domain: sdv spi

text:
MD Roxane Compagnon

PhD Baptiste Brun-Cottan

PhD Pauline Assemat

MD Julie Vial

Professor Jérôme Sales De Gauzy

Professor Pascal Swider
email: pascal.swider@imft.fr

Diffusion properties of asymptomatic lumbar intervertebral discs in a pediatric cohort; a preliminary study of apparent diffusion coefficient 1.2, *

Purpose: To explore the apparent diffusion coefficients of intervertebral discs in an asymptomatic pediatric cohort. Methods: We conducted a prospective MRI study of the lumbar spine from below the thoracolumbar junction to the lumbosacral junction on 12 subjects (mean age 13 y.o.) with no spinal pathology or spinal posture disorder. MRI imaging was carried out using a 1.5 T machine with acquisitions realized both in sagittal and coronal planes. First, disc hydration was determined and then, diffusion-weighted images (DWI) were obtained using an SE single-shot echo-planar sequence. Apparent diffusion coefficients (ADC) of anterior annulus fibrosus (AAF), nucleus pulposus (NP) and posterior annulus fibrosus (PAF) were measured in the sagittal plane. Results: Averaged hydration of 0.27 SD 0.03 confirmed the asymptomatic nature of discs. Average scaled values of ADC were 0.46 SD 0.01, 0.22 SD 0.09 and 0.18 SD 0.03 for NP, AAF and PAF, respectively. ADC of NP were almost constant along the spine, PAF values show a slight increase in the thorax-sacrum direction while AAF values showed a pronounced decrease. Locally, ADC of AAF was higher compared to ADC PAF values below the thoracolumbar junction and it reversed for subjacent discs. Conclusions: In our knowledge, our study provided the first diffusive properties of asymptomatic intervertebral discs in an adolescent cohort. ADC of NP was slightly higher than adults'. ADC evolutions of AAF were correlated with lordosis concavity which pointed out the role of compressive strain on fluid transport properties. This study could furnish information about segment homeostasis for exploration of pediatric spinal pathologies.

The inter-vertebral disc (IVD) is a large avascular fibrocartilaginous structure organized in three anatomical zones: the nucleus pulposus (NP) or internal complex, the annulus fibrosus (AF) and the cartilage end plates (CEP) [START_REF] Urban | Pathophysiology of the intervertebral disc and the challenges for MRI[END_REF]. The microarchitecture of the interface between NP and AF is diffuse but components of extracellular matrix can be distinguished. NP is constituted of a network of type-2 collagen involving proteoglycans which negative charged molecules ensure a significant hydration level. The cell fraction limited to 4000 cells/mm3, mainly concerns chondrocytes and fibrocytes. AF is constituted of tight and well-organized fibers of type-1 collagen with a weak proportion of proteoglycans and very low cellularity. CEP is constituted of a thick layer of hyaline cartilage permeable to small molecules, fluid and ions with an average cell fraction of 15000 cells/mm3. Water fraction represents 65 % to 90 % of the IVD volume and varies with diurnal cycle [START_REF] Urban | Pathophysiology of the intervertebral disc and the challenges for MRI[END_REF], [START_REF] Ludescher | T2-and diffusion-maps reveal diurnal changes of intervertebral disc composition: An in vivo MRI study at 1.5 Tesla[END_REF].

In fetal life and childhood until 2 years, IVD nutrition is supported by blood vessels from vertebrae through CEP. Then, this vascular supply decreases to almost disappear at puberty and the main nutritional support is maintained by convection and diffusion of fluid and micro nutriments. Nutritional alterations associated to biophysical IVD changes in adults are deeply investigated. This tends to conclude that disc degeneration is a continuum, starting from the second decade of life [START_REF] Pfirrmann | Magnetic resonance classification of lumbar intervertebral disc degeneration[END_REF], [START_REF] Yu | In vivo quantification of lumbar disc degeneration: assessment of ADC value using a degenerative scoring system based on Pfirrmann framework[END_REF].

Magnetic Resonance Imaging (MRI) is an imaging modality used to explore soft tissues hydration [START_REF] Brown | MRI: basic principles and applications[END_REF], [START_REF] Botchu | Current concept in upright spinal MRI[END_REF] and specifically disc degeneration signs [START_REF] Pfirrmann | Magnetic resonance classification of lumbar intervertebral disc degeneration[END_REF]. Main sequences based on signal relaxation time, i.e. T1 or T2, which discriminate specific tissue responses are associated to STIR imaging (Short Tau Inversion Recovery), in which fat components are filtered. Diffusion weighted imaging (DWI) allows describing the diffusion of free water molecules [START_REF] Bihan | Apparent diffusion coefficient and beyond: what diffusion MR imaging can tell us about tissue structure[END_REF]. Based on an echoplanar spin echo sequence (EPI-SE), DWI adds specific magnetic gradients before and after the 180° radio frequency impulsion and it results in hyper-signal in low molecular diffusion zones and hypo-signal in high molecular diffusion zones. The apparent diffusion coefficient (ADC) is a scalar measure of the magnitude of molecular diffusion obtained from DWI. In living tissue, diffusion is restricted by cells and extra cellular matrix components and lower to that of free water equal to 3×10 -3 mm 2 /s.

Concerning IVD, the literature review in adults showed large discrepancies of ADC mainly due to non-standardized protocols. DWI sequences and region of interest (ROI) are varying significantly. Indeed, often focused on NP center, the ROI surface can fluctuate between 2 mm 2 and 110 mm 2 [8]- [START_REF] Shen | Diffusion Weighted Imaging, Diffusion Tensor Imaging, and T2* Mapping of Lumbar Intervertebral Disc in Young Healthy Adults[END_REF]. Signals may intersect several tissues, a complexity which induces bias in the outcome standardization and frequently, a unique value is proposed whereas IVD is a complex multi-tissue structure. Despite these limitations, ADC range can be considered between 1.22 and 2.46×10 -3 mm 2 /s for asymptomatic IVD in adults with lower values for caudal discs [START_REF] Wu | Comparison of Apparent Diffusion Coefficient and T2 Relaxation Time Variation Patterns in Assessment of Age and Disc Level Related Intervertebral Disc Changes[END_REF]- [START_REF] Kealey | Assessment of apparent diffusion coefficient in normal and degenerated intervertebral lumbar disks: initial experience[END_REF]. Discs with degeneration signs show increased values of ADC correlated with age, disc level, Pfirrmann grade but not gender [START_REF] Pfirrmann | Magnetic resonance classification of lumbar intervertebral disc degeneration[END_REF], [START_REF] Wu | Comparison of Apparent Diffusion Coefficient and T2 Relaxation Time Variation Patterns in Assessment of Age and Disc Level Related Intervertebral Disc Changes[END_REF], [START_REF] Zhang | Assessment of apparent diffusion coefficient in lumbar intervertebral disc degeneration[END_REF], [START_REF] Kealey | Assessment of apparent diffusion coefficient in normal and degenerated intervertebral lumbar disks: initial experience[END_REF]- [START_REF] Yu | In vivo quantification of lumbar disc degeneration: assessment of ADC value using a degenerative scoring system based on Pfirrmann framework[END_REF]. This could reveal the potential presence of freely moving fluid contained within structural change, such as cracks and cavities. Some ADC of NP in adults and young adults, summarized in Table 1, show that values for asymptomatic discs are comprised between 1.2 and 2.35×10 -3 mm 2 /s and values for degenerative discs are comprised between 1.4 and 2.22.10 -3 mm 2 /s.

Much more is known in IVD aging than of the evolving properties during maturation [START_REF] Kerttula | Apparent diffusion coefficient in thoracolumbar intervertebral discs of healthy young volunteers[END_REF], [START_REF] Bolzinger | MRI evaluation of the hydration status of non-pathological lumbar intervertebral discs in a pediatric population[END_REF]. Furthermore, disabling pediatric diseases such as idiopathic scoliosis or spondylolisthesis might impact segment homeostasis and their roles in surgical outcomes. Indeed, the sagittal organization may have a leading role in pre-and post-operative behavior of lumbar discs [START_REF] Green | Long-term magnetic resonance imaging follow-up demonstrates minimal transitional level lumbar disc degeneration after posterior spine fusion for adolescent idiopathic scoliosis[END_REF]- [23]. In this context, completing control data can be clinically relevant and for this purpose, we measured diffusion properties of intervertebral discs in an asymptomatic children cohort. We hypothesized that variation of ADC differentiated according to disc structural components and localization had to be considered.

