Low-frequency internal friction of hydrogen-free and hydrogen-doped NiTi alloys

Acta Materialia 55 (2007) 4243–4252 www.elsevier.com/locate/actamat

Low-frequency internal friction of hydrogen-free and hydrogen-doped NiTi alloys F.M. Mazzolai b

a,*

, A. Biscarini a, B. Coluzzi a, G. Mazzolai a, E. Villa b, A. Tuissi

b

a University of Perugia, Department of Physics, Via A. Pascoli 5, 06123 Perugia, Italy Istituto per l’Energetica e le Interfasi, CNR-IENI, C.so Promessi Sposi 29, 29300 Lecco, Italy

Received 16 November 2006; received in revised form 25 February 2007; accepted 17 March 2007 Available online 29 May 2007

Abstract The internal friction (IF) and Young’s modulus of the Ni50.8Ti49.2 shape memory alloy have been measured as a function of temperature (130 K < T < 335 K) by a dynamic mechanical analyser at various strain amplitudes and frequencies. Besides the one associated with the austenite/martensite transformation, several other IF peaks have been observed both in the hydrogen-free and in the hydrogen-doped states of the material. Some of these peaks are non-thermally activated processes caused by stress-assisted hysteretic motions of twin boundaries and dislocations; some others represent thermally activated relaxations caused by reorientation of hydrogen elastic dipoles or by stress-induced motions of twin boundaries interacting with hydrogen. The present low-frequency measurements provide new information concerning the amplitude and frequency dependences of the damping processes, thus throwing new light on their structural mechanisms.  2007 Published by Elsevier Ltd on behalf of Acta Materialia Inc. Keywords: Martensitic phase transformation; Nickel alloys; Titanium alloys; Hydrides; Dynamic mechanical analysis

1. Introduction The NiTi-based alloys have attracted a lot of attention in the past few decades as they exhibit properties of technological interest [1] such as super elasticity, shape memory and, in their martensitic state, high mechanical damping (internal friction (IF)) [2–37]. The last property is primarily associated with transient phenomena, which occur at the austenite/martensite (A/M) transition temperatures and give rise to transformation damping peaks PAM (on cooling) and PMA (on heating) [2–7,22,23,37]. These peaks are high only for values _ of the ratio Tf P 0:02, where T_ is the cooling/heating rate and f is the vibration frequency. At constant temperature, the martensites of NiTi-based alloys usually exhibit rather small values (<0.02) of the energy dissipation coefficient Q1 so these alloys, actually, are not high damping materials.

*

Corresponding author. Tel.: +39 75 5852703; fax: +39 75 44666. E-mail addresses: fabio.mazzolai@fisica.unipg.it (F.M. Mazzolai).

Hydrogen impurities have been found to enhance the isothermal damping of NiTi-based alloys [12,28,29,31, 32,36] thanks to two anelastic relaxations PH and PTWH associated with stress-induced motions of H-dipoles (PH) [12,26,28,29] and of H-twin boundary complexes (PTWH) [12,16,28,29,31,36], respectively. From time to time an internal friction peak has been observed in non-intentionally H-loaded NiTi alloys at around 200 K for frequencies in the 1 Hz range [2,4– 7,19,22,23,34,35]. In the past this peak, hereafter labelled as the ‘‘200 K’’ peak, has been reported to be the result of a thermally activated process [1,5] and, recently, some of the present authors have shown that its relaxation time, within the experimental error, coincides with that of peak PH [26]. Consequently, it has been inferred that the ‘‘200 K’’ peak is, actually, an H-Snoek effect even though it had been observed in hydrogen undoped materials. As already noted in Ref. [26], this interpretation implies that some hydrogen impurities might have originally been present in the investigated materials or might have been picked

