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Relaxation and recovery of extrinsic stress in sputtered titanium–nickel thin films on (100)-Si
Materials Science and Engineering A273 – 275 (1999) 722 – 726 www.elsevier.com/locate/msea
Relaxation and recovery of extrinsic stress in sputtered titanium–nickel thin films on (100)-Si David S. Grummon *, Jinping Zhang, Thomas J. Pence Department of Materials Science and Mechanics, Michigan State Uni6ersity, East Lansing, MI 48824, USA
Abstract The relaxation and recovery of stresses by displacive phase transformations in near-equiatomic titanium-nickel thin films sputtered onto (100)-silicon have been studied using the wafer curvature method, X-ray diffraction and in-situ resistivity measurements in hard vacuum. Large extrinsic tensile stresses were relaxed and recovered by displacive transformations during cyclic thermal excursions between Mf and Af. More than 0.6 GPa could be relaxed by the R-phase transformation alone. Two-step B2 R B19% transformations were often observed on cooling, but for Ti-rich compositions, recovery of extrinsic tensile stresses proceeded via a one-step B19% B2 transformation, at stress-rates (ds/dT) as high as 60 MPa K − 1. Stress-rates, and details of hysteretic behavior, are discussed in terms the distribution of stress in multiphase intermediate (mid-transformation) microstructures formed by alternative development modes. An approach is suggested for the control of hysteresis through the use of functional composition gradients. © 1999 Published by Elsevier Science S.A. All rights reserved. Keywords: Shape memory; TiNi; Thin films; Stress; Microelectromechanical devices; Nitinol
1. Introduction In order to obtain a useful force-displacement product from any shape-memory alloy it is necessary to induce plastic deformation of the martensite. This is not difficult in macroscopic applications, but in the spatially and dimensionally constrained setting of thin-film micromachines, effecting the attachment of biasing elements and accomplishing discrete displacements of significant magnitude is more awkward. It has recently been shown, however, that a small-strain biasing arrangement can conveniently be derived from differential expansion of TiNi thin films sputtered on silicon [1–3], and one study has demonstrated a practical microactuator based on the relaxation and recovery of large extrinsic stresses via reversible martensite – austenite transformations in Ti(Ni+Cu) [2]. Here, differential thermal expansion is used to generate a stress that can deform the martensite phase, but the approach differs from the conventional bimetallic strip method in that cyclic shape-strains arise from displacive phase trans* Corresponding author. Tel.: +1-517-3534688; fax: + 1-5173539842. E-mail address: [email protected] (D.S. Grummon)
formations occurring over a relatively narrow temperature range. When titaniumnickel alloys are sputtered onto rigid substrates, stress may arise from several sources. Intrinsic stresses acquired during film growth can be large, depending mainly on film thickness, plasma energy, and the temperature and working gas pressure prevailing during deposition. Densification of the film during crystallization generally produces a small positive-going stress spike, at 650–750 K, but both intrinsic and extrinsic stresses relax rapidly at temperatures above 873 K. ‘Extrinsic’ stresses (connected with simple differential thermal expansion1) naturally arise, whose relaxation may occur by diffusion-controlled viscous flow and dislocation motion at high temperatures, or at low temperature by shear-variant boundary motion and stress-induction of low-symmetry phases. Stress which is relaxed by the latter mechanism can redevelop during 1
Extrinsic stress in a thin film on a rigid (thick) substrate evolves with temperature in the biaxial case as ds/dT= [Ef/(1 − n)](as − af)]. Taking aNiTi =15.4 ×10 − 6 [4], aSi =3 × 10 − 6 [8], ENiTi = 83 GPa [9] and n =0.33 [10], gives a stress versus temperature slope of − 1.5 MPa K − 1. Thus, a TiNi film which is relaxed to a stress-free state by annealing at 1000 K can develop more than 1 GPa tensile stress on cooling to room temperature.
0921-5093/99/$ - see front matter © 1999 Published by Elsevier Science S.A. All rights reserved. PII: S 0 9 2 1 - 5 0 9 3 ( 9 9 ) 0 0 4 0 4 - 9
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heating through the action of the shape-memory effect. This cyclic stress relaxation and recovery, and the associated hysteresis, have important consequences for exploitation of shape-memory thin films in microelectromechanical devices (MEMS), and are the subject of the present paper.