-Methods

The study included 12 consecutive subjects who underwent a spinal MRI. The collection of imaging exams was performed in accordance with the protocol approved by the Ethics Committee of University Children Hospital of Toulouse (France). Inclusion criteria were: a) age comprises between 7 and 20 years inclusive, b) no spinal pathology or spinal posture disorder diagnosed on MRI after validation by a pediatric imaging specialist. The mean age of the included subjects was 13.3 years (SD = 2.92) and our evaluation focused on the lumbar spine from below the thoracolumbar junction, i.e. L1-L2, to the lumbosacral junction, i.e. L5-S1.

MRI Imaging was carried out using a 1.5-T Toshiba Vantage Titan machine with both sagittal and coronal scans. The sagittal scans were as follows: gradient echo TR/TE 5.2/2.6 ms, slice thickness 10.0 mm, spacing 8.0 mm, field of view 30×25 cm, and matrix size 192×192. The coronal scans were as follows: gradient echo (GE), TR/TE: 5.2/2.6 ms, slice thickness 10.0 mm, spacing : 8.0 mm, field of view (FOV) 37×30 cm, and matrix size 192 ×192.

On T2 and STIR imaging, the IVD and NP volumes were reconstructed using dedicated image processing software developed with Matlab®. Disc segmentation was achieved using a tactile device Wacom® Cintiq 21 UX. Disc hydration was defined as the ratio between NP volume and disc volume [START_REF] Gervais | MRI signal distribution within the intervertebral disc as a biomarker of adolescent idiopathic scoliosis and spondylolisthesis[END_REF]. Lumbar discs L1-L2 to L5-S1 were studied, as shown in Figure 1a.

The diffusion-weighted images (DWI) were obtained using an SE single-shot echo-planar (EPI-SE) sequence as follows: TR/TE: 2727/100 ms, slice thickness: 5 mm, spacing: 5 mm, field of view: 37 ×30 cm, matrix size: 128×128, and number of excitation: 1. The diffusion-sensitizing gradients were applied sequentially in the x-, y-, and z-directions, z corresponding to main magnetic field and patient longitudinal axis.

The signal decrease is described by exponential expression (1a) where S0 is the baseline signal intensity and Sb is the signal intensity with applied diffusion gradients. The ADC is deducted from (1a) and expressed by equation (1b) with the diffusion-weighting factor associated with Sb so-called b-value. This value fixed to b = 600 s/mm 2 provided a good compromise between resolution and acquisition time of 132s, for the studied cohort.

1 (a) ln (b) b ADC b b0 0 S S S e ADC bS - =   = - (1
) Offline image analysis software was used to analyze maps of ADC (OsiriX DICOM software V2.31) in the sagittal plane. Three regions of interest (ROI) per disc were defined and located in anterior annulus fibrosus (AAF), nucleus pulposus (NP) and posterior annulus fibrosus (PAF). The circular ROI size was 10 mm 2 corresponded to a diameter of 3.57 mm. In the antero-posterior direction, AAF and PAF matched with lowest intensity signals of DW-EPI image, whereas NP matched with highest intensity. Along the local cranio-caudal axis, the three ROI were located at mid-distance of the top and bottom CEP. Initially, the S0 value maps were registered and then S600 value maps were superimposed while saving locations of ROI. Finally, equation (1b) was used to compute ADC values using integrated values of S0 and S600 into each ROI.

-Results

The determination of ADC value was achieved three times for each ROI segmentation in each sagittal maps and the reproducibility error was lower than 2 %.

The structure of discs was homogeneous with bright hyper intense white signal intensity and a normal disc height, as shown in Figure 1a. The cohort was ranked grade I (A) in Pfirrmann classification [START_REF] Pfirrmann | Magnetic resonance classification of lumbar intervertebral disc degeneration[END_REF].

Volumes of lumbar discs and NP were determined after segmentation of frontal and sagittal T2 images as shown in Figure 1b, and the averaged hydration of 0.27 SD 0.03 was obtained for L1-L2 to L5-S1 discs. The STIR image shown in Figure 1c associated with the DW-EPI intensity map of Figure 1d are provided as imaging data type. The resulting ADC of the cohort and and mean values per vertebral level are presented in Tables 2a, 2b and 2c. Mean ADC for AAF, NP and PAF for the whole spine were 2.22 mm 2 /s SD 0.04, 1.04 mm 2 /s SD 0.41 and 0.87 mm 2 /s SD 0.15, respectively.

Using ADC value of cerebrospinal fluid as reference, i.e. 4.18×10 -3 mm 2 /s measured at L3 location, statistical distribution of scaled ADC for NP, AAF and PAF are plotted in Figure 2 from L1-L2 to L5-S1. Mean values were 0.46 SD 0.01, 0.22 SD 0.09 and 0.18 SD 0.03, respectively. Standard deviations were minimal for NP and maximal for AAF. The difference between average ADC values of NP and AF per vertebral segment was significant with a t-test p-value of 7.1×10 -5 .

Evolutions of scaled ADC magnitude along the lumbar spine are shown in Figure 3 using longitudinal distance between L1-L2 and L5-S1 to describe the scaled path. Cubic polynomial interpolation were associated and coefficients were (0.11, -0.16, 0.07, 0.45) for NP, (1.1, -1.8, 0.55, 0.27) for AAF and (-0.05, 0.14, -0.01, 0.15). It showed that ADC values of NP were almost constant, PAF values show a slight increase and AAF values showed more variations and a global pronounced decrease. Minimal value of the coefficient of determination r 2 was 0.96.

Figure 4 shows the distribution of average scaled ADC along the local antero-posterior axis of discs. ADC value of NP and AAF -PAF distance are used to scale ADC magnitudes and path, respectively and a quadratic polynomial curve fitting was associated. AAF values show largest variations whereas PAF values are more constant. Indeed, ratios vary from one quarter to two third for AAF and about one third for PAF. Compared to PAF values, AAF values are higher for L1-L2 and L2-L3 but they reverse from L3-L4 to L5-S1. This is accompanied by the shift of distribution patterns associated with the NP migration toward the posterior direction.

-Discussion and conclusion

The aim was to explore diffusion properties of asymptomatic discs in a children cohort. According to our initial assumption, we found significant evolution of ADC internal to the discs and along the lumbar longitudinal axis.

Disc volume reconstruction and hydration calculations from T2 sequences confirmed the asymptomatic nature of discs [START_REF] Pfirrmann | Magnetic resonance classification of lumbar intervertebral disc degeneration[END_REF] since included in the range of normality [START_REF] Jarman | Intervertebral disc height loss demonstrates the threshold of major pathological changes during degeneration[END_REF]. ADC of nucleus pulposus was almost constant and slightly higher than adults' while being in the range of overall intervertebral disc values proposed in the literature as summarized in Table 1. Evolution of ADC can be associated to variation of free water content likewise water in an extracellular compartment. Free water content also can reflect the quality of nutrient supply, as a consequence of efficient exchanges between disc and vertebra, and this was confirmed by the higher values compared to adults found at the nucleus pulposus location.

The overlapping ADC values in Table 1 may be due to the natural variation of tissue properties whether they are asymptomatic or degenerated but also to non-standardized protocols assuming that all MR scanners were calibrated. Indeed, b -values, ROI shapes, sizes and location showed significant variations. Our protocol did not aim at defining a pediatric norm but at furnishing values of a pediatric cohort explored using a methodology usable in clinical setting.

In this framework, we found that ADC of annulus fibrosus was significantly lower than that of the nucleus pulposus. In addition, variations were associated with the evolution of lumbar lordosis towards the spino-pelvic alignment. Indeed, reversed ADC evolutions of anterior and posterior annulus fibrosus were correlated with the relative inclination of vertebral plateaus. It was found that ADC was weaker in the lordosis concavity, especially in AAF, and this pointed out that compressive strain could influence locally transport properties into the disc. Here, we could suggest that common exploration of differentiated diffusive properties and location-dependent biomechanical loadings and energies [24] could be considered to explore the segment homeostasis and beyond, to study the bifurcation towards pathological behavior. The methodology involving imaging protocol and associated post-treatment was designed to ensure a compromise between accuracy and feasibility in pediatric clinical setting. The annulus fibrosus being a fibrous structure, diffusion tensor imaging could potentially inform about the locationdependent anisotropic properties. Unfortunately, additional series of sequences and increased examination time were prohibitive with our pediatric cohort. Main limitation of our study concerned the limited number of subjects (and centers) and therefore it should be considered as a preliminary study. We suggested that evolution of ADC of discs could be described a polynomial form in the global reference of the spine. The interpolation degree sufficiently high, allowed physiological oscillations according to the spine anatomy to be predicted. In our knowledge, our study provided the first diffusive properties of asymptomatic intervertebral discs in an adolescent population with additional information about their spatial heterogeneity. T2 imaging reflects total water content and ADC evolution can be associated to variation of free water content. Their coupling could furnish information about segment homeostasis for early diagnosis, surgical outcome and patient follow-up in pathologies such as idiopathic scoliosis or spondylolisthesis.

