Ni4Ti3-precipitation during aging of NiTi shape memory alloys and its influence on martensitic phase transformations

Acta Materialia 50 (2002) 4255–4274 www.actamat-journals.com

Ni4Ti3-precipitation during aging of NiTi shape memory alloys and its influence on martensitic phase transformations Jafar Khalil-Allafi a, Antonin Dlouhy b, Gunther Eggeler a,∗ a

Institut fu¨r Werkstoffe, Ruhr-Universita¨t Bochum, Universita¨tsstrasse 150, D-44 780 Bochum, Germany b Institute of Physics of Materials, AS CR, Zizkova 22, CZ-616 62 Brno, Czech Republic Received 22 March 2002; received in revised form 7 June 2002; accepted 10 June 2002

Abstract The present work studies the microstructure of a Ni-rich NiTi shape memory alloy and its influence on the thermal characteristics of martensitic transformations. The solution annealed material state is subjected to various isothermal aging treatments at 773 K; this results in the nucleation and growth of lenticular coherent Ni4Ti3-precipitates, which were quantitatively characterized using transmission electron microscopy (TEM). Stress free aging for 36 ks results in a heterogeneous microstructure with precipitates near grain boundaries and precipitate free regions in grain interiors; this microstructure shows a three step (’multiple step’) transformation behavior in a differential scanning calorimetry (DSC) experiment on cooling from the B2 regime, which can neither be rationalized on the basis of a coherency stress argument (Bataillard et al., 1997) nor on the basis of varying Ni-concentrations between growing precipitates (KhalilAllafi et al., 2002). A new interpretation of evolving DSC chart features is proposed which takes the evolution of microstructures during stress free and stress-assisted aging into account. Most importantly it is shown that stresses as small as 2 MPa strongly affect the precipitation process.  2002 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. Keywords: Ni-rich NiTi shape memory alloys; Aging; Ni4Ti3 precipitation; Martensitic transformation; Transmission electron microscopy (TEM); Differential scanning calorimetry (DSC)

1. Introduction NiTi shape memory alloys combine good functional and structural properties [1–4]. There is an interest in Ni-rich NiTi alloys because phase transition temperatures can be controlled through the Ni-content [2,5]. Processing of NiTi alloys gener∗ Corresponding author. Tel.: +49 234 7003022; fax: +49 234 3214235. E-mail address: [email protected] (G. Eggeler).

ally involves thermo mechanical treatments, which lead to the precipitation of metastable Ni4Ti3-particles [2]. There is a good understanding of the crystallographic features of the Ni4Ti3-precipitates which are coherently precipitated in the matrix [2], have a lenticular shape [2] and can form eight variants [6] on {111}-planes [2,6]. The precipitates give rise to coherency stress fields and external stresses can favor the occurrence of certain precipitate variants [2,6,7]. It is well known that Ni4Ti3particles affect the features of the martensitic transformation in supporting the formation of the R-

1359-6454/02/$22.00  2002 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 9 - 6 4 5 4 ( 0 2 ) 0 0 2 5 7 - 4

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phase [8] and affecting the Ni-content of the matrix [9–11]. But the role of Ni4Ti3-precipitates on martensitic transformations as observed using differential scanning calorimetry (DSC) has been discussed controversially in the literature. Thus Bataillard et al. [12] ascribed multiple step martensitic transformations (one step—one distinct DSC peak, multiple steps—multiple distinct DSC peaks) to coherency stress fields around precipitates while KhalilAllafi et al. [13] explained two step and multiple step transformation behavior on the basis of evolving Ni-concentration profiles between particles and differences in nucleation barriers between R-phase and B19’. Two recent results show that aging of annealed, defect free materials results in heterogeneous grain boundary precipitation [14] and that small differences in preload strongly affect the creep behavior of Ni-rich NiTi alloys [11]; here it is important to highlight that creep rate is a sensitive probe for microstructural evolution. These two recent findings suggest that more experimental work is required to understand the precipitation processes in Ni-rich NiTi alloys. In order to contribute to a better understanding of precipitation processes and their influence on martensitic transformations, the present work uses transmission electron microscopy (TEM) to investigate how microstructures form during stress free and stress assisted aging and how these microstructures affect the thermal characteristics of martensitic transformations.

2. Experiments A binary nickel-rich NiTi alloy with a nominal composition of 50.7 at.-% Ni was investigated in the present study. It was purchased from Memory Metals, Weil am Rhein in the form of cylindrical rods of 1 m length and 13 mm diameter. A TEM micrograph of the microstructure after solution annealing (1123 K, 900 s) and water quenching is shown in Fig. 1. Solution annealing results in a homogeneous equiaxed microstructure with only a few Ti4Ni2O oxide particles and no Ni4Ti3 precipitates. Aging of the solution annealed and water quenched material states was performed at 773 K

Figure 1. TEM micrograph showing a homogeneous equiaxed microstructure of the Ni-rich NiTi alloy investigated in the present study (nominal composition: 50.7 at.-% Ni) after solution annealing (1123 K, 900 s) and water quenching. The grain size of the material as determined by optical microscopy was 35 µm. The TEM micrograph shows two grain boundaries (at the top of the micrograph) and a few Ti4Ni2O oxide particles (which were chemically analyzed in the TEM using EDAX).

for aging times of 3.6 ks, 36 ks and 360 ks. Experiments to study the effect of superimposed stresses on aging were carried out in creep machines using cylindrical specimens with three diameters (corresponding to stresses of 2, 8 and 20 MPa) to obtain information on the effect of three stress levels on aging (stress assisted aging); no accumulation of plastic strain was detected during stress assisted aging. A small piece of material was kept right next to the cylindrical specimen in the furnace to provide material, which was aged without stress (stress free aging). The details of the creep machines used in the present investigation have