2. Experimental methods Films of near-equiatomic TiNi with both Ti-rich and Ni-rich compositions were fabricated by sputtering from a 5-cm planar dc magnetron using power levels between 50 and 200 W, at Ar working-gas pressures between 465 and 931 mPa. Substrates, which included 50 mm diameter, 0.3 mm thick single-side polished (100) single-crystal Si wafers for stress-evolution measurements, and 1× 25 ×76 mm glass microscope slides for the production of free-standing films for resistivity measurements to verify zero-stress Ms and As temperatures, were mounted vertically at a working distance of 65 mm. The film thickness was measured with a Dektak IIA profilometer scanning over steps created by masking. Stresses were measured during isochronal cooling and heating by the wafer-curvature method in a custom built turbopumped UHV system [4] having a quartz bell-jar and an external resistance furnace capable of producing wafer temperatures in excess of 923 K. Realtime measurement of wafer curvature radius allowed determination of the film stress using the biaxial form of the well-known Stoney formulation [5 – 7]. Calibration was checked against profilometer measurements, and small corrections were made for initial wafer curva-
Fig. 1. Stress vs. temperature data for a nickel-rich crystalline TiNi film on (100)-Si which has been annealed to achieve a nominally stress-free state at 820 K, then cooled such that the extrinsic film stress rose to 600 MPa at 360 K. On continued cooling this tensile stress relaxed rapidly, but was subsequently recovered upon reheating. Cu – Ka X-ray diffraction data taken from the film at 298 K (as cooled from elevated temperature), are shown in the inset.
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ture and the effect of film thickness-falloff toward the edges of the wafer. Heating was performed at low rates, ranging from 0.016 to 0.05 K s − 1, and cooling at B 0.08 K s − 1, to insure continuous thermal equilibrium and accurate temperature readings. Transformation temperatures were obtained from free-standing films by 4-probe electrical resistivity measurements using heating and cooling rates of less than 0.017 K s − 1. Phase identification was conducted by X-ray diffraction using Cu–Ka radiation on a Scintag-2000 diffractometer.
3. Results Fig. 1 shows stress versus temperature data for a nickel-rich crystalline TiNi film on (100)-Si which has been annealed to achieve a nominally stress-free state at 820 K. On cooling from this temperature, the extrinsic thin film stress rose to 660 MPa at 360 K due to the more rapid thermal contraction of TiNi. On continued cooling however, this tensile stress relaxed rapidly to less than 30 MPa at 260 K. When the film was subsequently heated from this minimum temperature, the low stress level remained roughly constant until the temperature reached 330 K, after which the stress rapidly redeveloped, at a rate as high as 37 MPa K − 1, until the stress-temperature curve merged with the previously recorded cooling curve at temperatures above about 365 K. Noting the zero-stress Ms temperature for this film (marked on the plot), and considering the ability of stress to raise the effective martensite transformation temperature in TiNi by 5–7 MPa K − 1, the onset temperature for stress relaxation on cooling is seen to be consistent with stress-assisted martensite formation2. A Cu–Ka X-ray diffraction spectrum taken from the film at 298 K (as cooled from elevated temperature), given in the inset in Fig. 1, shows that a multi-phase B2/B19%, or possibly a B2/R/B19% structure3, existed at 300 K, meaning that the martensite transformation had not gone to completion at this temperature. The complex slope of the cooling curve further suggests that
2 The Clausius – Clapeyron relation gives the stress-dependence of the transformation temperature as ds/dT= − DH/TDo, where s, T, DH and Do are stress, temperature, transformation enthalpy, and the transformation strain in the direction of applied stress, respectively. Since the martensitic transformation is exothermic (DH is negative) and Do is positive if s is positive, transformation temperature is expected to increase under stress. For most TiNi alloys, Ms for the B19% phase increases with stress at 5 – 7 MPa K − 1. 3 With this data it was not possible to unambiguously differentiate between the diffraction spectra of the B2 and R-phases in the presence of multiple B19% peaks. Though spectra recorded at room temperature were similar whether the specimen had just been cooled from elevated temperature or heated from low temperature, the data may reflect multiphase B2/R/B19% structures in either case.
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rate of 60 MPa K − 1 is observed. In a similar experiment performed on a Ni-rich film, however, both resistivity and stress response to temperature cycling are consistent with a two-step transformation during both heating and cooling, as is apparent in Fig. 3. In this case, the peak stress-rates on both cooling and heating (7 and 32 MPa K − 1, respectively) are somewhat lower than for the previous example.