[23] Abelin-Genevois K, Estivalezes E, Briot J, Sévely A, Sales de Gauzy J, Swider P. 2015. Spino-pelvic alignment influences disc hydration properties after AIS surgery: a prospective MRI-based study. Eur Spine J.;24(6):1183-90.

[24] Brun-Cottan B, Assemat P, Doyeux V, Accadbled F, Sales de Gauzy J, Compagnon R, Swider P. 2021. An energy approach describes spine equilibrium in adolescent idiopathic scoliosis. Biomech Model Mechanobiol. 20(1):359-370.

Captions for tables and illustrations

Table 1: ADC in nucleus pulposus (10 -3 mm 2 /s) of adult and young adult population

Table 2 :Figure 1 -

 21 Figure 1 -Lumbar MR imaging in the sagittal plane: (a) T2 imaging, (b) Semi-automated segmentation and automated volume reconstruction of IVD from MRI slices using tactile device Wacom® Cintiq 21 UX, (c) STIR imaging, (d) Map of ADC (10 -6 mm 2 /s, grayrainbow clut) showing ROIs in nucleus pulposus (NP), anterior annulus fibrosus (AAF) and posterior annulus fibrosus (PAF).

Figure 2 -

 2 Figure 2-Box-plots of average dimensionless ADC: (a) ADC of anterior annulus fibrosus (AAF), (b) ADC of nucleus pulposus (NP), (c) ADC of posterior annulus fibrosus (PAF). Values are scaled using the ADC of cerebrospinal fluid at L3 (4.18×10 -3 mm 2 /s).

Figure 3 -

 3 Figure 3 -Evolution of average dimensionless ADC of nucleus pulposus (NP), anterior annulus fibrosus (AAF) and posterior annulus fibrosus (PAF) from below the thoracolumbar junction, i.e. L1-L2 to lumbosacral junction, i.e. L5-S1. ADC values are scaled using the ADC of cerebrospinal fluid (4.18×10 -3 mm 2 /s) at L3. Disc co-ordinates are scaled using L1-L2, L5-S1 distance.and cubic polynomial curve fittings are associated.

Figure 4 -

 4 Figure 4 -Evolution of average dimensionless ADC of nucleus pulposus (NP), anterior annulus fibrosus (AAF) and posterior annulus fibrosus (PAF) along local antero-posterior path of L1-L2 to L5-S1 discs. ADC values are scaled using ADC of local nucleus pulposus. Local co-ordinates are scaled using AAF, PAF distance and quadratic polynomial curve fittings are associated.

  reference

Table 2 :Figure 1 -

 21 Figure 1 -Lumbar MR imaging in the sagittal plane: (a) T2 imaging, (b) Semi-automated segmentation and automated volume reconstruction of IVD from MRI slices using tactile device Wacom® Cintiq 21 UX, (c) STIR imaging, (d) Map of ADC (10 -6 mm 2 /s, grayrainbow clut) showing ROIs in nucleus pulposus (NP), anterior annulus fibrosus (AAF) and posterior annulus fibrosus (PAF).

Figure 2 -Figure 3 -Figure 4 -

 234 Figure 2-Box-plots of average dimensionless ADC: (a) ADC of anterior annulus fibrosus (AAF), (b) ADC of nucleus pulposus (NP), (c) ADC of posterior annulus fibrosus (PAF). Values are scaled using the ADC of cerebrospinal fluid at L3 (4.18×10 -3 mm 2 /s).

Table 1 :

 1 ADC values of nucleus pulposus (10 -3 mm 2 /s) of adult and young adult population

				ex-vivo asymptomatic degeneration	ADC
	Kerttula et al. (2000)			x				1.2 -1.8
	Antoniou et al. (2004)	x						1.1 -1.3
	Kealey et al. (2005)				x				1.97 -2.35
									x		1.72 -2.22
	Tokuda et al. (2007)			x				1.94
	Ludescher et al. (2008)			x				1.2 -2.2
	Wu et al. (2013)				x				1.9
	Jarman et al. (2014)				x				1.5
	Yu et al. (2014)				x				1.61 -1.81
	Zhang et al. (2014)						x		1.4 -1.6
	Shen et al. (2016)				x				1.93 -2.17
	Wong et al. (2019)						x		2.08 -2.26
	a -NP					Subjects
	#1	#2	#3	#4	#5	#6	#7	#8	#9	#10 #11 #12	mean
	L1/L2 2.10 2.88 1.70 2.19 2.23 2.65 2.49 2.37 2.10 2.20 2.27 2.13 2.28 SD 0.3
	L2/L3 2.22 2.82 2.15 2.25 2.42 2.40 2.62 2.48 2.16 2.29 2.34 2.10 2.35 SD 0.21
	L3/L4 2.19 2.45 1.97 2.13 2.11 2.24 2.38 2.27 2.08 2.21 2.38 2.13 2.21 SD 0.14
	L4/L5 2.10 2.31 1.78 2.26 2.36 2.22 2.28 2.26 2.21 2.33 2.45 2.01 2.21 SD 0.18
	L5/S1 2.08 2.10 1.97 2.26 2.19 2.55 1.83 2.19 2.08 2.29 2.51 1.98 2.17 SD 0.21
	b -AAF
	L1/L2 0.38 0.06 0.50 0.38 0.22 1.05 0.97 0.32 0.93 0.56 0.71 0.81 0.57 SD 0.32
	L2/L3 0.83 0.10 0.60 0.45 0.99 0.81 0.89 0.25 0.84 0.41 0.88 0.43 0.66 SD 0.26
	L3/L4 0.74 1.50 1.10 1.80 0.52 1.46 1.53 1.09 0.86 0.20 1.71 0.83 1.11 SD 0.50
	L4/L5 1.03 1.90 1.50 1.76 1.42 1.86 1.81 0.92 2.56 1.35 1.90 1.15 1.53 SD 0.36
	L5/S1 1.38 1.31 1.20 1.29 1.32 1.22 1.34 0.97 1.44 1.81 1.86 0.49 1.30 SD 0.35
	c-PAF
	L1/L2 0.56 2.05 1.10 0.97 1.04 1.30 1.10 0.94 1.07 0.58 0.98 1.30 1.08 SD 0.38
	L2/L3 1.22 0.69 0.90 0.42 1.04 1.17 0.77 0.78 0.95 1.16 1.23 0.70 0.92 SD 0.26
	L3/L4 1.55 0.57 0.85 0.21 0.85 1.47 0.43 0.80 0.55 1.13 1.15 0.91 0.87 SD 0.40
	L4/L5 1.19 0.49 0.70 0.27 0.03 1.29 0.55 1.16 0.35 1.30 0.95 0.31 0.72 SD 0.45
	L5/S1 0.97 0.59 0.68 0.33 0.70 1.57 0.65 0.54 0.64 0.71 0.81 0.64 0.74 SD 0.30

Acknowledgements

We are grateful to the Fondation Cotrel (Institut de France) for its on-going support of our research on idiopathic scoliosis. We thank SFCR (Société Française de chirurgie Rachidienne) for R. Compagnon's scholarship (MD). We are grateful to C. Baunin MD who managed MRI data collection. We are grateful to Jérôme Briot PhD, who developed the Biomechlab® software.

data analysis and interpretation, validation of submitted version.


B Malard

J Pilch

P Sittner

R Delville²

C Curfs

In-situ investigation of the fast microstructure evolution during electropulse treatment of cold drawn NiTi wires

Keywords: shape memory alloys (SMA), recovery, recrystallization, Joule heating, superelasticity Naformátováno: Doprava

Microstructure changes taking place during the heat treatment of cold-worked NiTi alloy are of key interest in SMA technology since they are responsible for setting the austenite shape and functional properties of the heat treated alloy. Although these microstructure changes probably occur with extremely fast kinetics, conventional heat treatments of NiTi in a furnace commonly last for several minutes or hours. Short heat treatments can be performed e.g. via Joule heating by electric current or by laser treatments. In this work, microstructure changes taking place during non-conventional fast heat treatment of thin NiTi filaments by short pulse of controlled electric power were investigated by high speed in-situ synchrotron X-ray diffraction with simultaneous evaluation of tensile force and electrical resistance of the treated wire. The results provide direct experimental evidence on the evolution of the internal strain (stress) and density of defects during the fast heating of the wire from 20 o C to ~700 o C. This evidence is used, together with the earlier reported results of TEM investigations of microstructures in treated wires, to identify a sequence of dynamic processes responsible for the microstructure changes during the fast heating. Based on this knowledge an interpretation of the experimentally recorded variation of the tensile stress and electric resistance during the treatment is proposed.