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been described elsewhere [15] and the geometry of the specimen used for stress assisted aging will be published shortly [16]. From all aged materials, specimens were prepared for DSC measurements and for TEM investigations. The transformation behavior during heating and cooling was investigated using a differential scanning calorimeter DSC 2920 CE from TA Instruments. DSC specimens with masses between 20 and 50 mg were heated up to 373 K where they were held for three minutes to establish thermal equilibrium. Then the DSC measurement started by cooling down to 173 K in 0.17 K/s. At 173 K the specimen was again held for 3 min and then heated up to 373 K with a heating rate of 0.17 K/s. Recent neutron diffraction results confirmed that the matrix of the alloy investigated in the present study was B2 at 373 K and B19’ at 173 K [17]. DSC charts which are obtained during cooling (from the temperature where B2 is stable, ‘B2 regime’) and during heating (from the B19’ regime) are shown in Figs. 2 and 3. Transmission electron microscopy (TEM) was performed using a Philips CM20 analytical microscope operating at 200 kV. TEM specimens were cut perpendicular to the axis of the as received rod or to the axis of the cylindrical specimen used for stress assisted aging. The specimens were carefully ground to a thickness of 150 µm and then electro polished using a double jet thinning technique (Tenupol; Struers A8 electrolyte at 20V and intermediate flow rate). TEM was used to obtain micrographs, to identify phases by selected area diffraction (SAD) and for chemical analysis using EDAX. During the preparation of TEM foils an effort was made to keep the material from transforming into martensite by using an electrolyte temperature of 288 K where good thinning conditions were obtained and where sufficient parts of the matrix remained either austenitic or R-phase (for short and intermediate aging times). However, as can be seen from Fig. 2, the martensite finish temperature after 360 ks of stress free aging is high and therefore no reliable precipitate information was obtained after long-term aging. Precipitate volume fractions were evaluated from TEM foils where the thickness was measured using a stereo-pair method [18]. The particle shape was approximated as an ellipsoidal disk with a

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Figure 2. DSC charts on cooling from the B2 regime. The four DSC charts show the influence of aging time. The DSC chart of the solution annealed (1123 K, 900 s) and water quenched material is shown at the bottom. Three additional DSC charts were measured after 3.6, 36 and 360 ks of stress free aging at 773 K. The small vertical bars after 3.6 and 36 ks of aging (and the corresponding horizontal error bars) represent calculated peak temperatures based on TEM Ni4Ti3 precipitate volume fraction measurements and available data on the influence of Ni on phase transition temperatures (see text). For the 36 ks stress free aging conditions a small vertical arrow indicates the temperature where the transformation starts.

diameter ‘D’ and a thickness ‘t’. Tilting experiments were performed in order to determine D and t values. Fig. 4a and b show two TEM micrographs from a material which was aged at 773 K for 36 ks under 2 MPa. The two micrographs show the same region in the TEM foil for two different tilt positions. Fig. 4a and b demonstrate that TEM foils can be tilted into positions that allow measuring the precipitate diameter D (Fig. 4a) and in other positions where the precipitate thickness t can be obtained (Fig. 4b). For the material state shown in

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average to give a resulting volume fraction Vf of 6.7 ± 3.5% for the material state shown in the TEM micrographs of Fig. 4 (stress assisted aging: 773 K, 36 ks, 2 MPa). All Vf results presented in this paper are based on the evaluation of more than 100 particles. Details on the TEM procedure for determining precipitate volume fractions will be reported elsewhere [19]. In several cases the cube projection method was used to transfer crystallographic information (on directions and planes) from convergent beam electron diffraction patterns to TEM micrographs [20].

3. Results 3.1. Stress free aging

Figure 3. DSC charts on heating from the B19’ regime. The four DSC charts show the influence of aging time. The DSC chart of the solution annealed (1123 K, 900 s) and water quenched material is shown at the bottom. Three additional DSC charts were obtained after 3.6, 36 and 360 ks of stress free aging at 773 K. The small vertical bars after 3.6 and 36 ks of aging (and the corresponding horizontal error bars) represent calculated peak temperatures based on TEM Ni4Ti3 precipitate volume fraction measurements and available data on the influence of Ni on phase transition temperatures (see text).

Fig. 4, one TEM foil was evaluated. Measurements were performed at four locations of the TEM-foil. The corresponding foil thickness, numbers of precipitates, average precipitate diameters D and average particle thickness t are summarized in Table 1. The evaluation of the measurements presented in Table 1 yields weighted averages for 137 particles; average D and t values were obtained as 335 ± 120 nm and 32 ± 7 nm, respectively. Four foil volumes were calculated from the four foil thickness given in Table 1 and the areas of the corresponding micrographs (not listed in Table 1). Four volume fractions were thus obtained which

In this section we report the effect of stress free aging on martensitic transformations when cooling from the B2-regime to low temperatures and when heating B19’-microstructures. The corresponding DSC charts are presented in Fig. 2 (cooling from B2) and 3 (heating from B19’). We first consider the DSC charts in Fig. 2 where DSC charts evolve with aging time. There are three characteristic features that change with aging: (1) the type of transformation changes from one step (after solution annealing) through two steps (after 3.6 ks aging) and three steps (after 36 ks aging) back to one step (after 360 ks aging). (2) The width of the overall transformation temperature range changes from small (after solution annealing) through large (for short and intermediate aging times) back to narrow for (long aging times). (3) There are shifts in peak positions, and of temperatures where transformations begin and end. Table 2 lists all temperatures of distinct DSC peaks (’peak temperatures’) observed in Fig. 2 (cooling from B2-regime). Fig. 3 shows the DSC results that were obtained for heating from low temperatures. Again there is an evolution of DSC chart features with aging time. The type of transformation changes from one step (after solution annealing) through two steps (after short and intermediate aging times) back to one step (after long term aging). Three step transformations were not detected for the back transform-

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Figure 4. TEM micrographs of a microstructure after stress assisted aging at 773 K for 36 ks under 2 MPa. (a) TEM foil in tilt position to evaluate precipitate diameters D. (b) TEM foil in tilt position to evaluate the thickness t of precipitates. Table 1 Microstructural parameters from a material which was aged at 773 K for 36 ks under 2 MPa. Data for four locations in one TEMfoil are listed and average values of the local foil thickness, numbers of precipitates, the local mean precipitate diameter D and the local mean precipitate thickness t are reported Location

1 2 3 4

Foil thickness [nm]

Number of precipitates

78 111 131 87

32 29 34 42

ations. The peak positions observed in Fig. 3 are listed in Table 2. On cooling from the B2-regime, DSC charts of the Ni-rich NiTi material that was aged without stress show the following features: (1) the temperature where the transformation starts increases with aging time. (2) The position of the first distinct DSC peak on cooling shifts towards higher temperatures with increasing aging time. (3) The solution annealed material and the materials which were aged for short (3.6 ks) and intermediate (36 ks) aging periods have two common characteristics: after aging the positions of the last peaks on cooling correspond to the position of the single DSC peak obtained for the solution annealed

Mean precipitate diameters D [nm] 334 428 256 335

Mean precipitate thickness t [nm] 30 39 33 27

material; and in all three material states the transformations end at the same temperature (which generally is referred to as the martensite finish temperature, Mf). On heating from the B19’-regime the DSC charts of the material which was aged without stress can be described as follows: (1) The back transformations of the solution annealed material and the materials which were aged for short (3.6 ks) and intermediate (36 ks) aging times start at the same temperature. These three material states also show a distinct DSC-peak at the same temperature (single peak of the solution annealed material and the first peaks on heating of the aged materials). (2) The positions of the last distinct peaks shift to higher temperatures with increasing