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up by them at some stage of the sample processing, usually consisting of a solution treatment at high temperature in argon atmosphere followed by water quenching. Recent results with NiTiCu [31] and NiTiFe [32] alloys confirm our original view [26] showing that: (i) some contamination with H may indeed take place during the solution treatment at high temperature and (ii) one of the H peaks really indicates a H-twin boundary interaction effect. Apart from the peaks already mentioned (PAM, PMA, PH and PTWH), two additional IF peaks have been found at kHz frequencies with various NiTi-based alloys; one (PTWM) appeared at around 125 K in aged materials [11], the other, hereafter labelled as the ‘‘150 K’’ peak, appeared at around 150 K in materials annealed at high temperature [30]. The first peak has tentatively been attributed to stressinduced de-pinning processes of twin boundaries from point defects, and the second has been attributed to vacancy complexes. However, the nature of these two effects is not yet really understood and it is even doubtful whether they are two distinct effects or not, as they have never been seen simultaneously in a single temperature scan. The main aim of the present work was to investigate the complex IF spectrum of an H-free and H-doped NiTi alloy (Ni50.8Ti49.2) at low frequencies (0.1-50 Hz). In particular, we wanted to see whether the 1 Hz ‘‘200 K’’ peak was really absent in materials subjected to treatments which are able fully to remove H impurities. A further goal was to look at the frequency and amplitude dependences of the peak heights in order to shed further light on their structural mechanisms. 2. Experimental The NiTi sample used in the present experiments was a bar of dimensions 45 · 5 · 0.94 mm3 and nominal composition 49.2 at.% Ti. The treatments given in sequence to the sample are listed in Table 1. The anneals va1, va2 and va3 were carried out at 1173 K (va1 and va2 for 2 h, va3 for 5 h) under turbo-molecular vacuum (p = 105 Pa) and were followed by rapid cooling (200 K min1) down to room temperature. Rapid cooling was achieved by removing the furnace from around the quartz tube containing the sample. The H doping treatments hd1 and hd2 took place at 1000 K under the appropriate pressure of H2 gas and were followed by rapid cooling of the sample, kept in the gas atmosphere. The H content nH (nH = H/Me) Table 1 Sequence of thermal and H-doping treatments given to the alloy sample Alloy

Sample

Treatments subsequently given to the sample

Ni50.8Ti49.2

A2

1 Vacuum anneal (va1) 2 H doping (hd1); nH = 0.013 3 Vacuum anneal (va2) 4 Solubilization treatment plus water quenching (wq) 5 H doping (hd2); nH = 0.011 6 Vacuum anneal (va3)

was deduced from pressure changes monitored within the calibrated volume of the reaction chamber by a precision Datametrics capacitance manometer. Water quenching treatment consisted of 1 h solubilization at 1173 K under dynamic vacuum (p = 105 Pa) followed by quenching of the sample in a water bath at room temperature. The IF and Young’s modulus (E) were measured as a function of temperature (T) at various frequencies f (0.1, 1, 10, 20, 50 Hz) and strain amplitudes e (105, 104, 103, 3 · 103) by a Q800 dynamic mechanical analyser (DMA) supplied by TA Co and also by high frequency (typically 1 kHz) flexural free–free resonance methods. As usual the IF is expressed by the dissipation coefficient 1 DW Q1 ¼ 2p , where DW is the mechanical energy dissipated W in one vibration cycle and W is the maximum kinetic energy. Differential scanning calorimetry (DSC) measurements have also been made by a Perkin–Elmer apparatus (Piris) at the cooling/heating rate of 20 K min1. 3. Results 3.1. Vacuum annealed (va) state 3.1.1. Dependence on frequency The IF and Young’s modulus measured at 1 Hz frequency, 2 K min1 cooling/heating rate and at 104 strain amplitude are displayed in Fig. 1a and b, where earlier [30] high-frequency, low-strain data are also reported for comparison. The DSC measurements in Fig. 1a give the values of 234 K and 228 K for the martensite start- and martensite finish-temperatures, Ms and Mf, respectively. At 1 Hz frequency, two peaks appear on cooling (Fig. 1a), the major one (PAM) is asymmetric, reaches its maximum in the proximity of Mf and extends down to the two-phase region; the smaller one occurs at around 150 K in the fully martensitic state. Peak PAM, which is at least partly associated with the direct A ! M transition, is not present in the high frequency curve of Fig. 1a, where only the ‘‘150 K’’ peak appears. The Young’s modulus, on cooling, exhibits softening above Ms and a pronounced dip just below the DSC minimum. A change in the curvature of the E(T) relationship is visible over the temperature region of the ‘‘150 K’’ peak, which would then seem to be a thermally activated relaxation process. However, this is not the case since no appreciable shift of the peak along the temperature scale takes place on changing the frequency from 1 to 2590 Hz. On heating (Fig. 1b) the 1 Hz internal friction curve, apart from the ‘‘150 K’’ and PMA peaks exhibits a bump at around 200 K. This bump and peak PMA are not displayed by curves at 1270 Hz and the 107 strain amplitude, which, on the other hand, show a ‘‘150 K’’ peak similar to the one observed at 1 Hz frequency and 104 strain. 3.1.2. Dependence on strain amplitude The effect of strain amplitude e on the temperature dependence of IF and E is shown by the heating runs of