Introduction

Martensitically transforming shape memory alloys (SMA) such as the near equiatomic NiTi alloy [START_REF] Otsuka | [END_REF] have attracted considerable attention for their unique functional thermomechanical properties such as superelasticity or shape memory effect. Conventionally, NiTi wires are being produced from cast ingots by extrusion into bars followed by multiple hot working passes finished by a final cold drawing into thin wires. In this so called "cold-worked" (as-drawn, hard, etc.) state, the alloy possesses a heavily deformed microstructure resulting from severe plastic deformation [2] consisting of a mixture of austenite, martensite and amorphous phases with defects and internal strain [3]. In the cold-worked state, the wires do not show any functional property since the martensitic transformation is suppressed. As-drawn NiTi wires need to be heat treated so their cold-worked microstructure changes into an annealed microstructure in which the wire shows the desired functional properties. At the same time, if the shape of a SMA element is constrained during this final heat treatment, it acquires this shape as a new "parent austenite shape". The final thermomechanical treatment has thus two goals which must be fulfilled simultaneously -setting the functional properties and setting the shape of the NiTi wire.

The effect of severe cold working on microstructure and properties of NiTi was thoroughly investigated by several research groups using techniques such as cold drawing [4][5][6], cold rolling [2,7,8], high pressure torsion [9,10] or equal channel angular extrusion [11,12] all showing relatively easy partial amorphisation of NiTi. Subsequent heat treatment produces ultra-fine grained, i.e. nano-or sub-microcrystalline microstructures which provide NiTi with excellent mechanical and functional properties [2][3][4][5][6][7][8][9][10][11][12]. Conventionally, the final heat treatment of NiTi is being performed in environmental furnaces [13][START_REF] Morgan | proceedings of MPMD 2003[END_REF][START_REF] Pelton | [END_REF][16][17]. The effect of the final heat treatment temperature and time on the microstructures, martensitic transformations and mechanical properties of NiTi is now well documented [START_REF] Otsuka | [END_REF][START_REF] Morgan | proceedings of MPMD 2003[END_REF] and is routinely used to manufacture NiTi wires with optimized mechanical and functional properties [3,[START_REF] Pelton | [END_REF]. Depending on the alloy (chemical composition, cold work) and desired application, the typically used heat treatment conditions vary in the range of temperatures 400 o C -600 o C and time 10 -60 minutes [START_REF] Morgan | proceedings of MPMD 2003[END_REF][START_REF] Pelton | [END_REF]. In addition to the microstructure recovery, diffusion-driven processes such as precipitation or dissolution of precipitates [13] affecting the transformation temperatures and through them the functional properties may also take place depending on the alloy composition, temperature and time of the treatment. The obtained mechanical properties of the heat treated wire (strength, yield stress for plasticity, ductility) as well as functional properties (superelasticity, plateau stress, transformation strain) are thus affected by both the microstructure recovery and diffusion processes. This makes the heat treatment of superelastic NiTi rather complicated, particularly since it is typically performed in the temperature range 400 o C -600 o C, where the matrix composition can be varied [13] by precipitation and/or dissolution of Ti 3 Ni 4 precipitates and, at the same time, where recrystallization of the cold-worked microstructure takes place during the heat treatment. The influence of microstructure recovery and diffusion processes on functional properties must be hence carefully considered when searching for optimized heat treatment conditions for specific NiTi application [START_REF] Pelton | [END_REF]. It is of course possible to decouple these two effects by performing the short annealing treatments on solution treated NiTi alloys [13]. Such alloys are, however, out of the technological interest since their strength is low.

If the shape of the wire is constrained during the heat treatment, there is always a tensile stress increase appearing in the early stage of the heating since the cold-worked NiTi wire exhibits negative thermal expansion [18] and its elastic modulus increases with increasing temperature. The tensile stress likely affects not only the final shape [16] but also the functional properties of the treated wire. As a special case, a relatively small constant tensile force is applied during the straight annealing treatment of superelastic NiTi wires [3]. Although this stress (20 -100 MPa [START_REF] Pelton | [END_REF]) is an important technological parameter of the NiTi wire production process, little is known about its role in the shape and functional property setting mechanism [16].

Recently, the relatively long time of the conventional heat treatment of NiTi wires in environmental furnace has become an obstacle for emerging technology of hybrid textile fabrics knitted or woven using continuous NiTi filaments. Maximum respooling speed of ~1 m/ min achievable with the straight annealing treatment in conventional ~6 m long tubular electrical furnaces is painfully slow for textile processing of NiTi filaments. To solve this technological problem we have investigated the possibility to heat treat continuous long thin NiTi filaments by passing electric current through it [18][START_REF] Pilch | Proc. of the ESOMAT[END_REF][START_REF]Patent applications[END_REF][START_REF] Delville | [END_REF][22]. The electric current generates heat in the entire volume of the wire with extremely high speed. Taking advantage of that, we have developed a method called "Final ThermoMechanical Treatment by Electric Current" /FTMT-EC/ for fast processing of NiTi filaments [START_REF] Pilch | Proc. of the ESOMAT[END_REF][START_REF]Patent applications[END_REF] in hybrid textile production. The thin superelastic NiTi wires heat treated by the FTMT-EC method display excellent functional properties which can be relatively easily tailored to the end-user needs [START_REF] Pilch | Proc. of the ESOMAT[END_REF]. Fig. 1 [21] compares bright field TEM images of microstructures observed in NiTi wires treated by short electric current pulses with power P = 125 W for time t = 8, 12, 14, 18 ms with tensile superelastic stress-strain responses of these wires in 10 tensile cycles at room temperature. Note that following a single electric power pulse of 125 W lasting for 12 ms the wire shows excellent superelastic functional properties, high strength and relatively stable cyclic superelastic stress-strain response at room temperature (Fig. 1c). Though this is not very clear from TEM micrographs in Fig. 1, there is a very large difference between the microstructure of the cold-worked wire and the nanosized, partially polygonized/recrystallized microstructure of the 125 W / 12 ms treated wire. A dedicated TEM study of these microstructures can be found in [START_REF] Delville | [END_REF]. The processes responsible for the changes of microstructure and functional properties are of interest in this work. The processes bringing about the microstructure and functional property changes of the NiTi wires during the heat treatment can proceed very fast -in milliseconds instead of minutes or hours commonly used in conventional heat treatments in a furnace. It is essential that the temperature rise during the electric current heating with the rate of about 50000 o C.s -1 can be controlled with

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sufficient precision [START_REF] Delville | [END_REF]. The FTMT-EC method allows for performing in-situ experimental investigation of the recovery and recrystallization processes close to the rate at which they actually proceed during the heat treatment. We performed such investigation using in-situ high speed synchrotron X-ray diffraction with simultaneous tensile force and electrical resistance measurements. The results are reported in this paper. The aim was to better understand the processes responsible for the microstructure changes during the treatment as observed by TEM in our related work [18,[START_REF] Delville | [END_REF]22] as well as to interpret the complex variation of the tensile stress and electric resistance recorded during the FTMT-EC treatments [START_REF] Pilch | Proc. of the ESOMAT[END_REF]. The ultimate goal of this research was to establish a knowledge base for the relation between the parameters of the FTMT-EC treatment and superelastic functional properties of the treated NiTi filaments [START_REF] Pilch | Proc. of the ESOMAT[END_REF].

Experiment and method

Heat treatment

The experiments were performed using as-drawn NiTi wires (56.0 wt. % Ni) having a diameter d= 0.1 mm (Fort Wayne Metals #1). The wire is first mounted on the miniature deformation rig especially designed and built for efficient testing of functional thermomechanical properties of thin NiTi filaments in tension. The rig consists of a stepping motor, a 100 N load cell, electrically isolated grips, a Peltier furnace to control the environmental temperature and prevent air circulation, a laser micrometer for strain measurement and special electronics allowing to send controlled electric power pulse to heat the NiTi wire up to the melting point and perform simultaneously electric resistance measurement.