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Table 2 Overview summary of peak positions in the DSC charts of Figs. 2 and 3. The Table also shows results for peak positions which were calculated using Eqs. (1) and (3). Solution annealing was performed at 1123 K for 900 s. All subsequent aging treatments were performed at 773 K in the absence of an external stress Material/peak position:

1st peak on cooling [K]

2nd peak on cooling [K]

3rd peak on cooling [K]

predicted Mp [K]

solution annealed 1 h aging 10 h aging 100 h aging

255.8 278.1 289.4 291.4

– 254.1 280.1 ⫺

– – 256.3 ⫺

– 278.2±9 290.2±31 -

Material/peak position:

1st peak on heating [K]

2nd peak on heating [K]

3rd peak on heating [K]

predicted Ap [K]

Solution annealed 1 h aging 10 h aging 100 h aging

287.1 286 282.4 323.9

– 300.8 312.3 –

– – – –

– 309.2±9 321.2±31 –

aging times. During both heating and cooling the difference in peak temperatures between the single distinct peak observed for the solution annealed material and the single distinct peak observed after 360 ks aging is 35 K. The microstructures of the material states that were aged at 773 K (without stress) for 3.6 ks and for 36 ks are shown in the TEM micrographs of Figs. 5 and 6. Fig. 5 shows that heterogeneous nucleation of Ni4Ti3-precipitates is an important factor in the early stages of aging. Precipitation of small lenticular Ni4Ti3 precipitates only occurs on and near grain boundaries and near oxide particles (large globular particles stemming from processing and present in the as received material, see Fig. 1). The major part of the grain shown in Fig. 5 is free of precipitates. Increasing the aging time to 36 ks results in the microstructure shown in Fig. 6. Clearly, precipitates are coarser than after shorter aging times. The presence of particles in a belt trimming the grain boundaries is still a prominent feature; and in addition precipitates form irregular networks in the interior of the grain. But even after 36 ks of aging, large parts of the grain interior are free of precipitates. We now show the precipitate microstructures near the grain boundaries after 3.6 and 36 ks of aging at a higher magnification, Fig. 7a and b. The micrographs give a good impression on how pre-

Figure 5. TEM micrograph of a grain in a material which was subjected to stress free aging (773 K, 3.6 ks). There are two types of particles: (i) large globular Ti-rich Ti4Ni2O oxides can be found in the grain interior and near grain boundaries. (ii) fine lenticular Ni-rich Ni4Ti3 precipitates nucleate heterogeneously close to the grain boundaries and near the oxide particles.

cipitates grow during aging. Both micrographs are part of stereo pairs from which the spatial orientation of precipitates was determined; for this purpose, cubes with an inscribed tetraedron showing

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Figure 6. TEM micrograph of a grain in a material which was subjected to stress free aging (773 K, 36 ks). Ni4Ti3-precipitates are coarser than after shorter aging times (see Fig. 5). An important portion of the precipitates is located near grain boundaries. All other particles form irregular networks in the grain interior. There still are large areas in the grain interior which are precipitate free.

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the ⬍ 100 ⬎ - and ⬍ 110 ⬎ -directions of the cubic B2 matrix [20] are superimposed on the images of the upper grain in Fig. 7a and the lower grain in Fig. 7b. The cube projection method [20] allows differentiating between four {111} precipitate plane groups. After 3.6 ks aging the precipitates near the grain boundary (upper grain) belong mainly to the plane groups (11¯ 1¯ ) and (1¯ 1¯ 1). After 36 ks aging the lenticular particles close to the grain boundary (lower grain) are parallel to (11¯ 1¯ )-, (1¯ 1¯ 1)- and (111)-planes of the B2-matrix. No further effort was made in the present study to quantitatively account for the distribution of Ni4Ti3-precipitates into ⬍ 111 ⬎ -plane groups. In Table 3 we summarize the results on mean particle diameter D, mean particle thickness t, the interparticle spacing l and Vf- the volume fraction of precipitates which were obtained for the material subjected to stress free aging at 773 K for 3.6 and 36 ks. After 3.6 ks aging, precipitate volume fractions were determined for the grain boundary regions. For the 36 ks aging condition, precipitate volume fractions were determined from all regions containing precipitates; the precipitate free regions were not considered. Therefore the

Figure 7. TEM micrographs of particles near grain boundaries after stress free aging of a Ni-rich NiTi alloy at 773 K for (a) 3.6 ks and (b) 36 ks. (a) After 3.6 ks aging the precipitates near the grain boundary (upper grain) belong mainly to the plane groups (11¯ 1¯ ) and (1¯ 1¯ 1). (b) After 36 ks aging the lenticular particles close to the grain boundary (lower grain) are parallel to (11¯ 1¯ )-, (1¯ 1¯ 1)- and (111)-planes of the B2-matrix.

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Table 3 Microstructural data characterizing the Ni4Ti3-precipitate population after stress free aging for 3.6 and 36 ks at 773 K. Listed are the microstructural parameters D—the mean diameter of the main circle of the lenticular precipitates, t—the mean thickness of the lenticular precipitates, l—the interparticle spacing and Vf—the volume fraction of precipitates. After 3.6 ks aging the particle volume fraction was determined from grain boundary regions. After 36 ks aging the particle volume fraction was determined from grain boundary regions and from the irregular particle network regions in the grain interior (particle free areas were not considered!) Material state (stress free aging at 773 K)

D [nm]

t [nm]

l [nm]

Vf [%]

3.6 ks 36 ks

230±150 900±340

23±6 68±21

285±20 785±180

2.8±1.0 5.2±4.5

precipitate volume fractions reported here over predict the overall precipitate volume fraction for the 3.6 and 36 ks aging conditions. When taking a closer look at the Ni4Ti3 precipitates in the grain boundary regions (Figs. 5 and 7a, material state after stress free aging at 773 K for 3.6 ks) it can be seen that the precipitate size increases with increasing distance of the precipitates from the grain boundary; a quantitative evaluation is presented in Fig. 8. Fig. 5 to 7 clearly show that during aging pre-

Figure 8. Diameter D of lenticular Ni4Ti3 precipitates as a function of the distance from the grain boundary after stress free aging at 773 K for 3.6 ks. Two horizontal lines indicate mean particle diameters observed in microstructures with homogeneously distributed precipitates after stress assisted aging (dotted line: 773 K/2 MPa/3.6 ks; dashed line: 773 K/20 MPa/3.6 ks).