4. Discussion Fig. 2. Stress vs. temperature data for a titanium-rich crystalline TiNi film on (100)-Si cycled in a similar way to that for the specimen in Fig. 1. The inset shows the electrical resistivity of the film measured in-situ during heating and cooling.
Fig. 3. Stress vs. temperature data for a nickel-rich crystalline TiNi film on (100)-Si with an inset showing the electrical resistivity of the film.
multiple displacive transformations participated in the stress annihilation process, as discussed further below. On subsequent heating, the hysteretic reverse-transformation to the austenite begins at a temperature consistent with the nominal stress-free As temperature, and leads to a complete recovery of the previously relaxed tensile stress. However, the steep slope of the stress-recovery curve does not show an obvious connection to the Clausius – Clapeyron relationship, as will be discussed further below. Confirmation of the existence of a two-stage transformation on cooling was obtained by an experiment on a similar film in which simultaneous in-situ measurement of electrical resistivity was made during curvature measurement. The results, for a titanium-rich film, are shown in Fig. 2. On cooling, the onset of stress relaxation at 360 K is accompanied by an increase in resistivity identical to that commonly observed for Rphase transitions in TiNi, and the small hump in the stress-temperature curve that begins at 325 K is aligned with a drop in resistivity indicating the beginning of the B19% transformation. The resistivity behavior on heating is consistent with a direct reversion from the B19% phase to the B2 austenite, and a peak stress-
Although the general features of relaxation and recovery of extrinsic tensile stresses are not surprising in view of the nature of the shape-memory effect (which might be called ‘stress-memory’ in this context), the very high stress rate (ds/dT) shown in Fig. 2 for the martensite-to-austenite reaction on heating is worth comment. It might be anticipated that the rising tensile stress on heating would continually raise the austenitestart temperature of any remaining untransformed B19% phase. The lower bound for the overall stress rate would then be 5–7 MPa K − 1 as implied by the Clausius–Clapeyron relationship. However, this assumes a negligible through-thickness stress gradient such as would prevail only if a macroscopically homogenous microstructure existed at all times during the transformation. This would occur if the daughter phase (M on cooling, A on heating) developed as a distribution of initially isolated, roughly equiaxed islands embedded in a matrix of the parent phase. However, if the daughter phase were to form by the advance of planar transformation fronts limited by motion in a direction perpendicular to the plane of the film, the situation would then be different. In this case, at any given time during the transformation, the daughter phase would exist as a continuous sheet of material parallel to the biaxial stress axes. Any tendency toward such lamellar differentiation of the microstructure would lead to a macroscopic partitioning of the detailed stress distribution according to the relative stiffnesses of the phases. The local stress acting to either trigger the A–M transformation on cooling, or to inhibit the M–A transformation on heating, would be expected to depart from the average stress value as measured by the wafer-curvature method. Furthermore, for such lamellar stress-partitioning, the relative stiffnesses (low in M, high in A) are such as to suggest that the stress in the parent phase (A on cooling, or M on heating) would remain relatively constant during transformation The measured average stress change would result from the appearance of the new daughter phase, exerting new force levels, as the stress in the parent phase (high stress for the A-parent, low for the M-parent) stayed relatively constant. The observed average stress, being different from the local stress experienced by the parent phase prior to its
D.S. Grummon et al. / Materials Science and Engineering A273–275 (1999) 722–726
transformation, would exert little influence, in the thermodynamic sense, on the effective transformation temperature. Such lamellar microstructures might arise naturally from stress gradients present in the film due to the variation of shear stress from a zero value at the traction free outer surface, to a relatively high value at the interface. If, for example, heating a stress-relaxed (but detwinned) martensite causes the austenite to form in a nominally continuous layer beginning at the free surface (where shear stress and thus the As temperature might be lower), stress-partitioning between the austenite and martensite would be expected to occur because the microstructure develops as an effectively parallelconnected constant-strain ‘composite’ system. The observed rise in the average tensile stress during the M–A transformation would not then be fully felt by the relatively compliant parallel layer of martensite, and the As temperature there would remain fixed at near the nominal low-stress value. Continued transformation would then be expected to proceed rapidly on rising temperature. In the case of high stress rates observed in some cooling transformations, a similar continuous and lamellar orientation of the newly formed martensite (as the daughter phase) would produce a drop in stress only within this new layer. The remaining parent austenite, still experiencing elevated tensile stress, would continue to display elevated transformation temperature and thus proceed to rapidly transform on falling temperature. For the M– A transformation on heating, the argument essentially predicts that since the stress in the parent phase does not change significantly during transformation, the stress rate would not be the expected Clausius – Clapeyron slope, but rather: ds/dT : Ds/(Af −As)
(1)
where, Ds is the peak stress level, and (Af −As) is the characteristic stress-free austenite transformation range.