The initial length l 0 (~50 mm) and electrical resistance ρ 0 of the wire at room temperature were first measured. The wire was then preloaded to the tensile stress σ 0 = 400 MPa and its length was constrained. Following that, the treatment was performed by a single controlled electric power pulse P(t) (Fig. 2). The wire temperature, T(t) is calculated according to Eq. 1, taking into account the Joule heat supply P and the ambient temperature losses.

( ) ( ) 4 ) ( T A T t T h P t T dt d C ext p ⋅ ⋅ ⋅ - - ⋅ - = σ ε (1) 2 05 . 107 002645 . 0 647 . 24 - - + = T T C p (2)
The heat capacity C p was taken from the literature [23] in the form of Eq. 2, σ is a Stefan-Boltzman constant and A is the surface area of the wire. The specific heat transfer coefficient, h, describing the heat dissipation into air per unit time and the NiTi wire emissivity, ε, needed for the calculation of the radiation heat loss per unit time were indentified from a series of calibration experiments. Other effects influencing the wire temperature such as heat conduction losses into grips and latent heats were neglected. The Eq. 1 with particular coefficients h, ε, thus applies only for the environmental conditions at which the calibration was made.

In the experiments described below, only two parameters of the electric power pulse (maximum power P and pulse duration t_ 2 ) are used characterize the treatments for simplicity. Alternatively, each treatment can be characterized by the temperature history T = T(t) the wire is exposed during the treatment calculated by the equation 1 . Fig. 2b shows the wire temperature evolving during heating by electric pulses having parameters P= 2, 3, 4, 5, 6 W; t _2 = 0.9 s and P= 10 W, t _2 = 0.18 s. The values of electric power used throughout the paper to denote individual treatments are the normalized values for 100 mm long wire. Pulse durations t_ 2 = 0.9 s and 0.18 s were selected due to limited reading time of the X-ray detection. They are much longer than pulse durations t_ 2 =

0.001 -0.018 s used in the previous ex-situ studies [18,2,22]. Nevertheless, it will be shown below that one can obtain quite similar functional properties of the treated wires. As the temperature of the NiTi wire rises during the FTMT-EC treatment, the electrical resistivity of the wire should increase and tensile stress should decrease linearly with increasing temperature. This is exactly the case for an already heat-treated NiTi wire exposed to electric pulse (Fig. 2c,d).

Note that the applied voltage and current (Fig. 2c) vary with the electric resistance of the wire

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which is changing during the treatment. In case of the FTMT-EC treatment of the cold-worked wire, in addition to the reversible expansion and electric resistance changes, the microstructure of the cold-worked wire evolves towards the annealed microstructure during the treatment. This brings about additional significant irreversible variation of the electric resistance and tensile stress. These changes superimpose on the linear reversible changes of the electric resistance and tensile stress with temperature. As already mentioned, this paper deals with the results of in-situ synchrotron X-ray diffraction studies during the treatments. The electric resistance of the wire, macroscopic tensile force and X-ray diffraction signal varying during the treatment were simultaneously evaluated during the treatments. After the treatment was finished, superelastic response of the already treated wire was evaluated in 10 tensile cycles at room temperature using the same stress rig. Electric resistance of the NiTi wire was evaluated during the tensile testing.

The recorded superelastic stress-strain curves including their stability during cyclic loading serve in the following as measures of the achieved functional superelastic properties of the treated wires.

Synchrotron X-ray diffraction

Synchrotron radiation enables to extend the X-ray measurements from the static to the dynamic regime, thanks to its unique time structure and very high flux even at high energy, which reduces considerably the data collection time. Very fast time resolution down to the picosecond regime is achievable with stroboscopic studies of reversible phenomena [24]. In case of the irreversible microstructure evolution in metals, the X-ray data have to be acquired on a single shot basis requiring high flux source, very fast and sensitive data acquisition system and a high speed data transfer. This has become recently possible with hard synchrotron X-ray sources and latest X-ray camera detector development [25].

The experiment was performed on diffractometer ID11 at the European Synchrotron Radiation Facility (ESRF) in Grenoble. A monochromatic X-ray beam with energy of 45 keV (λ ~ 0.27552 Å) is obtained with a Laue monochromator. The beam is focussed down to 1 mm in vertical direction by bending the Laue crystal and down to 100 µm in horizontal direction. FreLON2K 2D camera with taper has been chosen as a fast detection system [25]. In order to speed up the data acquisition for the targeted 10 ms time resolution, a radial slice of the 2D detector (Fig. 3a) is used. The thin NiTi wire mounted between the grips of the stress rig is positioned vertically in the beam (Fig. 3a). The heat treatment experiment is performed with synchronized pulse, force, electrical resistivity and diffraction measurements (Fig. 4a). A strip of 2048 x 64 pixels is acquired and transformed in order to obtain a line of 2048 x 1 pixels. Then, this line is read out of the CCD and stored before the next image is acquired. Afterwards, 300 lines are put together into a single 2D binary image which represents the evolution of the diffraction patterns versus time, as illustrated in

Fig. 3b. To minimise the time needed to read out the line down to 10ms, the 64 active pixels have to be chosen at the bottom edge of the camera. The part of the detection area, which is not active, is masked by a lead mask. By using such kinetic mode of the data acquisition by the FReLON camera, it has been possible to acquire 100 diffraction patterns per second with a readout time of less than 1 ms between 2 images.

Fig. 4: Synchronisation between the electric power pulse and X-ray measurements

A calibration was performed to obtain a diffraction pattern of the intensity versus the diffraction angle for the kinetic mode as follows. A very fine capillary of 300 µm with LaB 6 powder was placed at the NiTi wire position and 2D diffraction pattern was acquired. The position of each LaB 6 peak in pixels was measured using the DASH software [26] and the corresponding diffraction angle was calculated. The calculated calibration function relating the diffraction angle to the pixel number was used to transform each line of the experimental pattern (intensity versus pixel) into a diffraction pattern (intensity versus diffraction angle). Since the beam centre is in the middle of the detector, the right side of the diffraction pattern is added to its left side to increase the data statistics.

In order to obtain an etalon for stress-free NiTi diffraction pattern, NiTi powder of similar composition as that of the wire was placed in the same container as used for the LaB 6 and diffraction pattern was acquired. Since the NiTi powder exists in a mixture of austenite and martensite phases at room temperature, the diffraction pattern contains both austenite and martensite diffraction lines. The NiTi powder gives diffraction pattern with much better resolution (Fig. 5a) than the thin as-drawn NiTi wires (Fig. 5b). This is due to the complex microstructure of the thin cold-worked NiTi wires consisting of a mixture of heavily deformed austenite, R-phase, martensite and amorphous phases with frozen-in internal stresses (Fig. 5b). On the other hand since the martensite phase in the as-drawn wire was created by stress during final cold drawing, not all marteniste peaks from Fig. 5a appear in the diffraction pattern in Fig. 5b due to the very strong texture in stress induced martensite [27]. During the heat treatment, as the temperature increases, the martensite and amorphous phases disappear together with defects and internal stress in the austenite phase. This is evidenced by the dramatic evolution of the X-ray diffraction pattern during heating (Fig. 5d-g). The pattern shifts left and right, increases in intensity and decreases in width during the treatment. Following all heat treatments the microstructure of the wire is essentially austenitic as evidenced by narrow profile corresponding to single {011} austenitic peaks of the treated wires (Fig. 5c). The recorded diffraction patterns were fitted using one austenite {110} and three martensite peaks (Fig. 5b). The {110} austenite reflection was analyzed for peak intensity, peak position and peak width (FWHM) using the LAMP software [28] as well as the GSAS software [29] considering the structure of the austenite phase Pm-3m, R phase P-3 and martensitic phase P2 1 /m [START_REF] Otsuka | [END_REF]. d-g show diffraction pattern evolution with time recorded during the electric pulse treatments with 2 W (d), 3 W (e), 6 W (f) and 10 W (g). In the case of the P= 6 W/ 0.9 s treatment there is missing data due to the fact that the wire moves out of the X-ray beam.