cipitates continue to nucleate and grow. However, precipitate growth is not simply characterized by an Ostwald ripening type of process [21,22], because (i) the microstructure has not yet reached global thermodynamic equilibrium and (ii) there are additional crystallographic aspects that need to be considered. Thus Fig. 9 shows diffraction patterns from small (3.6 ks aging, Fig. 9a) and large Ni4Ti3-precipitates (36 ks aging, Fig. 9b). Both diffraction patterns show the characteristic precipitate spots that subdivide the reciprocal distance associated with ⬍ 321 ⬎ B2 into seven intervals [6]. In the case of small precipitates (like those shown in Fig. 7a) the diffraction spots are weak and are only associated with one type of precipitate variant, Fig. 9a. Large precipitates (which are shown in the TEM-micrograph of Fig. 7b) create stronger spots and can consist of two precipitate variants as can be seen from the twin related rows of corresponding spots, Fig. 9b. Another TEM observation after stress free aging at 773 K for 3.6 ks is shown in Fig. 10; here precipitates form two parallel chains. These chains of precipitates can be rationalized on the basis of a scenario where one precipitate nucleates in the stress field of another; this type of auto catalytic heterogeneous precipitation has been described for other systems [23] and contributes to the formation of the irregular networks observed after longer term aging (see Fig. 6). 3.2. Stress assisted aging We now report the thermal and microstructural results which were obtained for the material states subjected to stress assisted aging; it is important to underline that small stresses of 2, 8 and 20 MPa

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Figure 10. TEM micrograph after stress free aging at 773 K for 3.6 ks. Precipitates form two parallel chains. One precipitate nucleates in the stress field of another.

Figure 9. Diffraction patterns from Ni4Ti3 precipitates after stress free aging at 773 K. (a) a small particle (3.6 ks aging, Fig. 7a) and (b) a large particle (36 ks aging, Fig. 7b). Both diffraction patterns show the characteristic precipitate spots [6] which subdivide the reciprocal distance associated with ⬍ 321 ⬎ B2 into seven intervals. (a) For a small precipitate the particle spots (highlighted in the diffraction pattern) are weak and are associated with one precipitate variant. (b) One large particle can consist of two precipitate variants from the same plane group as can be seen from the twin related rows of corresponding spots (highlighted in diffraction pattern).

were considered which at 773 K did not result in any detectable plastic deformation. Fig. 11 shows the effect of stress-assisted aging on the DSC chart features on cooling. The DSC chart of the solution annealed (1123 K, 900 s) and water quenched material is shown at the bottom. Nine additional DSC charts were measured after 3.6, 36 and 360 ks of stress-assisted aging (2 MPa—solid line, 8 MPa—dashed line, 20 MPa—dotted line) at 773 K. The DSC charts (on cooling from the B2 regime) after stress assisted aging in Fig. 11 significantly differ from the DSC charts after stress free aging presented in Fig. 2; the actual stress level during stress assisted aging does not strongly affect the DSC chart features after 36 and 360 ks of aging. After 3.6 ks aging, increasing stresses promote a three-step transformation: a third dis-

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Figure 11. DSC charts of the Ni-rich NiTi alloy investigated in the present study on cooling from the B2 regime. The four graphs show the influence of stress assisted aging on the thermal effects associated with the martensitic transformations. The DSC chart of the solution annealed (1123 K, 900 s) and water quenched material is shown at the bottom. Nine additional DSC charts were measured after 3.6, 36 and 360 ks of stress assisted aging (2 MPa—solid line, 8 MPa—dashed line, 20 MPa—dotted line) at 773 K. For the 36 ks stress assisted aging condition a small vertical arrow indicates the temperature where the transformations start.

tinct DSC peak (which cannot be clearly detected in the DSC chart observed after stress assisted aging under 2 MPa and which is absent after 3.6 ks of stress free aging in Fig. 2) becomes clearly visible when aging under stresses of 8 and 20 MPa. After 360 ks, all materials that were aged under stress show a broad transformation peak that has two distinct maxima (while there was only one sharp peak after stress free aging, Fig. 2). It is also interesting to note that after 36 ks of aging at 773 K the transformations on cooling start significantly

earlier after stress assisted aging as compared to stress free aging (see small vertical arrows pointing to the start of transformations in Figs. 2 and 11). In Table 4 we summarize the DSC peak temperatures that characterize stress assisted aging on cooling from the B2-regime. Fig. 12 shows the effect of stress assisted aging on the transformation behavior during heating from the B19’ regime. The DSC chart of the solution annealed (1123 K, 900 s) and water quenched material is shown at the bottom. Nine additional DSC charts were measured after 3.6, 36 and 360 ks of stress-assisted aging (2 MPa—solid line, 8 MPa—dashed line, 20 MPa—dotted line) at 773 K. As a striking difference between the DSC charts after stress free aging (Fig. 3) and the DSC charts obtained after stress assisted aging we note that the pronounced two step transformation which is observed for 3.6 and 36 ks of stress free aging can no longer be detected. It should not be overlooked, however, that 3.6 ks aging under 20 MPa results in a peak which has a pronounced shoulder on its high temperature side; the same microstructure produces three distinct DSC peaks on cooling, Fig. 11. In Table 5 we summarize the DSC peak temperatures which characterize stress assisted aging on heating from the B19’ regime. The differences in DSC transformation behavior between the material states subjected to stress free and stress assisted aging is due to the difference in corresponding microstructures. Four characteristic TEM micrographs that document the microstructures after stress-assisted aging at 773 K are shown in Fig. 13. The top and bottom rows of Fig. 13 show microstructures after 3.6 and 36 ks of stressassisted aging, respectively. The left and right columns of Fig. 13 show microstructures that were aged at 773 K in the presence of stresses of 2 and 20 MPa, respectively. As can be seen from Fig. 13, stress assisted aging results in a homogeneous distribution of precipitates for all levels of applied stress; in this respect it does not seem to matter whether stress assisted aging was performed under 2 or 20 MPa. However, higher stress levels are associated with slightly larger precipitates. Fig. 13 also clearly shows that precipitates coarsen with time. The results of the quantitative TEM evaluation for the microstructures shown in Fig. 13 are

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Table 4 Overview summary of peak positions in the DSC charts of Fig. 11. The table also shows results for peak positions which were calculated using Eqs. (1) and (3). All stress assisted aging treatments were performed at 773 K under stresses of 2, 8 and 20 MPa Material/peak position

1 h aging, 2 MPa 1 h aging, 8 Mpa 1 h aging, 20 MPa 10 h aging, 2 MPa 10 h aging, 8 MPa 10 h aging, 20 MPa 100 h aging, 2 MPa 100 h aging, 8 MPa 100 h aging, 20 MPa a