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In the present study, this apparent range varied between approximately 25 and 37 K (with an average of approximately 30 K), which is typical of TiNi alloys [11], suggesting that the last austenite to form did so at relatively low local stress. The hypothesis is illustrated schematically in Fig. 4 for the simplified case of uniaxial stress in a two-dimensional coordinate system having the y-axis perpendicular to the plane of the film. Here, the nature of the microstructural development is presumed to fall somewhere between two limiting cases which can be characterized by the direction of the limiting phase-front velocity vector 6. In the more-or-less conventional case with 6 =(9 6, ) the phase front moves in the plane of the film such that the phases are series-coupled with respect to the stress-axis. This results in a nominally constant stress condition throughout the microstructure, and a broadened hysteresis results from the changing stress in the parent phase. However, if 6= ( 96), then the result is a planar evolution of microstructure in which the parent and daughter phases coexist as parallel sheets which must experience a common strain. This would be expected to give rise to a significantly narrowed hysteresis since the stress in the parent phase would not be expected to change appreciably during the transformation. At present, the mechanism remains somewhat speculative, and additional experimental and analytical work is in progress to clarify the issue. It is of particular interest to learn whether conditions promoting narrow overall hysteresis and very high stress rates can be stabilized against prolonged thermomechanical cycling, perhaps by provision of functional through-thickness composition gradients in the film. This approach would involve the preparation of a film having thin, specially designed top and bottom layers (arrayed on opposite sides of a much thicker ‘working’ layer) that are intended to stabilize planar zones of the martensite and
Fig. 4. Schematic alternative modes of microstructural development for transformations occurring in a dynamic uniaxial state.
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Fig. 5. Approach to the promotion of narrow overall hysteresis and high stress rates by provision of functional through-thickness composition gradients in the film. Preparation of the film involves deposition of thin top and bottom layers (arrayed on opposite sides of a thicker ‘working’ layer) that are intended to stabilize planar zones of the martensite and austenite phases, respectively.
austenite phases respectively, as indicated schematically in Fig. 5. For example, by depositing a Ti – 52at.%Ni film (with Af B 250 K) as an austenite stabilizer on one side of the actuator film, and Ti – 21at.%Hf – 49at.%Ni (with As \500 K) as a martensite stabilizer on the other side, the approach would seek to cause the parent-todaughter phase-front to shuttle back and forth (with 6 = [ , 9 6]) between the respective M and A stabilization layers during thermal cycling. Finally, it is pointed out that a rigid substrate is not strictly required to support the effects discussed above, as long as some form of through-thickness gradient is able to induce a planar transformation front that moves perpendicular the plane of the thin film element. It may thus be possible to engineer similarly steep stress-rates and narrow hysteresis for MEMS systems using freestanding thin-film ligaments operating in uniaxial tension.
Acknowledgements This work was conducted with the support of the National Science Foundation under grant c MSS 9302270, and by the Michigan State University Com-
.
posite Materials and Structures Center. The authors are additionally grateful to Z. Zhao for assistance in design and construction of the wafer-curvature apparatus.