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Fig. 1. (a) Comparison of internal friction (Q1) and Young’s modulus (E) data taken at 1 Hz frequency and 104 strain amplitude by dynamic mechanical analysis (DMA) and earlier data obtained at 2590 Hz and 107 strain amplitude by the free–free resonance methods (flexural vibration mode) for the same sample submitted to the same thermal treatments [30]. DSC data were taken at the cooling rate of 20 K min1 [30]. (b) As for (a) but for heating measurement runs.

Fig. 2. Similar trends are also displayed by data taken on cooling, which are omitted for brevity. As seen in Fig. 2, the height of PMA slightly decreases with increasing e while a remarkable increase in the damping takes place below 250 K for e > 104. The temperature of the ‘‘150 K’’ peak remains unchanged with changing e while that of the ‘‘200 K’’ bump decreases from 200 K to 180 K. Young’s modulus is insensitive to strain in the range 105 to 104 and decreases below 250 K for e > 104. A clearer picture of the effect of strain on IF and E is provided by Fig. 3, where the differences DQ1 and DE between the values of Q1 and E measured at 103 and 105 strain levels are plotted against T. Data for the cooling measurement run are also reported in this figure for completeness. The amplitude dependent part DQ1 of the damping has a maximum at around 150 K, which is associated with a remarkable modulus defect, indicated by the double arrow drawn in the Fig. 3. A smaller amplitude dependence is also exhibited by the IF and Young’s modu-

Fig. 2. Dependence on the strain amplitude e of internal friction (Q1) and Young’s modulus (E), measured on heating.

Fig. 3. Amplitude dependent part DQ1 = Q1 (e)  Q1(e0) of the internal friction and of Young’s modulus DE = E(e)  E(e0). Here e0 = 105 is the minimum used strain amplitude. DEM and DEA represent the amplitude dependent parts of the modulus defect in the martensite and austenite, respectively. Cooling/heating data for DSC were taken at 20 K min1 in the va alloy.

lus of the austenite, which is expected to be caused by dislocations. It is remarkable that the temperature dependence of DQ1 and DE in Fig. 3 gives a much clearer indication of the A/M transition than do the Q1(T) and E(T) curves of Fig. 1a and b. In particular, the transition regions, both on cooling and on heating, are clearly indicated by narrow IF dips closely correlated with the DSC anomalies. These dips confirm a decrease, in the close vicinity of the martensitic transition, of the IF with increasing the strain amplitude. In the martensitic state both DQ1 and DE exhibit thermal hysteresis even far below Mf (228 K) and on heating the DQ1(T) curve shows maxima at 150 K and 200 K indicating a strong dependence on e of the ‘‘150 K’’ and ‘‘200 K’’ peaks.

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3.1.3. Effect of H doping Fig. 4 shows the effect of H doping (treatment hd1) on the IF and Young’s modulus of the vacuum annealed sample as measured on heating. As shown, the ‘‘150 K’’ peak is cancelled by H impurities (nH = 0.013), PMA is unaffected and a tall peak is introduced at around 200 K, which, for reasons that will become clear later is here labelled as peak PH. One of the main issues to be discussed in the next section will be whether the ‘‘200 K’’ bump appearing in the va material is due to residual H or is an intrinsic feature of the martensite. Young’s modulus of the austenite (T > 250 K) is not altered by H doping, whereas that of the martensite (T < 228 K) is markedly increased. These observations basically confirm our previous data at kHz frequencies and are indicative of pinning of twin boundaries by H atoms [12,30]. 3.2. Solution treated and water quenched state 3.2.1. Dependence on frequency Fig. 5a and b illustrate the effect of frequency changes on the temperature dependence of IF and E as measured

Fig. 4. Effect of H doping on the internal friction and Young’s modulus as measured on heating after treatment hd1 in Table 1.