1st peak on cooling [K]

2nd peak on cooling [K]

289.3 289 289 293.7 293.6 293.7 293.7 295.9 296.2

3rd peak on cooling [K]

281.2a 274.9 272.9 277.3 277.7 279.1 285.1 288.3 288.7

259.9 260.9 260.6 – – – – – –

Predicted Mp [K]

270.2±9 – 274.2±10 295.2±26 – 296.2±17 – – –

no distinct peak

summarized in Table 6. The mean values of the diameters D of the lenticular precipitates after 3.6 ks of stress-assisted aging (at 2 and 20 MPa) are included in Fig. 8. Stress assisted aging (even under stresses as small as 2 MPa) results in homogeneous precipitation throughout the microstructure; and with increasing aging time precipitate volume fractions increase and precipitates coarsen, Fig. 13. Fig. 14 shows a constant number density of Ni4Ti3 precipitates after stress-assisted aging (773 K/20 MPa/3.6 ks). A two-beam condition was adjusted for the grain on the right side of the grain boundary that traverses the micrograph vertically (g: (1¯ 10)). The area marked “A” on the left side of the grain boundary is shown in the TEM micrograph of Fig. 15 under a different contrast condition. The image contrast in Fig. 15 was obtained using a g of (101¯ ). It can be clearly seen that the precipitates near the grain boundary (region A) differ in contrast from the majority of precipitates that fill the interior of the grain. Both types of precipitates have similar number densities and size distributions. However, they belong to different Ni4Ti3 variant groups. Most importantly, the precipitates that show the strongest contrast (precipitate plane group(1¯ 1¯ 1)) are absent near the grain boundary (region A).

4. Discussion 4.1. Precipitation in Ni-rich NiTi alloys during aging The results of the present study confirm many of the previous experimental and analytical results reported in the literature on nucleation and growth of Ni4Ti3 precipitates [6,7,24–28]. Most importantly they confirm the recent findings of Filip and Mazanec [14] who reported that Ni4Ti3 precipitates form mainly at grain boundaries when the over saturated NiTi matrix is defect free. The results of our study show that heterogeneous grain boundary precipitation is the dominant feature of Ni-rich NiTi microstructures after solution annealing and subsequent aging at 773 K for times up to 36 ks. The present investigation shows that this heterogeneous grain boundary precipitation is no longer observed, when the aging is performed in the presence of stresses as small as 2 MPa. Such stress assisted aging results in microstructures with a homogeneous distribution of precipitates in terms of number density; however, there is a difference between grain interiors and regions near grain boundaries in terms of the precipitate variants that are observed, Figs. 14 and 15. Grain boundaries are well known as representing

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Figure 12. DSC charts of the Ni-rich NiTi alloy investigated in the present study on heating from the B19’ regime. The four graphs show the influence of stress assisted aging on the thermal effects associated with the martensitic transformations. The DSC chart of the solution annealed (1123 K, 900 s) and water quenched material is shown at the bottom. Nine additional DSC charts were measured after 3.6, 36 and 360 ks of stress assisted aging (2 MPa—solid line, 8 MPa—dashed line, 20 MPa—dotted line) at 773 K.

locations for heterogeneous nucleation in solidstate precipitation processes for a number of reasons [29]. In Ni-rich NiTi alloys there may well be a higher Ni-concentration at the grain boundaries; moreover grain boundaries energetically favor nucleation by decreasing the interfacial energy between the precipitate and the parent phase [29]. The results shown in Figs. 5, 7 and 8 can be interpreted as follows: initially many precipitates form at the grain boundary; their sizes remain small because there is competitive growth. The coherency stress fields of the early precipitates assist in the nucleation of other precipitates which form less frequently in some distance from the

grain boundary and therefore can grow to larger sizes. It is interesting to note that the sizes of grain boundary precipitates after stress free aging at 773 K for 1 h are comparable to the dimensions of precipitates in the grain interior after stress assisted aging at 773 K for one hour in the presence of an external stress of 2 and 20 MPa, Fig. 8. Small grain boundary stresses may therefore well be important in triggering grain boundary precipitation; simple formulas for the stress distributions near grain boundaries (modeled by dislocation arrays) are given in [30]. Using formula (1978) from [30] and assuming a dislocation spacing of 10 nm in the boundary one can estimate stresses of the order of 1 MPa in distances of the order of 20 nm from the boundary; therefore short range stress fields associated with grain boundaries also need to be considered when discussing grain boundary precipitation of Ni4Ti3 in solution annealed Ni-rich NiTi alloys during stress free aging as presented in Figs. 5, 7 and 8. However, this does not explain the microstructural heterogeneity shown in Fig. 15 that occurs under conditions of aging at 773 K for 1 h in the presence of a stress of 20 MPa. In a zone of 2 µm near the grain boundary (region A in Fig. 15) one precipitate variant that shows good contrast in the grain interior is absent. This microstructural heterogeneity which evolves under stress assisted aging may well be associated with a non homogenous stress distribution in the microstructure due to different orientations of two neighboring B2 grains with respect to the loading axis; further work is required to clarify this point. For the present work it is important to highlight that Ni4Ti3 precipitation during short term aging at 773 K can be heterogeneous no matter whether the material is aged in the presence or in the absence of stress; under conditions of stress free aging, a microstructure forms which is characterized by precipitate belts which trim the grain boundaries. In the presence of small stresses the environments of grain boundaries contain other precipitate variants than the grain interiors. From the results reported in the present study it can also be concluded that the nucleation is much more sensitive to the presence/absence of an external stress than the subsequent precipitate coarsening (see mean values in Tables 3 and 6); Fig. 13 clearly

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Table 5 Overview summary of peak positions in the DSC charts of Fig. 12. The table also shows results for peak positions which were calculated using Eqs. (1) and (3). All stress assisted aging treatments were performed at 773 K under stresses of 2, 8 and 20 MPa Material/peak position

1st peak on heating [K]

2nd peak on heating [K]

3rd peak on heating [K]

1 h aging, 2 MPa 1 h aging, 8 MPa 1 h aging, 20 MPa 10 h aging, 2 MPa 10 h aging, 8 MPa 10 h aging, 20 MPa 100 h aging, 2 MPa 100 h aging, 8 MPa 100 h aging, 20 MPa