References [1] J. Zhang, H. Li, D.S. Grummon, Proc. Mater. Res. Soc. 459 (1997) 451. [2] P. Krulevitch, A. Lee, P. Ramsey, J. Trevino, J. Hamilton, M. Northrup, J. Microelectromech. Sys. 5 (1996) 270. [3] Q. Su, T. Kim, Y. Zheng, M. Wuttig, Proc. SPI 2441 (1995) 179. [4] D.S. Grummon, L. Hou, Z. Zhao and T.J. Pence, Proc. International Conference on Martensitic Transformations, J. Phys. France IV 5 (1995) C8 – 665. [5] R.W. Hoffman, in: J.C. Anderson (Ed.), The Use of Thin Films in Physical Investigations, Academic Press, New York, 1966, p. 261. [6] M. Ohring, Mater. Sci. Thin Films (1992) 403. [7] F.J. von Pressig, J. Appl. Phy. 66 (1989) 4262. [8] A. Goldsmith, T. Waterman, H. Hirschorn, Handbook of Thermophysical Properties of Solid Materials, Amor Research Foundation, Pergamon, New York, 1961. [9] W.J. Beuhler, F.E. Wang, Ocean Eng. 1 (1968) 105. [10] W. Cross, A. Kariotis, F. Stimler, Nitinol Characterization Study, NASA CR-1433, 1969. [11] H. Funakubo, Shape Memory Alloys, vol. 1, Gordon and Breach, New York, 1987.
Relaxation and recovery of extrinsic stress in sputtered titanium–nickel thin films on (100)-Si David S. Grummon *, Jinping Zhang, Thomas J. Pence Department of Materials Science and Mechanics, Michigan State Uni6ersity, East Lansing, MI 48824, USA
Abstract The relaxation and recovery of stresses by displacive phase transformations in near-equiatomic titanium-nickel thin films sputtered onto (100)-silicon have been studied using the wafer curvature method, X-ray diffraction and in-situ resistivity measurements in hard vacuum. Large extrinsic tensile stresses were relaxed and recovered by displacive transformations during cyclic thermal excursions between Mf and Af. More than 0.6 GPa could be relaxed by the R-phase transformation alone. Two-step B2 R B19% transformations were often observed on cooling, but for Ti-rich compositions, recovery of extrinsic tensile stresses proceeded via a one-step B19% B2 transformation, at stress-rates (ds/dT) as high as 60 MPa K − 1. Stress-rates, and details of hysteretic behavior, are discussed in terms the distribution of stress in multiphase intermediate (mid-transformation) microstructures formed by alternative development modes. An approach is suggested for the control of hysteresis through the use of functional composition gradients. © 1999 Published by Elsevier Science S.A. All rights reserved. Keywords: Shape memory; TiNi; Thin films; Stress; Microelectromechanical devices; Nitinol
1. Introduction In order to obtain a useful force-displacement product from any shape-memory alloy it is necessary to induce plastic deformation of the martensite. This is not difficult in macroscopic applications, but in the spatially and dimensionally constrained setting of thin-film micromachines, effecting the attachment of biasing elements and accomplishing discrete displacements of significant magnitude is more awkward. It has recently been shown, however, that a small-strain biasing arrangement can conveniently be derived from differential expansion of TiNi thin films sputtered on silicon [1–3], and one study has demonstrated a practical microactuator based on the relaxation and recovery of large extrinsic stresses via reversible martensite – austenite transformations in Ti(Ni+Cu) [2]. Here, differential thermal expansion is used to generate a stress that can deform the martensite phase, but the approach differs from the conventional bimetallic strip method in that cyclic shape-strains arise from displacive phase trans* Corresponding author. Tel.: +1-517-3534688; fax: + 1-5173539842. E-mail address: [email protected] (D.S. Grummon)
formations occurring over a relatively narrow temperature range. When titaniumnickel alloys are sputtered onto rigid substrates, stress may arise from several sources. Intrinsic stresses acquired during film growth can be large, depending mainly on film thickness, plasma energy, and the temperature and working gas pressure prevailing during deposition. Densification of the film during crystallization generally produces a small positive-going stress spike, at 650–750 K, but both intrinsic and extrinsic stresses relax rapidly at temperatures above 873 K. ‘Extrinsic’ stresses (connected with simple differential thermal expansion1) naturally arise, whose relaxation may occur by diffusion-controlled viscous flow and dislocation motion at high temperatures, or at low temperature by shear-variant boundary motion and stress-induction of low-symmetry phases. Stress which is relaxed by the latter mechanism can redevelop during 1
Extrinsic stress in a thin film on a rigid (thick) substrate evolves with temperature in the biaxial case as ds/dT= [Ef/(1 − n)](as − af)]. Taking aNiTi =15.4 ×10 − 6 [4], aSi =3 × 10 − 6 [8], ENiTi = 83 GPa [9] and n =0.33 [10], gives a stress versus temperature slope of − 1.5 MPa K − 1. Thus, a TiNi film which is relaxed to a stress-free state by annealing at 1000 K can develop more than 1 GPa tensile stress on cooling to room temperature.