Experimental Results

Heat treatment experiments

The heat treatment experiments were performed using different power P= 2, 3, 4, 5, 6 W (t_ 2 = 0.9 s) and 10 W (t_ 2 = 0.18 s). Same experiments were performed once with simultaneous in-situ X-ray diffraction measurement and several times without the X-rays. The reproducibility is very good in the sense that same functional properties of the wires were achieved in treatments performed with the same P, t_ 2 parameters. The results are shown in Fig. 6 as the variations of the supplied electric power (1, blue), tensile stress (2, black), temperature (3, red) and electric resistivity (4, green) during the FTMT-EC pulse on the left side and the obtained superelastic stress-strain response with superimposed variation of the electric resistivity of the wire on the right side. The left side in-situ responses serve as a kind of "signature" for the performed FTMT-EC treatment which can be associated with the achieved superelastic functional response of the treated wire. More detailed results of multiple FTMT-EC treatments using P= 2 -7 W/ t_ 2 = 0.9 s can be found in related work [START_REF] Pilch | Proc. of the ESOMAT[END_REF].

As already mentioned, the experimentally measured evolution of tensile stress and electric resistance during the heat treatment of the cold-worked wire reflects the progress of the microstructure recovery of the cold-worked wire. The relevant responses are, however, superimposed on the linear thermal dependences of the strain (and hence the tensile stress due to the applied constraint) and electrical resistivity (see Fig. 2d). Interpretation of the experimentally observed tensile stress and electric resistance responses during the treatments of cold-worked NiTi wire (Figs. 6 and7) is thus not easy. It is expected that the tensile stress evolves with time (temperature) due to the several possible mutually competing deformation mechanisms including: i) reverse transformation of martensite and relaxation of residual stress frozen in the as-drawn wire, ii) thermal expansion/contraction, iii) dynamic recrystallization and/or plastic deformation processes at high temperature and stress, iv) martensitic phase transformations B2-R-B19'.

The tensile stress starts to increase with increasing temperature right after the onset of heating (Fig. 6). We assume that this is due to the reverse transformation of the retained martensite coupled with the relaxation of residual stress frozen in the heavily cold-worked microstructure of the asdrawn NiTi wire (i). Note that the mechanism (i) results in wire shortening even if the mechanism (ii) (conventional thermal expansion) acting simultaneously tends to elongate the wire. As a result, the cold-worked wire shows negative thermal expansion. Because of that the tensile stress increases with the increasing temperature from the preset 400 MPa at room temperature up to ~ 350 o C (depending on the used heating rate), where it reaches a maximum of ~650 MPa (Figs. 6 and7) and then falls down, basically till zero stress if the maximum reached temperature is high enough. As explained in detail further below, we propose that this dramatic change in tensile stress response to increasing temperature is due to the termination of the activity of the mechanism (i) combined with plastic deformation associated with dynamic recrystallization at elevated temperature and stress (iii) and thermal expansion (ii). Upon cooling, the stress varies basically due to conventional thermal contraction (ii) and stress-induced B2-R phase transformation below 50 o C. The electric resistivity is expected to evolve with time (temperature) due to: i) intrinsic thermal dependence of the resistivity of a metallic wire, ii) recovery processes causing irreversible microstructure changes, iii) dynamic recrystallization and/or plastic deformation processes at high temperature and stress, iv) martensitic phase transformations B2-R-B19'.

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The electric resistivity does not change with increasing temperature till ~200 o C (Figs. 6 and7) where it starts to decrease. It decreases monotonically during further heating until it reaches a plateau at ~75 % of its starting value (Fig. 7). We assume that the decrease of the electric resistivity of the wire with increasing temperature is caused by the recovery and/or recrystallization processes responsible for the microstructure changes during the treatment. Note that if this is the case, the microstructure changes causing essential decrease of the density of defects terminate much before the maximum temperature is reached. Upon cooling, the electrical resistivity decreases due to conventional thermal dependence of the electric resistance of a metal (see Fig. 2d). Finally, as the temperature decreases down to ~50 ° C, the electrical resistivity may increase again due to the B2-R phase transformation (Fig. 7 curves b,c) since the R-phase has a higher electrical resistivity then the B2 phase [30]. The total change of the electric resistance before treatment (1.45 Ωµm) and after treatment (0.88 Ωµm) treatment reaches ~ 40 % in case of fully treated wires (Fig. 7 curves d-f). The change of electric resistivity measured at room temperature before and after treatment can be fully ascribed to the microstructure changes caused by the treatment. Note that the above outlined qualitative interpretation of the results of in-situ tensile stress and electric resistance measurements is apparently based only on the concerned evidence. In fact, it is not quite that, we could arrive to it only with the help of the direct structural sensitive information on the irreversible microstructure changes taken from the in-situ synchrotron X-ray studies presented below. The interpretation is hence more detailed in section 4.1 after the presentation of X-ray results in the next section.

Heat treatment experiments with in-situ X-ray diffraction

In contrast to the in-situ tensile stress and electric resistance, the in-situ synchrotron X-ray data reflects mainly the irreversible microstructure changes during the FTMT-EC treatment. Exception is the change of the peak position with temperature which is partially due to reversible thermal expansion/contraction. Figs. 3b, 5d-g show the evolution of the diffraction patterns as it was measured by the 2D detector during the X-ray diffraction experiments using pulses with power P= 2, 3, 6 and 10 W. It can be seen that the broadened diffraction pattern corresponding to the complex microstructure of the as-drawn wire (Fig. 5b) evolves into the well-defined narrow single austenite peak of the heat-treated NiTi wire (Fig. 5c). The results of the analysis of the fit of the profile of the {110} austenitic peak (Fig. 5b,c) are plotted in dependence on the time and temperature in Fig. 8.

In order to present the complete data obtained from the in-situ synchrotron X-ray experiment, Figs. 8a-d show the evolution of the tensile stress (Figs. 8a,b) and electric resistivity (Figs. 8c,d) evaluated simultaneously with the X-ray data. The results are essentially the same as those reported in Fig. 7. Small differences come from different sample environments: no Peltier furnace was used and a vertical orientation of treated wire was used in the in-situ X-ray experiment Figs. 8e,f show the evolution of the intensity of the {110} austenite peak (peak height) during heat treatments with P= 2, 3, 6 and 10 W pulses. The higher is the temperature reached in the treatment, the larger is the maximum peak intensity after the treatment. The change of the peak intensity is related mainly to the change of its profile during the treatment (Fig 5d-g). Integrated intensity (Figs. 8k,l) is changing marginally during the heat treatment. In later stages of the heating, the increase of the peak intensity is also due to the texture evolution during heating which could not be evaluated in this experiment since only single diffraction peak was analyzed. Partial information on the evolution of austenite texture during the FTMT-EC treatment can be obtained from the results of the related ex-situ X-ray studies [18]. The change of the peak intensity by the treatment is permanent and increases with maximum temperature reached in the treatment. In case of the P= Naformátováno: Doprava Naformátováno: Angličtina (USA) 10 W/ 0.18 s treatment the peak intensity starts and stops to increase earlier due to the fact that the temperature rises faster for this shorter pulse (Fig. 2b).

Figs. 8g,h show the evolution of {110} austenite peak position recalculated into "radial strain"lattice strain of the {110} austenitic peak (Eqs. (3-5)) for treatment with P= 2, 3, 6 and 10 W pulses. Radial strain refers to the transverse component of the elastic strain in family of grains of the austenite phase oriented with <110> direction oriented perpendicularly to the wire axis. Using the Bragg law (Eq. ( 3)) and the definition of lattice strain (Eq. ( 4)), an expression for the radial strain of the {110} austenitic peak ε 110 is given by Eq. ( 5).

∆ = - = ε ε ε ε (4) 110 , 0 110 110 θ θ θ θ ε ε ε ε - = ( 5
)
θ 110 is the value of the Bragg angle of the {110} austenitic peak in the wire during the heat treatment and θ 0, 110 is the value of the Bragg angle of the {110} austenitic peak measured on the NiTi powder. Because the radial strain in the wire before the heat treatment is strongly negative, it means that the grains of the austenite phase oriented with <110> direction oriented perpendicularly to the wire axis in the as-drawn NiTi wire experience a tensile stress along the wire axis. Recall, however, that there are other austenite grains as well as the martensite and amorphous phases in the microstructure of the as-drawn wire. Since the stress must be balanced, we take the measured negative radial strains as an evidence for the existence of very strong internal intergranular stresses existing in the microstructure of the cold-worked wire. Note also that before and after treatments at room temperature, the wire is under ~400 MPa external tensile stress which affect the evaluated radial strain (see Figs. 6 and7).

