. Bidaux, R. Gotthardt, Phil. Mag. A 78, 327 (1998) 5. J. Khalil-Allafi, A. Dlouhy, G. Eggeler, Acta. Mater. 50, 4255 (2002) 6. P. Filip and K. Mazanec, Scripta Mater. 45, 701 (2001) 7. V. Zel dovich, G. Sobyanina and T.V. Novoselova, J. Phys. IV France 7, 299 (1997) 8. J. Khalil Allafi, X. Ren, G. Eggeler, Acta. Mater. 50, 793 (2002) 9. W. H. Zou, X. D. Han, R. Wang, Z. Zhang, W-Z Zhang, J. K. L. Lai, Mater. Sci. Eng. A 219, 142 (1996) 10. K. Gall, H. Sehitoglu, Y.I. Chumlyakov, I.V. Kireeva, H.J. Maier, J. Eng. Mat. Tech. 121, 19 (1999) 11. D.Y. Li and L. Q. Chen, Acta. mater. 45, 471 (1997) 12. C. Somsen, Mikrostrukturelle Untersuchungen an Ni-reichen Ni-Ti Formgedächtnislegierungen, Shaker Verlag, (2002) 13. M.J. Hÿtch, Scanning Microscopy 11, 54 (1997) 14. M.J. Hÿtch, E. Snoeck, R. Kilaas, Ultramicroscopy 74, 131 (1998) 15. M.J. Hÿtch, T. Plamann, Ultramicroscopy 87, 199 (2001) 16. W. Tirry, D. Schryvers, Acta. Mater. (accepted for publication; October 2004) 17. T. Mura, Micromechanics of defects in solids, Nijhoff : Boston, (1982) 18. Jun-Ho Choy, Jong K. Lee, Mat. Sci. Eng. A 285, 195 (2000) 19. R. Mueller, D. Gross, Comp. Mat. Sci 11, 35 (1998) 20. R. F. Egerton, Electron Energy-Loss Spectroscopy in the Electron Microscope, New York, (1996). 21. G. Cliff and G. W. Lorimer, J. Microscopy, 103, 203(1975).