0921-5093/99/$ - see front matter © 1999 Published by Elsevier Science S.A. All rights reserved. PII: S 0 9 2 1 - 5 0 9 3 ( 9 9 ) 0 0 4 0 4 - 9
D.S. Grummon et al. / Materials Science and Engineering A273–275 (1999) 722–726
heating through the action of the shape-memory effect. This cyclic stress relaxation and recovery, and the associated hysteresis, have important consequences for exploitation of shape-memory thin films in microelectromechanical devices (MEMS), and are the subject of the present paper.
2. Experimental methods Films of near-equiatomic TiNi with both Ti-rich and Ni-rich compositions were fabricated by sputtering from a 5-cm planar dc magnetron using power levels between 50 and 200 W, at Ar working-gas pressures between 465 and 931 mPa. Substrates, which included 50 mm diameter, 0.3 mm thick single-side polished (100) single-crystal Si wafers for stress-evolution measurements, and 1× 25 ×76 mm glass microscope slides for the production of free-standing films for resistivity measurements to verify zero-stress Ms and As temperatures, were mounted vertically at a working distance of 65 mm. The film thickness was measured with a Dektak IIA profilometer scanning over steps created by masking. Stresses were measured during isochronal cooling and heating by the wafer-curvature method in a custom built turbopumped UHV system [4] having a quartz bell-jar and an external resistance furnace capable of producing wafer temperatures in excess of 923 K. Realtime measurement of wafer curvature radius allowed determination of the film stress using the biaxial form of the well-known Stoney formulation [5 – 7]. Calibration was checked against profilometer measurements, and small corrections were made for initial wafer curva-
Fig. 1. Stress vs. temperature data for a nickel-rich crystalline TiNi film on (100)-Si which has been annealed to achieve a nominally stress-free state at 820 K, then cooled such that the extrinsic film stress rose to 600 MPa at 360 K. On continued cooling this tensile stress relaxed rapidly, but was subsequently recovered upon reheating. Cu – Ka X-ray diffraction data taken from the film at 298 K (as cooled from elevated temperature), are shown in the inset.
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ture and the effect of film thickness-falloff toward the edges of the wafer. Heating was performed at low rates, ranging from 0.016 to 0.05 K s − 1, and cooling at B 0.08 K s − 1, to insure continuous thermal equilibrium and accurate temperature readings. Transformation temperatures were obtained from free-standing films by 4-probe electrical resistivity measurements using heating and cooling rates of less than 0.017 K s − 1. Phase identification was conducted by X-ray diffraction using Cu–Ka radiation on a Scintag-2000 diffractometer.
3. Results Fig. 1 shows stress versus temperature data for a nickel-rich crystalline TiNi film on (100)-Si which has been annealed to achieve a nominally stress-free state at 820 K. On cooling from this temperature, the extrinsic thin film stress rose to 660 MPa at 360 K due to the more rapid thermal contraction of TiNi. On continued cooling however, this tensile stress relaxed rapidly to less than 30 MPa at 260 K. When the film was subsequently heated from this minimum temperature, the low stress level remained roughly constant until the temperature reached 330 K, after which the stress rapidly redeveloped, at a rate as high as 37 MPa K − 1, until the stress-temperature curve merged with the previously recorded cooling curve at temperatures above about 365 K. Noting the zero-stress Ms temperature for this film (marked on the plot), and considering the ability of stress to raise the effective martensite transformation temperature in TiNi by 5–7 MPa K − 1, the onset temperature for stress relaxation on cooling is seen to be consistent with stress-assisted martensite formation2. A Cu–Ka X-ray diffraction spectrum taken from the film at 298 K (as cooled from elevated temperature), given in the inset in Fig. 1, shows that a multi-phase B2/B19%, or possibly a B2/R/B19% structure3, existed at 300 K, meaning that the martensite transformation had not gone to completion at this temperature. The complex slope of the cooling curve further suggests that
2 The Clausius – Clapeyron relation gives the stress-dependence of the transformation temperature as ds/dT= − DH/TDo, where s, T, DH and Do are stress, temperature, transformation enthalpy, and the transformation strain in the direction of applied stress, respectively. Since the martensitic transformation is exothermic (DH is negative) and Do is positive if s is positive, transformation temperature is expected to increase under stress. For most TiNi alloys, Ms for the B19% phase increases with stress at 5 – 7 MPa K − 1. 3 With this data it was not possible to unambiguously differentiate between the diffraction spectra of the B2 and R-phases in the presence of multiple B19% peaks. Though spectra recorded at room temperature were similar whether the specimen had just been cooled from elevated temperature or heated from low temperature, the data may reflect multiphase B2/R/B19% structures in either case.