311.1 307.1 306.1 319.6 318.2 317.5 327.7 323.2 321.9

– – – – – – – – –

– – – – – – – – –

shows that an increase of one order of magnitude in aging time has a much stronger effect on precipitate size than a one order increase in the level of the superimposed external stress. Ti4Ni2O oxides that form during material processing [2] also act as preferential nucleation sites for Ni4Ti3 precipitates, Figs. 5 and 6. Since the density of oxides is small for the present material this contribution to microstructural heterogeneity is not considered further. 4.2. Precipitation and Ni-concentration of the matrix In the previous section we have discussed Ni4Ti3 precipitation (Ni-concentration cP of precipitates: 57.1 at.-%) in a supersaturated Ni-matrix with a Ni-concentration c0 of 50.7 at.-%. TEM was used to determine precipitate volume fractions Vf as precisely as possible. Growth of Ni-rich precipitates results in a decrease of Ni-concentration in the matrix where the average Ni-concentration cNi for a given volume fraction of precipitates Vf is given by [9,11] cNi ⫽

c0⫺Vf·cP 1⫺Vf

(1)

In a recent literature review Tang et al. [5] report the dependence of the martensite start temperature Ms in solution annealed NiTi alloys on Ni-concentration cNi; some of the data from [5] are shown in Fig. 16 (original sources referenced in [5]: [31–

predicted Ap [K]

301.2±9 – 305.2±10 326.2±26 – 327.2±17 – – –

35]). A polynomial fit of fifth degree rationalizes all Ms-data in Fig. 16 (literature data [5,31–35] and the experimental result of the solution annealed material of the present study): Ms(cNi) ⫽ (a0 ⫺ a1·cNi ⫹ a2·c2Ni ⫺ a3·c3Ni

(2)

⫹ a4·c4Ni ⫺ a5·c5Ni)K The dashed line which rationalizes all Ms-data in Fig. 16 is obtained using the coefficients a0 to a5 listed in Table 7. In the present study we assume that we can represent Mp-data by shifting the fit obtained for the Ms-data in Fig. 16 (Eq. (2) and coefficients in Table 7) down to our experimental Mp-value. These Mp-data are then represented by: Mp(cNi) ⫽ (b0 ⫺ b1·cNi ⫹ b2·c2Ni ⫺ b3·c3Ni

(3)

⫹ b4·c4Ni ⫺ b5·c5Ni)K The solid line that shows the Mp-behavior, which we assume in the present study, is obtained using the coefficients b0 to b5 listed in Table 7. We now estimate Mp-values based on our volume fraction measurements (Tables 3 and 6). From Eq. (1) we obtain corresponding cNi-values that we then input in Eq. (3) to obtain Mp-estimates. The results are listed in Tables 2 and 4 and are also presented as small vertical bars (with horizontal error bars reflecting the inherently large scatter in TEM volume fraction measurements) in the corresponding DSC-charts shown in Figs. 2 and 11. This approach does not attempt to fully account for all DSC chart features. But the results confirm that

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Figure 13. TEM micrographs showing representative microstructures after stress assisted aging at 773 K. Top row: 3.6 ks aging. Bottom row: 36 ks aging. Left column: 2 MPa. Right column: 20 MPa. (a) 2 MPa, 3.6 ks (b) 20 MPa, 3.6 ks (c) 2 MPa, 36 ks (d) 20 MPa, 36 ks.

Figure 14. Low magnification TEM micrograph showing a constant number density of Ni4Ti3 precipitates after stress assisted aging (773 K/20 MPa/3.6 ks) everywhere in the microstructure. A two beam condition was adjusted for the grain on the right side of the grain boundary which traverses the micrograph vertically (g: (1¯ 10)). The area marked ‘A’ on the left side of the grain boundary is shown in Fig. 15 under a different contrast condition.

Table 6 Microstructural data characterizing the Ni4Ti3-precipitate population after stress assisted aging for 3.6 and 36 ks at 773 K. Listed are the microstructural parameters D—the mean diameter of the main circle of the lenticular precipitates, t—the mean thickness of the lenticular precipitates, l—the interparticle spacing and Vf—the volume fraction of precipitates Material state (stress assisted aging at 773 K)

D [nm]

t [nm]

l [nm]

Vf [%]

3.6 ks, 2 MPa 3.6 ks, 20 MPa 36 ks, 2 MPa 36 ks, 20 MPa

115±30 145±50 335±120 405±110

7.7±3.0 8.9±2.9 32±7 30±6

145±20 160±20 300±20 330±20

1.7±1.0 2.2±1.1 6.7±3.5 7.1±2.1

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Figure 15. TEM micrograph of the grain on the left side of the grain boundary shown in Fig. 14 (material state: stress assisted aging—773 K/20 MPa/3.6 ks). The position A from Fig. 14 is highlighted. Image contrast: g—(101¯ ). It can be clearly seen that the precipitates near the grain boundary (region A) differ in contrast from the majority of precipitates which fill the interior of the grain. Both types of precipitates have similar number densities and size distributions. However, they belong to different variant groups (see text). Most importantly, the precipitates which show the strongest contrast (precipitate plane group (1¯ 1¯ 1)) are absent near the grain boundary (region A).

Mp temperatures are expected to increase as the precipitate volume fractions increase. Also Apestimates can be made on the basis of the expected Mp-data. First the shift ⌬T(cNi) between the estimated Mp(cNi) and the temperature for the single peak of the solution annealed material (on can be calculated cooling) ‘Mp(50.7)’ (⌬T(cNi) ⫽ Mp(cNi)⫺Mp(50.7)). Then Ap(cNi) simply is obtained by adding ⌬T(cNi) to the temperature obtained for the single peak of the solution annealed material (on heating)

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Figure 16. Dependence of Ms-temperatures on the Ni-concentration of solution annealed NiTi alloys. The data were reported in the review of Tang et al. [5] and stem from five different sources [31–35]. The figure also contains two experimental data points (Ms and Mp from our solution annealed and water quenched material) obtained in the present work. A polynomial fit (dashed line) represents all Ms-data (literature data and our result). A Mp data line (solid line) was obtained by shifting the polynomial fit for the Ms-data down to the experimental Mp of the solution annealed material of the present study.

‘Ap(50.7)’: Ap(cNi) ⫽ Ap(50.7) ⫹ ⌬T(cNi). The predicted Ap(cNi) temperatures are included in Figs. 3 and 12 (small vertical bars with corresponding horizontal error bars) and in Tables 2 and 5. The results show that we expect DSC peaks to shift to higher temperatures. In cases where the transformations keep their single step character after the thermomechanical treatments, there is reasonable agreement between predicted and measured peak positions; this is the case for the back transformation of the materials which were subjected to stress assisted aging at 773 K for 3.6 and 36 ks in the presences of stresses of 2 and 20 MPa, Fig. 12. For all other cases the direction of the shift also is predicted but other factors need to be considered to fully rationalize all DSC chart features.