after solubilization (under dynamic vacuum) and water quenching. The data at 2170 Hz in Fig. 5a were taken on the same sample by the free–free resonance method. As shown in this figure, at the lowest frequencies (0.1 and 1 Hz) a remarkable broad peak PAM occurs at around 230 K; its height rapidly decreases with increasing f to disappear completely at f P 10 Hz. The background damping of the martensite (T < Mf) also diminishes with increasing f. A reverse behaviour is exhibited by Young’s modulus of the martensite, which increases with increasing f. The ‘‘150 K’’ peak is about the same as the one occurring in the va state (see Fig. 1a and b) and, similar to that case, its temperature does not appreciably depend on frequency. This finding definitely excludes the peak from representing a thermally activated relaxation, as it had already been inferred from inspection of Fig. 1a and b. On heating (Fig. 5b) PMA occurs at around 255 K and an additional broad peak, whose temperature does not depend on frequency, appears at around 200 K. We are again dealing with a non-thermally activated peak, whose height rapidly decreases with increasing f to disappear completely at f > 10 Hz. A similar behaviour is exhibited by the much narrower peak PMA. The IF decrease is accompanied by a concomitant increase in Young’s modulus of the martensite. It is likely that the damping process responsible for the ‘‘200 K’’ peak is also operative on cooling and gives rise to the apparent marked asymmetry of peak PAM in Fig. 5a. Its height, however, should be much smaller on cooling than on heating as no indication of it is apparent on the low-temperature branch of PAM in Fig. 5a. The ‘‘150 K’’ peak on heating is about the same as on cooling. The frequency dependence of IF at 200 K and 255 K for the heating run is shown in the log–log plot in Fig. 6, where row data as well as data corrected for background taken as the IF measured at 50 Hz are reported. The observed linear relationship in the plots of Fig. 6 suggests the following dependence of Q1 on f

Fig. 5. (a) Frequency dependence of the internal friction (Q1) and of Young’s modulus (E) of the water quenched alloy. The low and high frequency data were taken on cooling with the same sample at 104 and 107 strain amplitude, respectively. (b) As in (a), but on heating.

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Fig. 6. Log–log plot of IF row data (Q1) and the frequency dependent damping (DQ1) calculated at the temperatures of the ‘‘200 K’’ and PMA peaks; DQ1 = Q1(f)  Q1 (50 Hz).

Q

1

1 / n f

ð1Þ

with n equal to 0.41 at 200 K and 0.42 at the temperature of PMA (255 K). A similar plot for the cooling runs provides slightly smaller values of n (0.38 and 0.39) at 200 K and at the temperature of PAM (233 K), respectively. Thus, as far as the frequency dependence is concerned, the ‘‘200 K’’ and PMA (PAM) peaks behave similarly. From isothermal low-frequency IF data (103 Hz 6 f 6 10 Hz) reported in the literature for a Ni50.4Ti49.6 alloy (Ref. [38], Fig. 5) quite similar values of n are deduced near the start-temperature As (As = 370 K) of the reverse martensitic transition (n = 0.53 at 361 K) and further down in the fully martensitic state (n = 0.51 and 0.46 at 333 K and 304 K, respectively). These values, which are close to those determined from our own measurements, suggest that relation (1) also holds for the ‘‘stationary’’ damping, measured under isothermal conditions. 3.2.2. Effect of H doping The temperature dependence of IF and E of the water quenched and H doped sample (treatment hd2) is shown in Fig. 7, where heating data are reported. As seen, two peaks are exhibited by curves at 1, 10 and 50 Hz and a single one by that at 0.1 Hz. At the lowest frequencies a bump is also distinguishable at around 255 K, which is the counterpart of the better developed peak PMA observed in the va and wq states of the material. Following our previous notation [12] the two H peaks are named PTWH and PH. Their temperature increases with increasing vibration frequency, thus, they represent thermally activated relaxation processes. The ‘‘150 K’’ peak is suppressed by the H doping hd2, similar to the case of treatment hd1 already examined. It is worth noting in Fig. 7 that the IF of the martensite decreases and E increases with increasing f over the temperature range of the two peaks, while outside this range both IF and E are only slightly affected by frequency changes.

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Fig. 7. Effect of hydrogen doping (nH = 0.011) on the internal friction and Young’s modulus of prior water quenched material.