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rate of 60 MPa K − 1 is observed. In a similar experiment performed on a Ni-rich film, however, both resistivity and stress response to temperature cycling are consistent with a two-step transformation during both heating and cooling, as is apparent in Fig. 3. In this case, the peak stress-rates on both cooling and heating (7 and 32 MPa K − 1, respectively) are somewhat lower than for the previous example.
4. Discussion Fig. 2. Stress vs. temperature data for a titanium-rich crystalline TiNi film on (100)-Si cycled in a similar way to that for the specimen in Fig. 1. The inset shows the electrical resistivity of the film measured in-situ during heating and cooling.
Fig. 3. Stress vs. temperature data for a nickel-rich crystalline TiNi film on (100)-Si with an inset showing the electrical resistivity of the film.
multiple displacive transformations participated in the stress annihilation process, as discussed further below. On subsequent heating, the hysteretic reverse-transformation to the austenite begins at a temperature consistent with the nominal stress-free As temperature, and leads to a complete recovery of the previously relaxed tensile stress. However, the steep slope of the stress-recovery curve does not show an obvious connection to the Clausius – Clapeyron relationship, as will be discussed further below. Confirmation of the existence of a two-stage transformation on cooling was obtained by an experiment on a similar film in which simultaneous in-situ measurement of electrical resistivity was made during curvature measurement. The results, for a titanium-rich film, are shown in Fig. 2. On cooling, the onset of stress relaxation at 360 K is accompanied by an increase in resistivity identical to that commonly observed for Rphase transitions in TiNi, and the small hump in the stress-temperature curve that begins at 325 K is aligned with a drop in resistivity indicating the beginning of the B19% transformation. The resistivity behavior on heating is consistent with a direct reversion from the B19% phase to the B2 austenite, and a peak stress-
Although the general features of relaxation and recovery of extrinsic tensile stresses are not surprising in view of the nature of the shape-memory effect (which might be called ‘stress-memory’ in this context), the very high stress rate (ds/dT) shown in Fig. 2 for the martensite-to-austenite reaction on heating is worth comment. It might be anticipated that the rising tensile stress on heating would continually raise the austenitestart temperature of any remaining untransformed B19% phase. The lower bound for the overall stress rate would then be 5–7 MPa K − 1 as implied by the Clausius–Clapeyron relationship. However, this assumes a negligible through-thickness stress gradient such as would prevail only if a macroscopically homogenous microstructure existed at all times during the transformation. This would occur if the daughter phase (M on cooling, A on heating) developed as a distribution of initially isolated, roughly equiaxed islands embedded in a matrix of the parent phase. However, if the daughter phase were to form by the advance of planar transformation fronts limited by motion in a direction perpendicular to the plane of the film, the situation would then be different. In this case, at any given time during the transformation, the daughter phase would exist as a continuous sheet of material parallel to the biaxial stress axes. Any tendency toward such lamellar differentiation of the microstructure would lead to a macroscopic partitioning of the detailed stress distribution according to the relative stiffnesses of the phases. The local stress acting to either trigger the A–M transformation on cooling, or to inhibit the M–A transformation on heating, would be expected to depart from the average stress value as measured by the wafer-curvature method. Furthermore, for such lamellar stress-partitioning, the relative stiffnesses (low in M, high in A) are such as to suggest that the stress in the parent phase (A on cooling, or M on heating) would remain relatively constant during transformation The measured average stress change would result from the appearance of the new daughter phase, exerting new force levels, as the stress in the parent phase (high stress for the A-parent, low for the M-parent) stayed relatively constant. The observed average stress, being different from the local stress experienced by the parent phase prior to its
D.S. Grummon et al. / Materials Science and Engineering A273–275 (1999) 722–726
transformation, would exert little influence, in the thermodynamic sense, on the effective transformation temperature. Such lamellar microstructures might arise naturally from stress gradients present in the film due to the variation of shear stress from a zero value at the traction free outer surface, to a relatively high value at the interface. If, for example, heating a stress-relaxed (but detwinned) martensite causes the austenite to form in a nominally continuous layer beginning at the free surface (where shear stress and thus the As temperature might be lower), stress-partitioning between the austenite and martensite would be expected to occur because the microstructure develops as an effectively parallelconnected constant-strain ‘composite’ system. The observed rise in the average tensile stress during the M–A transformation would not then be fully felt by the relatively compliant parallel layer of martensite, and the As temperature there would remain fixed at near the nominal low-stress value. Continued transformation would then be expected to proceed rapidly on rising temperature. In the case of high stress rates observed in some cooling transformations, a similar continuous and lamellar orientation of the newly formed martensite (as the daughter phase) would produce a drop in stress only within this new layer. The remaining parent austenite, still experiencing elevated tensile stress, would continue to display elevated transformation temperature and thus proceed to rapidly transform on falling temperature. For the M– A transformation on heating, the argument essentially predicts that since the stress in the parent phase does not change significantly during transformation, the stress rate would not be the expected Clausius – Clapeyron slope, but rather: ds/dT : Ds/(Af −As)
(1)
where, Ds is the peak stress level, and (Af −As) is the characteristic stress-free austenite transformation range.
