Non-ergodic Processes in Athermal Martensitic Alloys Revealed by X ...

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ScienceDirect Materials Today: Proceedings 2S (2015) S929 – S932

International Conference on Martensitic Transformations, ICOMAT-2014

Non-ergodic processes in athermal martensitic alloys revealed by X-ray photon correlation spectroscopy: bulk properties M. Wideraa,*, M. Sprungb U. Klemradta a

II. Institute of Physics and JARA-FIT, RWTH Aachen University, D-52056 Aachen, Germany b Deutsches Elektronen Synchrotron (DESY), Notkestrasse 85, D-22607 Hamburg, Germany

Abstract The vast majority of martensitic transformations (MT) is classically viewed as being athermal, although time-dependent phenomena such as incubation time and/or aging effects have been known for a long time. Using highly coherent X-rays it has become possible to access non-equilibrium, intermediate states of the MT. X-ray photon correlation spectroscopy (XPCS) can reveal non-equilibrium dynamics using two-time correlation functions, where fluctuating intensities of X-ray speckle pattern are auto-correlated. Here we report XPCS experiments on a Ni63Al37 alloy. The revealed isothermal dynamics shows non-equilibrium features on long time scales, superimposed with microstructural avalanches. The dynamics supports the “symmetry conforming short-range-order” model based on short range diffusion. © 2014 The TheAuthors. Authors.Published Published Elsevier © 2015 byby Elsevier Ltd.Ltd. This is an open access article under the CC BY-NC-ND license Selection and Peer-review under responsibility of the chairs of the International Conference on Martensitic Transformations (http://creativecommons.org/licenses/by-nc-nd/4.0/). This is Peer-review an open access article under theofCC license (http://creativecommons.org/licenses/by-nc-nd/3.0/). 2014. Selection and under responsibility the BY-NC-ND chairs of the International Conference on Martensitic Transformations 2014. Keywords: slow time-dependent phenomena, aging, incubation time, symmetry-conforming short-range-order model, X-ray photon correlation spectroscopy, microstructural avalanches

1. Introduction The martensitic transformation (MT) is characterized as a shear-dominant, lattice-distortive, diffusionless transformation occurring by nucleation and growth [1]. Classical steels are characterized by a strong first order transformation, whereas for shape memory alloys (SMA), a weak first order transition is realized. The conjunction of

* Corresponding author. Tel.: +49-241-80-20326; fax: +49-241-80-22306. E-mail address: [email protected]

2214-7853 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Selection and Peer-review under responsibility of the chairs of the International Conference on Martensitic Transformations 2014. doi:10.1016/j.matpr.2015.07.434

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M. Widera et al. / Materials Today: Proceedings 2S (2015) S929 – S932

a weakly first order, martensitic phase transformation with highly mobile habit planes is a key feature for SMA. Classically, the MT is classified as athermal, but slow time-dependent phenomena such as incubation time and/or aging effects have been known for a long time. Especially with respect to aging phenomena, martensite stabilization and rubber-like behavior (RLB) have been observed in a variety of SMA (CuAlNi [2], AuCd [3], InTl [4]). Martensite stabilization is characterized by an increase of the austenite-finish-temperature Af, whereas RLB is a pseudoelastic response to stress. Both phenomena can be observed after a certain aging time in the martensitic phase. The time for a noticeable aging effect spreads over a wide range from seconds (InTl) to months (CuAlNi). Therefore, diffusion seems to play a key role for aging phenomena. Using the ratio of the MT temperature M s to the melting temperature Tm, the role of diffusion can be estimated for those SMA showing time-dependent behavior. A ratio close to 1 indicates fast aging, whereas a lower ratio stands for slow aging [5,6]. Various attempts to unify athermal and isothermal dynamics have been published, however, the “symmetry conforming short-range-order” model (SC-SRO model) is able to explain both phenomena on the same footing [5]. The SC-SRO model explains aging effects by diffusion of point defects, subsequent to the diffusionless MT. Most of the previously suggested models invoked some change of the average martensite structure to explain martensite aging (for a comprehensive overview see [6]). Following the SC-SRO model, ”the symmetry of SRO configuration of point defects in equilibrium should conform to the symmetry of the crystal lattice” [7]. Due to the diffusionless character of the MT, the austenite SRO probability is transferred to the martensite phase, leading to a thermodynamic non-equilibrium state. During martensite aging, the non-equilibrium SRO gradually changes due to a rearrangement of point defects into an equilibrium state, which corresponds to the low-symmetry martensite phase [6,7]. Since the martensite is now in a thermodynamically favorable state, more energy is needed for the reverse transition (martensite stabilization). In case of the RLB, the diffusionless detwinning of variants leads to a thermodynamic unfavorable SRO state, giving rise to a macroscopic restoring force, which acts upon the former variants. The kinetics connecting the thermodynamic equilibrium states can be assessed using X-ray photon correlation spectroscopy (XPCS). 2. Method and experimental setup Only few techniques are suitable for the investigation of non-equilibrium processes at the microscopic state, owing to limited spatial and/or temporal resolution. Using 3rd generation synchrotron radiation sources, it has become possible to access slow dynamics on the microscopic scale with coherent X-rays. The development of coherent investigation techniques has led to the relatively novel XPCS method, which tracks down slow time-dependent phenomena in soft and solid condensed matter systems. In particular, a wide range of time scales (10-6 – 106 s) relevant for incubation time effects in martensite can be investigated [8]. The interaction of coherent Xray with the individual arrangement of scatterers in real crystals gives rise to a grainy diffraction pattern, also known as speckle pattern (see Fig. 1). If the discorded systems changes with time, also the speckle pattern changes, which leads to time-dependent intensity fluctuations [9]. Taking a times series of this fluctuating intensities I(t), one can reveal the evolving dynamics through an auto-correlation. In case of equilibrium processes, the dynamics can be analyzed using the one-time correlation function (CF) [10]