The log–log plot in Fig. 8, where the difference DQ1 = Q1(f)  Q1(50 Hz) is plotted for the heating data, shows that the frequency dependence expressed by relation (1) is also valid for the H doped material; the values of n at the temperatures of PH and PTWH are 0.41 and 0.38, respectively. For the cooling data, the corresponding values are 0.38 and 0.34. The above values of n are about the same as those obtained for the H-free material. Thus, it can be concluded that the frequency dependent part of the damping, DQ1, is primarily associated with structural causes other than the one responsible for PH. However, since the greatest changes in IF and E with changing f occurs in the temperature region of PH and PTWH, some influence on the strength of these peaks cannot be excluded and will be discussed in Section 4. 3.2.3. Dependence on strain amplitude The effect of the strain amplitude on the IF and E of the H doped material is shown in Fig. 9 where data taken on heating are reported as a function of temperature. For values of e higher than 104 the damping increases and

Fig. 8. Log–log plot of the frequency dependent damping (DQ1) calculated at the temperatures of peaks PH and PTWH; DQ1 = Q1(f)  Q1 (50 Hz).

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Fig. 9. Effect of strain amplitude on the temperature dependence of the internal friction and Young’s modulus of the prior water quenched and then H doped (treatment hd2 of Table 1) material.

Young’s modulus decreases with increasing e, similar to the case of the H undoped alloy. The strain increase also leads to a shift of the peaks towards lower temperatures. To a minor extent, amplitude dependence is also exhibited by the austenitic phase above 255 K. For e < 104 the IF and E do not depend on the strain amplitude. The differences DQ1 = Q1(e)  Q1(e = 105) and DE(e)  E(e = 105) between the values of Q1 and E measured at 3 · 103 and 104 and those at 105 strain amplitudes are plotted against T in Fig. 10. As seen, DQ1 reaches its maximum value just in the proximity of the PH temperature and, like DE, exhibits thermal hysteresis. Similar to the undoped state, the temperature dependences of DQ1 and DE give much clearer indications of the A/M transition than do the Q1(T) and E(T) curves of Fig. 9. On heating, a narrow dip is seen in the close vicinity of the reverse martensitic transition, again indicating a decrease

Fig. 10. Amplitude dependent parts of the internal friction DQ1 = Q1(e)  Q1(e0) and of Young’s modulus DE = E(e)  E(e0). Here e0 = 105 and e104 and 3 · 103 are the minimum and current values of the strain amplitude, respectively. DEM and DEA represent the amplitude dependent parts of the overall modulus defect of the martensite and of the austenite, respectively.

in the IF in response to an increase in the strain amplitude. On cooling, the form of the DE(T) and DQ1(T) curves is somewhat different and suggests a two-step (cubic austenite ! trigonal R-phase ! monoclinic B19’martensite) rather than a single-step (cubic austenite ! monoclinic martensite) transition. The curves in Fig. 10 exhibit some similarities to those in Fig. 3. Namely, they both display thermal hysteresis and go through maxima of comparable height at similar temperatures. The main difference is that in the case of the Hloaded material the amplitude-dependent damping is markedly reduced at the lowest temperatures, owing to the disappearance of the ‘‘150 K’’ peak. The above noted similarities suggest that, most likely, the amplitude dependent damping is related to causes other than the ones giving rise to the H peaks, in analogy to the case of the frequency dependence illustrated in the previous subsection. 4. Discussion The main issues to be discussed here are about whether: (i) the ‘‘200 K’’ bump observed at low frequencies and at high strains (105 to 3 · 103) in the va and wq states of the material is identifiable with PH or PTWH; (ii) the frequency and amplitude dependences of the IF below Mf and within the coexistence region of the austenite and martensite agree with the predictions of some of the available theories [39–46]; (iii) the low-frequency data on PH and PTWH are compatible with the high frequency ones [26]; (iv) the well developed ‘‘200 K’’ peak often reported in the literature [2,4–7,19,22–24,34,35] is indeed an H effect, as it was recently supposed to be [26]; (v) a frequency and amplitude dependence of PH is conceivable; (vi) the non-thermally activated ‘‘150 K’’ peak is the same as the one previously observed at about the same temperature for frequencies in the kHz range [30]. The reply to the first issue is straightforward. Namely, the ‘‘200 K’’ bump is not thermally activated, therefore, although occurring over the same temperature range as the H peaks is not identifiable with anyone of them. The question then arises about which might be the origin of this bump and, more generally, of the IF in the martensitic state (issue ii). The frequency dependences of IF in the twophase and single-phase (martensite) regions are similar to each other, and thus the sources of damping should not markedly vary in the two cases. Nevertheless, account is to be taken of the fact that the sensitivity of IF to strain is different in the two situations. As a matter of fact, with increasing e, Q1 decreases in the two-phase region but increases in the single-phase martensitic state (see Fig. 3). Most likely, the ‘‘200 K’’ bump and, more generally, the IF in the single-phase region, are associated with stressinduced reorientation of the martensite variants. This reorientation process, which can be assimilated to a stress-induced transition, does not involve appreciable free energy changes and, consequently, is not associated with