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In the present study, this apparent range varied between approximately 25 and 37 K (with an average of approximately 30 K), which is typical of TiNi alloys [11], suggesting that the last austenite to form did so at relatively low local stress. The hypothesis is illustrated schematically in Fig. 4 for the simplified case of uniaxial stress in a two-dimensional coordinate system having the y-axis perpendicular to the plane of the film. Here, the nature of the microstructural development is presumed to fall somewhere between two limiting cases which can be characterized by the direction of the limiting phase-front velocity vector 6. In the more-or-less conventional case with 6 =(9 6, ) the phase front moves in the plane of the film such that the phases are series-coupled with respect to the stress-axis. This results in a nominally constant stress condition throughout the microstructure, and a broadened hysteresis results from the changing stress in the parent phase. However, if 6= ( 96), then the result is a planar evolution of microstructure in which the parent and daughter phases coexist as parallel sheets which must experience a common strain. This would be expected to give rise to a significantly narrowed hysteresis since the stress in the parent phase would not be expected to change appreciably during the transformation. At present, the mechanism remains somewhat speculative, and additional experimental and analytical work is in progress to clarify the issue. It is of particular interest to learn whether conditions promoting narrow overall hysteresis and very high stress rates can be stabilized against prolonged thermomechanical cycling, perhaps by provision of functional through-thickness composition gradients in the film. This approach would involve the preparation of a film having thin, specially designed top and bottom layers (arrayed on opposite sides of a much thicker ‘working’ layer) that are intended to stabilize planar zones of the martensite and
Fig. 4. Schematic alternative modes of microstructural development for transformations occurring in a dynamic uniaxial state.
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Fig. 5. Approach to the promotion of narrow overall hysteresis and high stress rates by provision of functional through-thickness composition gradients in the film. Preparation of the film involves deposition of thin top and bottom layers (arrayed on opposite sides of a thicker ‘working’ layer) that are intended to stabilize planar zones of the martensite and austenite phases, respectively.
austenite phases respectively, as indicated schematically in Fig. 5. For example, by depositing a Ti – 52at.%Ni film (with Af B 250 K) as an austenite stabilizer on one side of the actuator film, and Ti – 21at.%Hf – 49at.%Ni (with As \500 K) as a martensite stabilizer on the other side, the approach would seek to cause the parent-todaughter phase-front to shuttle back and forth (with 6 = [ , 9 6]) between the respective M and A stabilization layers during thermal cycling. Finally, it is pointed out that a rigid substrate is not strictly required to support the effects discussed above, as long as some form of through-thickness gradient is able to induce a planar transformation front that moves perpendicular the plane of the thin film element. It may thus be possible to engineer similarly steep stress-rates and narrow hysteresis for MEMS systems using freestanding thin-film ligaments operating in uniaxial tension.
Acknowledgements This work was conducted with the support of the National Science Foundation under grant c MSS 9302270, and by the Michigan State University Com-
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posite Materials and Structures Center. The authors are additionally grateful to Z. Zhao for assistance in design and construction of the wafer-curvature apparatus.
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