As the temperature increases during the heat treatment, the austenite lattice expands in radial direction presumably due to three processes: i) isotropic thermal expansion, ii) directional decrease of the frozen-in internal tensile stress and iii) decrease of the external tensile stress varying nonmonotonously during the treatment (Fig. 7a). The radial strain recorded at temperatures different from the room temperature is thus biased by the reversible thermal expansion/contraction. The radial strain thus increases and decreases with the raising and falling temperature (process i) and external stress (process iii) during the FTMT-EC treatment (Fig. 8h). Nevertheless, we clearly see that the radial strain after cooling down to room temperature never returns to its original starting value after any of the studied treatments. Particularly, after the 6 W and 10 W treatments, the radial strain approaches nearly zero (slightly negative value is due to external tensile stress). One should note in this respect that if the cold-worked wire is heat treated in stress-free conditions, it shortens ~3 % and radial strain becomes zero. We explain this by assuming that the internal stress frozen in the wire after the final cold drawing (tensile in austenite, compressive in amorphous) disappears together with the disappearance of the martensite and amorphous phases from the microstructure before the temperature reaches about ~600 o C (Fig. 7). This is why the radial strains after all treatments are in the first approximation similar, small internal stresses probably remained in the microstructure after 3 W and particularly 2 W treatment. Additional evidence supporting the claim that internal strains quickly disappear in relatively early stages of the treatment comes from the related ex-situ X-ray studies [18] showing the behaviour of more components of elastic strain in three austenite peaks during heating. Figs. 8i,j show the evolution of the Full Width at Half Maximum (FWHM) of the {110} austenitic peak for experiments with P= 2, 3, 6 and 10 W pulses. In case of the broadened profile of the coldworked wire (Fig. 5b), the FWHM of the {110} austenitic peak was evaluated to be 0.58 o . It decreases with increasing temperature mainly due to the decrease of the density of defects in the cold-worked microstructure and related strain fields. Theoretically, FWHM may also decrease due to the increase of the grain size of the recrystallized microstructure but this does not seem to be the case since NiTi wires having microstructures with very different grain sizes exhibit {110} austenitic peak profile of the same width (see Fig. 8 in [18]). Following the P= 6 W and 10 W treatments, the FWHM falls down to the saturated value of about 0.1°. The FWHM decreases to only 0.35 ° and 0.2 ° in case of the 2 W and 3 W treatments, respectively, suggesting that the microstructures of such treated wires still contain many crystal defects and related strain fields.

Discussion

The results of the present in-situ experiments basically supplement the results of post heat treatment studies of the same NiTi wires performed earlier by ex-situ synchrotron X-ray [18] and TEM [START_REF] Delville | [END_REF]22] methods. Despite the very different electric power and time used, there are little doubts that the evolution of microstructure, texture and functional properties is similar to that reported in the ex-situ studies [18,[START_REF] Delville | [END_REF]22] (Fig. 1). The lower power P and longer pulse time t _2 were used in present experiments to slow down the progress of the microstructure evolution during the FTMT-EC treatment so that the in-situ X-ray measurements during the selected electropulse treatments could be performed with the targeted 10 ms time resolution. More detailed evidence on the superelastic property setting of NiTi wires by the FTMT-EC method using electric power varying in the range P= 2 -7 W was reported in the closely related article [START_REF] Pilch | Proc. of the ESOMAT[END_REF].

Interpretation of the in-situ tests

The in-situ records of the supplied power, temperature, electric resistance and tensile stress during the heat treatment (Fig. 6) characterize the microstructure evolution during the FTMT-EC treatment. Basically, for a given wire segment, the microstructure evolution in the treated wire is fully controlled by selecting cold worked wire, power pulse parameters and mechanical constraint.

The achieved microstructure is associated with particular functional superelastic response of the wire. The evolution of the electric resistance and tensile stress recorded during the heat treatment provides indirect information on the processes responsible for the microstructure evolution which is relatively easily accessible but difficult to interpret. Recording the electric resistance and force is in fact now routinely used in practical FTMT-EC treatments of NiTi filaments prior to their textile processing [START_REF] Pilch | Proc. of the ESOMAT[END_REF]. In these treatments, electric power parameters and mechanical constraint are selected by the user to achieve the desired superelastic properties of the treated filament. The recorded electric resistance and tensile stress evolution during the treatment are saved as process characteristics for later use. Although the FTMT-EC treatment can be performed without detailed understanding of the physical processes and microstructure evolutions responsible for the electric resistance and tensile stress evolutions, the lack of this knowledge is a barrier for further development of the method. Direct structural and phase specific information on the progress of the recovery processes during heating (Table 1) available from the present X-ray studies is hence of great value in this respect.

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Table 1: Physical processes responsible for fast evolution of the microstructure of cold-worked NiTi wires during electropulse treatment. The processes take place in sequence I-IV as the temperature increases and those dominating in given temperature range are in bold. Plastic deformation occurs only if the wire is exposed to stress. Since we deal with very short time exposure to the high temperatures, any possible creep and diffusion processes having much slower kinetics thought to be suppressed. Results of the in-situ X-ray studies, electrical resistivity and tensile force from the P= 10 W/ 0.18 s treatment are plot together in Fig. 9. The tensile stress increases right from the onset of heating and electric resistance starts to fall at 200 °C before any significant change of the diffraction profile could be detected. Such changes, however, might be below the detection limit of the in-situ X-ray method. There is a large experimental error associated with the analysis of the {110} austenite peak recorded at temperatures up to 300 °C due to restrictions adopted in the fast detection mode.

Physical process occurring during electropulse heating

The increase of the tensile stress with increasing temperature is thus taken as a main evidence for the activity of the process I (Table 1). The process I includes reverse martensitic transformation of the relict martensite coupled with changes of intergranular stresses in the microstructure responsible for the negative thermal expansion of the cold-worked wire. This process is reversible if the maximum achieved temperature remains below 200 o C. It is expected that no irreversible microstructure changes take place upon heating till 200 o C. An alternative way of looking at the process I upon heating below 200 o C would be considering the cold-worked wire as a strain glass which is thermally cycled above Tg [31]. If the maximum temperature achieved in the 2W treatment stays below ~350 o C, the tensile stress response is still in large extent reversible although the forward and reverse branches are different (curve a in Fig. 7). The process I dominates upon fast heating up to ~350 o C (Fig. 7). However, the simple fact that the electric resistance of the wire is not restored after cooling back to room temperature in this case, clearly evidences that irreversible microstructural changes had already taken place during the 2W treatment. Since all parameters of the {110} austenite reflection are clearly different before and after 2 W treatment (Fig. 8), the diffraction results provide a supplemental evidence for that. So what happens in the wire between 200 o C and 350 o C? Electric resistivity (3) and FWHM (5) decreases and the radial strain (4) increases with increasing temperature. This suggests that the density of defects starts to decrease and internal stresses start to disappear from the microstructure between 200 o C and 350 o C reflecting the irreversible microstructure changes due to the process II (Table 1). The 2W treated wire still does not show superelasticity (Fig. 6a) but the density of defects and internal stress in it is significantly lower than in the cold-worked wire. In terms of the strain glass approach [31], the 2 W treated wire would represent a strain glass with less concentration of lattice defects. This view is, however, not further elaborated here. The process II includes recovery of lattice defects through migration, redistribution and annihilation and rearrangement of crystal defects (polygonization) proceeding in parallel with the crystallization from amorphous phase [START_REF] Delville | [END_REF]. At about ~400 o C, the tensile stress (2) passes through a maximum and starts to fall with increasing temperature. The rate of change of electric resistance (3), radial strain (4) and FWHM (5) with increasing temperature (Fig. 9b) is fastest. This is interpreted as follows. As the process I slows down due to the disappearance of martensite and internal stress, the thermal expansion and plastic deformation due to the starting dynamic recrystallization (process III) start to have dominating influence on the tensile stress which starts to decrease. In this stage of the microstructure recovery, the heat treated wire starts to show functional properties due to the phase transformation. The example is the 3 W treated wire (Fig. 6b) for which the electric resistance (curve b in Fig. 7) as well as diffraction results (Fig. 8) clearly evidence that pronounced irreversible microstructure changes due to the process II had already taken place.

At about 500 o C, the tensile stress (2) decrease is fastest while the {110} austenite peak profile changes most dramatically. This is interpreted as being due to pronounced activity of the process III dominated by dynamic recrystallization. The alloy is extremely susceptible to plastic deformation in this stage. Since the plastic deformation is due to the dynamic recrystalization, no additional lattice defects are introduced into the microstructure. The P= 4 W treatment (curve c in Fig. 7) represents an example of a treatment in which the recrystallization had already partially

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taken place. The functional properties of the 4 W treated wire are not, however, yet fully developed. Such treated wires typically show R-phase transformation during tensile cycling as evidenced by the hysteretic electric resistance-strain dependence (Fig. 6c).