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calorimetry anomalies, in agreement with the experiments. An amplitude dependence of the twin boundary motions, responsible of the reorientation of variants, is conceivable and models have been envisaged to account for this [41,42]. One model [41] assumes that the growth of favourably oriented variants at the expense of the unfavourably oriented ones can only take place for applied stresses of amplitude r0 higher than a certain critical value rc. The following expression for the dependence on r0 has been provided: "  3 # 2A om rc 1 1 Q ¼ tan d ¼ 2 r0 ð2Þ 3p or r0 Here om represents the mass of material that transforms or from one type of variant to another per unit stress change. A fit to the experimental data of relation (2) is reasonably good; however, it provides for rc an unreasonably low value (600 Pa). Furthermore, the model predicts an independence of Q1 on frequency in contrast with experiment. Thus, it appears to be inadequate to account for the present results. The other model [42], also based on interphase or twin boundary motions, leads to markedly different dependences of IF on frequency and stress in the low- and high-frequency regimes. In the first case, Q1 is expected to decrease when increasing both frequency and strain, which is in total contrast to the present results (see Figs. 2 and 3). In the second case, Q1 should decrease with increasing frequency and increase with increasing strain amplitude in qualitative agreement with the present observations. The following relationship has been found for Q1(e, f):   1 B 1 Q ¼ A 1 exp  ð3Þ e f e2 Here A and B are quantities, independent of frequency and strain, the expressions of which provided for them contain parameters that are not directly measurable. Thus, they are difficult to evaluate. The dependence of IF on strain observed experimentally could be accounted for in terms of relation (3), not on frequency, as the experimental exhibits values of n (0.38–0.42) are much smaller than that (1.0) predicted by theory. Several models [39–46] have been developed to account for the main features of the IF peak PAM (PMA) occurring at first order martensitic phase transitions, such as its dependence on frequency, strain amplitude and rate of temperature change. Some of these theories are based on stress-assisted nucleation processes [39,42], and some others are based on stress-induced motions of austenite/martensite interfaces. The results of the present investigation strongly support the idea that the IF in the two- and single-phase regions arises from similar sources; thus, mechanisms of PAM (PMA) based on stress-assisted motions of austenite/martensite interfaces and of twin boundaries seem to be more realistic. Most of these models [40–44]

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predict a dependence of IF on f of the type expressed by relation (1) with an unitary value of n. This prediction is only in partial agreement with the present and previous [38] experiments since the expected functional dependence of IF on f is found to be correct, but not the numerical value of n. Two theories based on stress assisted motion of phase interfaces [45,46], nonetheless, allow n to vary between 0 and 1; thus, they appear better suited to account for the observed frequency dependence of IF in the two phase regions. However, from these two theories a dependence of IF on strain at the phase transition is not expected. Accordingly, they are unable to explain the narrow dips observed in the close vicinity of the transition (see Figs. 3 and 10). A decrease in the height of PAM (PMA) with e is instead expected from the model of Ref. [44], which, therefore, is in agreement, at least qualitatively, with the experimental results. This model has also been found to account satisfactorily for the non-linear dependence of the height of PAM (PMA) on the rate of temperature change T_ [44], a feature not investigated in the present work. Thus, the only unsatisfactory aspect of the model appears to be its predictions concerning the frequency dependence. As a general conclusion of issue 2 (ii) it can be stated that a model capable of explaining all the observed features of the peak does not exist yet. To exploit issues from (iii) to (vi) it is useful to examine first the Arrhenius plot of Fig. 11, where all the available data concerning PH, PTWH and the ‘‘150 K’’ peaks are collected. As can be seen, the high- and low-frequency (filled symbols) data for PH are aligned along the same straight line, which also fits most of the data previously reported for the ‘‘200 K’’ peak (open symbols). This finding supports our earlier conclusion, only based on the high frequency data for PH [26], that the ‘‘200 K’’ peaks previously observed in H undoped materials, actually coincide with peak PH associated with H impurities present in

Fig. 11. Arrhenius plot for some of the observed internal friction spectra. Filled symbols: present measurements, open symbols: results from the literature. The recent data from Ref. [32], which refer to a thermally activated ‘‘200 K’’ peak, are perfectly aligned with the ones for PH, thus confirming our view that the two peaks represent an identical relaxation process (H-Snoek relaxation).