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Table 7 Coefficients a0 to a5 and b0 to b5 used in Eqs. (2) and (3) to obtain the fit of the Ms—data (dashed line) and the assumed Mp— dependence (solid line) in Fig. 16 Fit coefficients for Eq. (2) a0 a1 a2 a3 a4 a5

Fit coefficients for Eq. (3) 2027077615 205968221.1 8370845.646 170093.5974 1728.050544 7.022069029

4.3. DSC chart features Before we now discuss the features of the DSC charts for all solution annealed and aged material states we briefly summarize four important microstructural results described in the previous sections: (1) no Ni4Ti3 precipitates are detected after solution annealing, (2) short term stress free aging results in heterogeneous microstructures with precipitates in grain boundary areas and remaining precipitate free regions in the grain interiors, (3) stress assisted aging results in a homogeneous distribution of precipitates throughout the microstructure in terms of numbers of precipitates per volume (but there are regions near grain boundaries and in the interior of grains which differ in terms of the types of Ni4Ti3 variants present) and (4) higher stresses during stress-assisted aging result in higher growth rates of precipitates. We also keep in mind that precipitation affects the Ni-content of the supersaturated matrix that in turn affects martensite transformation temperatures. It is well known from the literature that DSC chart features can evolve during aging. Morawiecz and co-workers [36,37] and Huang and Liu [38] investigated Ni-rich NiTi materials which were predeformed (50. 6 at.-% Ni-cold rolling: [36,37], 50.85 at.-% Ni-wire drawing: [38]). These authors [36–38] subjected their materials to aging treatments at different temperatures and observed 1-23-1 [36,37] and 1-2-1 [38] step transformations in their DSC charts on cooling and 1-2-1 [36,37] and 2-1 [38] step transformations on heating. Bataillard [39] also found an evolution in DSC chart features with aging temperature; but he did not attempt to rationalize this evolution and instead focused his

b0 b1 b2 b3 b4 b5

2027077588.5 205968221.1 8370845.646 170093.5974 1728.050544 7.022069029

attention on an explanation for multiple step transformation behavior for one particular aging condition (solution annealing at 1173 K for 1.8 ks followed by aging at 793 K for 1.8 ks) [12,39]. Recently Khalil-Allafi et al. [13] (who only considered the transformation on cooling) showed that DSC chart features evolve with aging time at a constant aging temperature: for stress free aging at 673 and 723 K they observed a 2-3-2 transformation behavior. Khalil-Allafi et al. [13] pointed out that coherency stress arguments [12,35,36] are not sufficient to explain such type of DSC chart evolutions; one problem is, that the formation of Rphase represents a stress relaxation process, and secondly, the coherency stress argument of Bataillard et al. [12] only rationalizes the three step transformation behavior but not the very clear evolution of DSC charts with aging time. Khalil-Allafi et al. [13] propose a new explanation for the 2-3-2-transformation behavior that is based on two basic elements: (1) the composition inhomogeneity that evolves during aging as Ni4Ti3 precipitates grow. (2) The difference between nucleation barriers for R-phase (small) and B19’ (large). Based on these two elements Khalil-Allafi et al. [13] were able to rationalize the evolution of DSC charts; but they did not provide microstructural evidence and they did not consider the features of the back transformation on heating. We first discuss the evolution of DSC charts after stress free aging, Figs. 2 and 3. On cooling Fig. 2 documents a 1-2-3-1-transformation behavior while the back transformation in Fig. 3 shows a 1-2-2-1 characteristic. It can be clearly seen in Fig. 2 that the last peaks on cooling after 3.6 and 36 ks aging occur at the same temperature

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as the single peak of the solution annealed material. And it is clear from Fig. 3 that the first peaks on heating after 3.6 and 36 ks aging appear in the same temperature range as the corresponding single peak of the solution annealed material. Our microstructural results suggest that the last peaks on cooling after 3.6 and 36 ks of aging are due to single step transformations from B2 to B19’ in the precipitate free regions of the microstructure; their intensity decreases with aging time because the precipitate free volume gradually decreases with aging time as precipitation proceeds, Figs. 5 and 6. And the first peaks on heating (after 3.6 and 36 ks aging) correspond to the single step back transformation from B19’ to B2 in the precipitate free regions. In contrast, the first peak on cooling after 3.6 ks aging and the first two peaks on cooling after 36 ks of aging is associated with microstructural regions with precipitates. So far it was generally assumed that two distinct DSC peaks on cooling always result from the formation of R-phase (B2→R-phase, first distinct DSC peak) followed by a transformation from R-phase to B19’ (second distinct peak). Only recently it was shown that there are cases where already after the first peak on cooling (in an overall two step transformation) both R-phase and B19’ coexist [17]. Therefore we do not attribute the first peak on cooling after 3.6 ks of stress free aging to the formation of R-phase alone; instead we expect that during this first exothermal event a mixture of R-phase (major constituent) and B19’ (minor constituent) forms. After 36 ks of stress free aging the two first peaks on cooling represent the classical two step transformation in precipitate microstructures where precipitates favor the R-phase because of its smaller transformation strain as compared to B19’ (for a detailed discussion see [8]). It seems reasonable to assume that precipitate regions only give rise to one endothermic peak on heating from B19’: the back transformation from B19’ to B2 does not have an energetical advantage from passing through an intermediate R-phase stage; the transformation strains for a transformation from B19’ to R-phase and from B19’ to B2 are almost the same. Therefore we suggest that the two step back transformations on heating from B19’ after 3.6 and 36 ks of

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aging are due to a first transformation peak associated with the back transformation in the precipitate free regions and a second transformation peak in the remainder of the microstructure. Further work is required to support this interpretation. After 360 ks of aging there only appears one peak on cooling and one peak on heating, Figs. 2 and 3. After 360 ks of aging Ni4Ti3 precipitates have consumed all excess Ni in the matrix; they are very big and widely spaced and no longer affect the martensitic transformations on cooling. The shift of the peaks after 360 ks of aging when comparing to the solution-annealed material can be explained with the decrease of matrix Nickel concentration. It can be noted that the widths of the peaks after 100 h of aging are narrower than after solution annealing; we suggest that this is due to a more uniform distribution of Nickel after 360 ks of aging. Now we discuss the DSC charts that were obtained after stress assisted aging, Figs. 11 and 12. After stress assisted aging under stresses of 2, 8 and 20 MPa microstructures are homogenous in terms of precipitate density. Therefore there is no reason for two step back transformations to occur on heating from the B19’ regime, Fig. 12. We always observe one step back transformations on heating from the B2 regime; we note, however, that there is a small shoulder in the DSC chart of the material that was aged for 1 h in the presence of a stress of 20 MPa. It is interesting to see that this material state produces the only three-step transformation that is observed on cooling from the B2regime, Fig. 11. As can also be seen in Fig. 11, this three step type of transformation after 3.6 ks aging is favored by high aging stresses: it can hardly be seen for an aging stress of 2 MPa; it is clearly more pronounced when aging in the presence of a stress of 8 MPa and it is fully developed for the material which was subjected to 3.6 ks aging at 773 K under 20 MPa. We attribute these small effects to the microstructural features reported in Fig. 15, where microstructures near grain boundaries and in the grain interior differ with respect to Ni4Ti3 variants. We expect that micro structural regions with all types of possible Ni4Ti3 variants are more effective in assisting martensite nucleation and the subsequent formation of