g (2) q ,

I q, t I q, t

,

I 2 q, t

(1)

with an arbitrary zero-point in time. In the case of non-equilibrium systems, the zero-point in time does matter, and one has to take the two-time correlation function C(t1 , t 2 )

I(t1 ) I(t 2 ) I 2 (t1 )

I(t1 )

2 1/2

I(t1 ) I 2 (t 2 )

I(t 2 ) I(t 2 )

2 1/2

,

(2)

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hence defined as the covariance of the scattered intensity [11]. Equilibrium dynamics can be parameterized by a stretched exponential function; a frequently used function is the Kohlrausch-Williams-Watts (KWW) form [9]

g (2)

1 A exp

2 ( /

0

) ,

(3)

with identical form for > 1 and < 1. The exponent ≠ implies that the decay is faster ( > 1: solid-like is a characteristic collective dynamics) or slower ( < 1: liquid-like diffusive dynamics) than exponential and relaxation time [12]. The experiment was carried out at the coherence beamline P10 of the PETRA III synchrotron at DESY, using a standard Bragg scattering geometry (see Fig. 1). For the investigations of slow time-dependent phenomena, a Ni63Al37 single crystal with a (001) polished surface and the corresponding (001) Bragg reflection ( = 13,51°) was chosen. X-rays with energy of 9.3 keV were focused by compound refractive lenses to a spot size of about 5 μm2 (FHWM) at the sample. The diffracted X-rays were detected by a Pilatus 300K detector (487 × 619 pixels, pixel size 172 × 172 μm2) placed 4975 mm downstream of the sample. Different times series of the (001) Bragg reflection were recorded for temperatures few Kelvin above and during the MT, with a temperature stability of ±3 mK. Data were taken with an exposure time of 1 sec, followed by a readout time of 3 msec. The local Ms temperature of the spot investigated here was determined to be Ms = 278.5 K, since at this temperature the speckle pattern changed dramatically, indicating massive structural rearrangement. 3. Results In the direct vicinity of the MT, a time series over more than 4000 seconds had been taken, to ensure a complete record of the non-equilibrium dynamics. Using two-time CF (see eq. 2), non-equilibrium dynamics could be revealed, apparent in the diverging colour contor in the two-time correlation plot (see Fig. 2). Using non-averaged one-time CF g(2)( -t, +t) at a given age of the system (see eq. 3), the development into a equilibrium state can be quantified and associated with the system age tage = (t1 + t2)/2 (see Fig. 2). Furthermore, sharp cuts in the two-time CF can be observed, which indicate microstructural avalanches passing the spot illuminated by the X-ray beam. These cuts (or breakdowns) of the correlation function have also been reported for the MT of Gold-Cadmium [13] and Cobalt [14], and can be associated with incubation time effects. These indicate either a local MT in the sample or a variant movement due to self-accommodation processes. The stress relaxation associated with avalanches is indicated by regular drops of the stretching exponent from a value close to 2 to a value near 1 (see for example Fig. 2 interval A with ~ 1.8 to ~ 1.1). Since an exponent of is associated with diffusion, we interpreted this as a signature of the diffusional rearrangment as predicted by the SC-SRO model. However, as stress builds up again prior to the next avalanche, the exponent changes as well and assumes again values for solid-like dynamics. This interplay of microstructural avalanches and diffusion is observed repeatedly during the duration of the experiment.