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the starting materials or picked up by them during processing. This last supposition has been confirmed by recent observations [31] showing that H contamination may really occur during solution treatment at high temperature in argon atmospheres. However, the results of the present work also show that in H-free materials a non-thermally activated bump may occur at around 200 K, which is not identifiable with PH. Thus, the ‘‘200 K’’ peak reported in the literature may actually have coincided sometimes with the non-thermally activated intrinsic lattice effect (‘‘200 K’’ bump) and sometimes with the PH relaxation. In those cases where thermal activation has been observed [2,5,32] people have certainly been dealing with PH relaxation. The straight line plotted in Fig. 11, which represents the best fit of data points for PH, also goes through the hightemperature data for H diffusion in the austenite [26] and provides for PH an activation energy W (0.52 ± 0.05 eV) which, within the experimental error, coincides with that (WD) for H diffusion within the austenite (WD = 0.48 ± 0.05 eV) [47]. Furthermore, it also provides a value (10(13±0.2) s) for the limit relaxation time s0 which is perfectly in line with those of the Snoek relaxations either involving heavy interstials (O, N, C) (see Ref. [48, p. 236]) or H [49,50]. These facts prove at the same time that the H diffusion rate in the austenite and in the martensite are about the same and that PH is indeed an H Snoek-type of relaxation, as it had already been inferred to be [26]. Although the amplitude and frequency dependence of IF in the H doped material is mostly attributable to causes not involving H, nevertheless, an amplitude and frequency dependence of the relaxation strength of PH and PTWH cannot be excluded. Thus, an explanation of this eventual effect, particularly that of PH, is desirable and may be given for the following reasoning guidelines. For high stresses (e > 104) and low frequencies (f < 50 Hz) variant reorientation occurs and, within the volume fraction of reoriented variants, H atoms may not only reorient themselves as isolated elastic dipoles, thus giving rise to the usual Snoek effect, but may also redistribute over the sub-lattice of the interstitial sites, thus changing the degree of short-range directional order of the H–H bonds and thus giving rise to the H-Zener effect. Such an effect, associated with the redistribution of substitutional atoms within variants reoriented by an applied stress seems has, actually, been found to be responsible for the rubber effect in AuCd alloys [50]. Both processes (Zener and Snoek) take place through a single jump of the individual H atoms, thus justifying the coincidence of W and WD. Along this interpretation line an eventual amplitude and frequency dependence of the combined Snoek–Zener effect will reflect that of the stress-induced motion of twin boundaries. The straight line fitting the overall data points of PTWH gives W = 0.58 ± 0.09 eV and s0 = 9 · 10(15±2) s. This value of s0 is too small for PTWH to be associated with stress-induced motions of isolated H atoms, suggesting that we are dealing with an interaction effect of H with other