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self accommodating martensitic microstructures than regions where only some of the eight possible Ni4Ti3 variants are present; therefore we expect that the second peak on cooling corresponds to the formation of B19’ in regions where all precipitate variants are present (like the grain interiors in Fig. 15) while the third peak on cooling corresponds to regions like the area A in Fig. 15; further work is required to clarify this point. All other DSC charts after stress assisted aging show a two-step transformation behavior on cooling from the B2 regime that can be rationalized in terms of precipitates favoring the occurrence of R-phase [8]. Another significant difference between DSC charts obtained for materials subjected to stress free (Fig. 2) and stress assisted aging (Fig. 11) is that the transformations on cooling start at significantly higher temperatures as highlighted by the small arrows pointing to the start of transformation on cooling after 36 ks of aging. Since the volume fractions of precipitates were shown to be more or less the same, this effect cannot be attributed to the average Ni concentration. We suggest that it is the small interparticle spacing (characterizing the microstuctures after stress assisted aging) which allows the coherency stress fields of the small precipitates to favor the occurrence of R-phase; this is the reason for significantly higher Rs-temperatures after stress assisted aging (Fig. 11) as compared to stress free aging (Fig. 2). The competitive growth of the higher number of precipitates after stress assisted aging keeps the precipitate size smaller than after stress free aging. Therefore after 360 ks of stress-assisted aging interparticle spacings are still not large enough to allow for an unconstrained martensitic transformation of the matrix. And if Rs were only governed by the local thermodynamic equilibrium between precipitate and matrix (as was implicitly assumed in the model of Khalil-Allafi et al. [13]) then one would expect the Rs-temperatures after stress free and stress assisted to be the same; this is not the case when we compare Figs. 2 and 11 and therefore precipitate sizes and spacings also have to be considered. Further work is required to clarify this point. Finally it is clear from what has been outlined so far that the three step transformation after 36 ks of stress free aging (Fig. 2) cannot be rationalized

on the basis of coherency stress arguments [12,36,37]; neither can it be explained on the basis of a varying Ni-concentration between growing precipitates [13]. It is the heterogeneous precipitate microstructure (regions with and without precipitates) that is responsible for this behavior.

5. Summary and conclusions The present paper studies precipitation processes in a polycrystalline Ni-rich NiTi shape memory alloy (nominal composition 50.7 at.-% Ni). Transmission electron microscopy (TEM) was used to study the effects of different aging treatments (stress free and stress assisted) on microstructures (B2-matrix and Ni4Ti3-precipitates). The behavior of different precipitate/matrix-systems during martensitic transformations was characterized using differential scanning calorimetry (DSC). The following results were obtained: 1. Precipitation processes in solution annealed NiTi alloys with 50.7 at.-% Ni during aging at 773 K are strongly affected by the presence of external and internal stresses in the nucleation stage. Stresses of the order of 2 MPa are sufficient to completely change the precipitation behavior in solution annealed Ni-rich NiTi alloys during aging from heterogeneous to homogeneous. 2. The present study shows how microstructures evolve during stress free and stress assisted aging in terms of precipitate size, volume fraction, interparticle spacing and distribution of precipitates in the microstructure. These parameters were found to evolve during aging treatments. Accordingly, the related characteristics of DSC charts during subsequent martensitic transformations depend on aging time. 3. Short term and intermediate term stress free aging results in heterogeneous microstructures where precipitates are mainly found within 2 µm wide regions around grain boundaries while grain interiors exhibit precipitate-free zones. These microstructures show three step transformations on cooling (interpretation: 1. distinct peak—formation of R-phase in the regions con-

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4.

5.

6.

7.

8.

taining precipitates, 2. distinct peak—formation of B19’ in the regions containing precipitates, 3. distinct peak—transformation of B2 to B19’ in precipitate free regions). The three step transformations observed in the present work cannot be rationalized on the basis of coherency stress fields [12] and they cannot be explained by varying Ni-concentrations between precipitates during aging [13,16]. It is the heterogeneous microstructure (with regions with and without precipitates) that is responsible for this behavior. On heating, microstructures which form during short term stress free aging result in two step transformations (interpretation: 1. distinct peak—back transformation of precipitate free regions into B2, 2. distinct peak—back transformation of the regions containing precipitates into B2). As precipitates grow to large sizes during long term stress free aging (773 K, 360 ks) the interparticle spacings become so large that the martensitic transformation of the matrix is no longer affected by the presence of precipitates. Large precipitates may moreover well loose coherency and therefore loose their potential to affect the nucleation of martensitic phases. It was found that increasing the aging time from 3.6 to 36 ks has a much larger effect on precipitate sizes than increasing the level of applied stress from 2 to 20 MPa. The level of superimposed stresses does not affect nucleation rate (which is high for all stress levels) but there is a small increase of coarsening rates with increasing superimposed stress. After 20 MPa stress assisted aging for 3.6 ks, microstructures are homogenous in terms of number density and volume fraction of precipitates. However, Ni4Ti3 variants differ between regions in the grain interior (all variants) and near grain boundaries (only some variants). This type of precipitate variant heterogeneity can also give rise to a three-step transformation on cooling from the B2-regime. From precipitate volume fractions measured using TEM, the Ni-depletion of the supersaturated B2 matrix can be calculated. It is then possible to rationalize the increase of phase

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transition temperatures observed in the present study on the basis of data reported on the influence of Ni on Ms-temperature in the literature.

Acknowledgements The authors would like to acknowledge funding by the Deutsche Forschungsgemeinschaft (DFG) in the framework of the shape memory center SFB 459 (’Formgeda¨ chtnistechnik’). AD acknowledges traveling support from the Grant Agency of the Czech Republic (contract no.: 106/99/1172).

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