Fig. 1. Schematic setup for X-ray photon correlation spectroscopy at the beamline P10. See text for further details.

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Fig. 2. (left) Two-time CF C(t1,t2) at a temperature of 278.5 K. The diverging color contours quantify the degree of correlation between the speckle patterns, where 1 stands for strong correlation. Two main features can influence the state of correlation: diffusion leads to a decorrelation within a characteristic time scale, and a massive redistribution of atoms leads to a dramatic breakdown (indicated by black arrows) of the twotime CF. The system age tage = (t1 + t2)/2 corresponds to the diagonal from the lower left to the upper right corner. (The two vertical and horizontal dark blue lines are artefacts arising from detector readout error). (right) Characteristic time scales and corresponding KWW exponents extracted from the two-time CF using non-averaged one-time CF at a given age of the material. The stretching exponent varies repeatedly between 1 and ca. 2, indicating the build-up of internal stress fields that relax temporarily by microstructural avalanches that partially transform the sample.

4. Conclusion XPCS allows to investigate the actual transition from the austenitic to the martensitic state by (locally) tracking the non-equilibrium states connecting these. The use of one-time and two-time CFs provides a framework for revealing and quantifying highly non-stationary dynamics in the direct vicinity of a MT in Ni63Al37. The non-ergodic dynamics can, in a model-free way, already be inferred from the diverging color contours in the two-time correlation plot. The finding of slow dynamics and non-ergodicity is in disagreement with the conventional classification as athermal martensite, but in agreement with the previous observation of incubation time in Ni-Al [15]. The observation of diffusional rearrangements following avalanches is in agreement with the SC-SRO model. Acknowledgements Parts of this research were carried out at the light source PETRA III at DESY, a member of the Helmholtz Association. We would like to thank Alessandro Ricci and Sergej Bodarenko for assistance in using beamline P10. References [1] J.W. Christian, G.B. Olson, M. Cohen, J. Phys. IV 5 (1995) 11–19. [2] H. Sakamoto, K. Otsuka, K. Shimizu, Scr. Metall. 11 (1977) 603–611. [3] N. Nakanishi, T. Mori, S. Miura, Y. Murakami, S. Kachi, Phil. Mag. 28 (1973) 277–292. [4] M.W. Burkart, T.A. Read, Trans. AIME 197 (1953) 1516–1524. [5] K. Otsuka, X. Ren, Mater. Sci. Eng. A 312 (2001) 207–218. [6] X. Ren, K. Otsuka, Phase Trans. 69 (1999) 329–350. [7] X. Ren, K. Otsuka, Nature 389 (1997) 579–582. [8] L. Müller, U. Klemradt, T.R. Finlayson, Mat. Sci. Eng. A 438 (2006) 122–125. [9] G. Grübel, A. Madsen, A. Robert, Soft Matter Characterization. Springer Science+Business Media, LCC, New York, 2008. [10] A. Madsen, R.L. Leheny, H. Guo, M. Sprung, O. Czakkel, New J. Phys. 12 (2010) 055001 (16 pp.). [11] A. Malik, A.R. Sandy, G.B. Stephenso, S.G.J. Mochrie, I. McNulty, M. Sutton. Phys. Rev. Lett. 81 (1998) 5832–5835. [12] O.G. Shpyrko, E. D. Isaacs, J. M. Logan, Yenjun Feng, G. Aeppli, R. Jaramillo, H. C. Kim, T. F. Rosenbaum, P. Zschack, M. Sprung, S. Narayanan, A.R. Sandy, Nature 447 (2007) 68–71. [13] L. Müller, M. Waldorf, C. Gutt, G. Grübel, A. Madsen, T.R. Finlayson, U. Klemradt, Phys. Rev. Lett. 107 (2011) 105701. [14] C. Sanborn, K.F. Ludwig, M.C. Rogers, M. Sutton. Phys. Rev. Lett. 107 (2011) 015702. [15] M. Aspelmeyer, U. Klemradt, T.R. Finlayson, R.L. Wood, S.C. Moss, J. Peisl, Phys. Stat. Sol. A 174 (1999) R9–10.