lattice defects, notably with twin boundaries. This conclusion, which had already been reached in previous works based on the dependence of the height of PTWH on nH [12,28,29], is confirmed by recent observations showing that both H and twin boundaries are required for the appearance of the peak in NiTiCu alloys [31]. The activation energy of PTWH is only slightly higher than that for the H-Snoek effect, similar to the case of dislocations interacting with interstitial impurities in body centred cubic (bcc) metal alloys (Snoek–Koester effect (see Ref. [48, p. 406]). The analogy, nevertheless, is not complete as PTWH occurs at temperatures lower than the H-Snoek effect while the reverse is true for the Snoek–Koester relaxation. This is a consequence of the relatively small value of the PTWH limit relaxation time s0, which, similar to the case of dislocations, is expected to be controlled by geometrical features of twin boundaries as well as by the H concentration near these bi-dimensional defects. Finally, it is worth noting that that the values of the relaxation parameters W and s0 of PTWH are not accurate enough to allow final conclusions to be drawn concerning the structural mechanism of this relaxation. One well-established result of the present low-frequency measurements is the appearance at around 150 K of a damping peak, which turns out to be enhanced by an increase in the exciting strain amplitude (see Fig. 2) and fully removed by H impurities (see Figs. 4 and 6). The present results, furthermore, definitely show that this peak is not thermally activated, contrary to the indications provided by our earlier high frequency data [30]. The question now arises about which might be the origin of this and of the other non-thermally activated processes (‘‘200 K’’ bump and PTWM peak (125 K) [11]) and which their interrelationships may be. This is a puzzling task owing to the complex and still scarcely known phenomenology of these effects; thus, we shall limit ourselves to proposing only some speculative approaches. The temperatures of the ‘‘150 K’’ and PTWM peaks differ only slightly from each other and, furthermore, the two effects have never been seen simultaneously to occur in a single temperature run. Therefore, they probably represent the same phenomenon, thus being identifiable with each other. In the following we shall take this as a working assumption and refer to them as the ‘‘150 K’’–PTWM effect. This effect and the ‘‘200 K’’ bump appeared as distinct features in several measurement runs (see Figs. 1b and 5b) and their heights exhibited different dependences on frequency. Thus, they certainly represent two distinct physical phenomena. The most illuminating aspect of the ‘‘150 K’’– PTWM process is its disappearance in the presence of H impurities, whose jump frequency, at the temperature of the peak (150 K), should be several orders of magnitude smaller than that of the applied alternating stress (the HSnoek effect occurs at around 200 K). Hence, H atoms will probably act as immobile pinning points for extended lattice defects such as twin boundaries (or dislocations), thus impeding their motions and, consequently, cancelling the

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effect. Furthermore, the ‘‘150 K’’–PTWM peak is not thermally activated and its height depends on the strain amplitude. These features suggest that a hysteretic de-pinning process for the involved extended defect from weak pinning points seems to be the most convincing model to account for this effect. In addition, a de-pinning process could also explain the softening of the Young’s modulus of the martensite observed at the highest strain amplitude (see Fig. 2) as well as the hardening of the martensite induced by H impurities (see Fig. 4). The ‘‘200 K’’ bump increases with increasing e and decreases with increasing f; it also exhibits thermal hysteresis as it is clearly visible only on heating. These phenomenological aspects indicate that some kind of lattice change occurs during cooling, probably consisting in readjustments of the twin boundary network. Thus, the question arises about which might be the difference between the mechanisms of the ‘‘200 K’’ and the ‘‘150 K’’–PTWM peaks. To date we can only speculate. For example, we could assume that the ‘‘150 K’’–PTWM peak and the ‘‘200 K’’ bump are associated with stress-assisted readjustments of dislocations and twin boundaries, respectively. Two arguments would be in favour of the first attribution, one is based on the fact that the height of the ‘‘150 K’’– PTWM peak increases with the increasing number of thermal cycles through the martensitic transition region [51]; the other is that the peak also occurs in heavily coldworked materials not exhibiting the martensitic transition [30]. On the other hand, an argument supporting a twin boundary-related mechanism for the ‘‘200 K’’ bump is the fact that it decreases with increasing f, completely disappearing at f > 10 Hz and that it is strongly amplitude dependent and occurs at temperatures only slightly higher than that of the H-twin boundary relaxation.

5. Conclusions The main conclusions to be drawn from the present lowfrequency work are as follows: 1. The transformation peak PAM, on cooling, is much broader than the DSC anomaly, owing to damping processes associated with twin boundaries that undergo irreversible changes during cooling. The height of PAM depends on frequency according to a relation which is only in partial agreement with most of the theories proposed so far. 2. The ‘‘150 K’’ peak previously studied at kHz frequencies turns out not to be thermally activated. This peak coincides with peak PTWM and is presumably caused by hysteretic de-pinning processes of dislocations or twin boundaries from some kind of weak pinning point. 3. A non-thermally activated bump, which is only observable at around 200 K on heating and at frequencies lower than 20 Hz, is due to hysteretic stress-induced de-pinning processes at twin boundaries. This peak occurs at

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the same temperature as the thermally activated peak PH owing to H (for 1 Hz frequency). The ‘‘200 K’’ peak often reported in the literature may sometimes have coincided with the non-thermally activated bump, sometimes with the better developed hydrogen peak PH. 4. In the H doped material, the frequency and strain dependent damping is mainly due to stress-assisted twin boundary motions, similar to the case of the H undoped material. At high stress levels (>104) the hydrogen peak PH may result from the superposition of the Snoek and Zener effects, the last one being due to stress-induced changes in the short-range directional order of H–H bonds within the martensite variants reoriented by the applied stress.

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