At about ~600 o C, the rate of the decrease of electric resistivity (3) with increasing temperature suddenly slows down giving rise to the characteristic knee point on the electric resistivity-time (temperature) records (Figs. 7 and9). This is considered to be an important threshold point in the microstructure evolution upon heating [START_REF] Delville | [END_REF] which is roughly associated with the termination of process II. The processes III, however, further continues on heating beyond 600 o C. Tensile stress (2) decreases to zero, FWHM (5) approaches its minimum saturated level, and the radial strain (4) increase slows down. Although the plastic deformation stops as the tensile stress reaches zero, the wire continues to elongate with increasing temperature due to thermal expansion. This deformation is however reversible on cooling. Since the wire is not stretched by the tensile force for a short time it can move out of the beam. This unfortunately happened in case of 6W treatment. It is the reason for the gap in the diffraction results taken during the 6W treatment (Fig. 8). The shape setting of the NiTi wire is completed [START_REF] Sittner | Behind the shape setting of NiTinol[END_REF] in this stage which roughly corresponds to the 5W treated wire (curve d in Fig. 7). The functional superelastic properties are fully developed (Fig. 6d). However, the intensity of the austenite peak (6) further increases with increasing temperature. This is most likely due to the dramatic change in texture evolution during heating related to the completion of the recrystallization and grain growth now at zero external stress (process IV). Direct evidence on the grain growth and change of texture evolution during the electropulse heat treatment was brought in the related article [18]. The growth of recrystallized grains beyond 600 o C in case of the 6 W treated wire (curve e in Fig. 7) causes a significant deterioration of the functional properties of the wire -yield stress for plasticity and strength decrease [START_REF] Pilch | Proc. of the ESOMAT[END_REF] and superelastic response of the wire during cyclic tensile loading (Fig. 6e) [22] becomes unstable. If the tensile stress persists up to temperatures above 600 C plastic deformation due to slip in the newly formed austenite grains takes place [START_REF] Sittner | Behind the shape setting of NiTinol[END_REF]. This, however, is never the case in present experiments so it is not discussed here.

One may ask what kind of shape setting we refer to if the wire has the same shape and length after treatment as it had before the treatment. Note that the tensile stress levels recorded at room temperature before and after the treatment are similar (Figs. 6). Since elastic modulus of the wire did not change that much during the treatment, this suggests that the length of the wire did not change during the treatment in the first approximation. Considering the high temperature and stress involved (Figs. 7 and9) in the treatments this is apparently surprising. On the other hand this is what the shape setting is for. Recall that an unconstrained wire, if treated by P= 10 W/ 0.18 s, becomes ~3 % shorter while the internal stress and retained martensite disappear from the microstructure. The treated wire does not show the negative thermal expansion characteristic for the untreated cold-worked wire. This can be interpreted as if some sort of plastic deformation processes did occur during the 10W treatment even if the wire length did not change (Fig. 9). The plastic elongation due to process III compensates for the shortening driven by the process I. The P= 10 W/ 0.18 s treatment is thus sufficient for shape setting of the wire and results in its optimal functional properties. Since the shape (length) of the wire is set at the highest temperatures reached in the treatment and the wire shortens upon cooling, tensile stresses recorded at room temperature after all treatments are similar (~400 MPa). The fact that the wire was preloaded to 400 MPa is only coincidence. The shape setting is a remarkable phenomenon and a technologically important process. It deserves a special attention and is treated separately elsewhere [START_REF] Sittner | Behind the shape setting of NiTinol[END_REF]. Let us only emphasize an important point coming out from the present experiments that the shape setting process allowing for setting simultaneously the shape and functional properties of the cold worked filament is directly linked to the dynamic recrystallization process III.

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Finally, the responses recorded during cooling are much easier to understand since no microstructure changes take place during cooling with the exception of possible B2-R phase transformation at lowest temperatures. The tensile stress (2) increases and radial strain (4) decreases during cooling due to linear thermal contraction of the wire under the condition of its constant length. The electric resistivity (3) decreases linearly due to conventional linear thermal dependence of electric resistance of a metal. The peak intensity (6) slightly increases with decreasing temperature and FWHM (5) does not change upon cooling. As the temperature decreases below ~70 o C, the stress (electrical resistivity) starts to slightly decrease (increase) resulting in local maxima (minima) recorded at temperature of about 50 o C (see Figs 7 and9). This is due to the B2-R transformation taking place upon cooling of the already heat treated wire under external constraint. The situation upon cooling is a more complicated in case of low power treatments (curves a,b in Fig. 7), where complete relaxation of internal stresses in the microstructure was not achieved (see radial strain and FWHM in Fig. 8). In fact, depending on the applied treatment, the tensile stress may linearly increase or decrease with increasing temperature during subsequent thermal cycling of the wire (see fig 2b and curve a in fig 6a). This offers an attractive opportunity to tune the coefficient of thermal expansion of the treated filament in a wide range from a negative to positive value. Considering the high strength and low modulus of the low power treated NiTi wires (Fig. 6a), this opportunity to adjust the negative coefficient of thermal expansion of the NiTi wire as required brings additional benefits for its smart structure or textile applications.

Application and peculiarities of the FTMT-EC treatment

Taking into account also the results of earlier TEM [START_REF] Delville | [END_REF]22] and X-ray [18] studies, it can be concluded that essential microstructure changes bringing about the functional properties of the NiTi wire take gradually place in present heat treatments as the temperature is raising from ~200 o C to ~700 C. If one wants to set the functional properties as desired, one needs to be able to control the progress of the microstructure evolution during heating due to the processes I-III (Table 1 and above discussion of Fig. 9). The question is whether it is possible to control the progress of these processes since they are triggered at different temperatures and have very different kinetics at different temperatures as discussed above. In conventional furnace treatment, the processes basically occur in an uncontrolled manner as soon as the wire enters the pre-heated furnace.

Obviously, precise control of the progress of the multiple processes having fast kinetics (timescale < 1 ms) at different temperatures is not possible using environmental furnace treatment. Hence, the temperature in the furnace must be selected so that the progress of the desired recovery processes slowly reaches saturation during the relatively long heat treatment time of several minutes or hours. This brings into play diffusion processes [13] characterised by much slower kinetics (timescale > 10 minutes). The diffusion processes such as precipitation or dissolution of precipitates taking place during the longer exposure of the wire to elevated temperatures affect the functional properties of medical thin NiTi wires as well [17]. Hence, using furnace treatments, it becomes difficult to distinguish whether the functional property change caused by the heat treatment is due to the microstructure recovery or due to the diffusion processes. Since the activity of the precipitation processes is thought to be largely suppressed in the short time FTMT-EC treatments, it is possible to establish the true heat treatment parameter -microstructurefunctional property relationship for the treated NiTi wires [18,[START_REF] Delville | [END_REF].

As noted in the introduction practical motivation for this research was to find out the parameters of the FTMT-EC treatment which lead to optimum superelastic functional properties of the treated NiTi wires. The FTMT-EC treatment relies mainly on the precise control of the temperature profile T(t) during heating. It comes out that, among the performed treatments, the optimal ones would be the P= 5 W/ 0.9 s or P= 10 W/ 0.18 s. The P= 3 W/ 0.9 s treatment is not sufficient to allow for the

full development of the stress-induced transformation and plateau type superelasticity during tensile test, while the P= 6 W/ 0.9 s treatment results in a loss of stability of the superelastic behaviour due to plastic deformation accompanying the stress-induced phase transformation during tensile cycling. It is known from the earlier ex-situ studies performed using P= 125 W and pulse time 1 -18 ms [START_REF] Delville | [END_REF] that the microstructure corresponding to optimum stable superelastic response of the wire is a partially polygonized/recrystallized microstructure with grain size 20 -50 nm. The P= 10 W/ 0.18 s treated wire is assumed to possess a very similar microstructure to that found in the 125W/ 12ms treated wire (Fig. 1c) although no direct TEM evidence is available. As reported in the related paper [22], the superelastic response of such treated wire is stable since the stress-induced martensitic transformation can proceed in the nanosized microstructure while the dislocation generation at the propagating habit plane interfaces and/or slip in the martensite phase are suppressed by the small grain size.

The FTMT-EC treatment of thin NiTi filament is conveniently characterized by the evolution of temperature, electric resistivity and tensile stress during the treatment. Based on the results of the in-situ X-ray studies reported in this paper it became possible to interpret the rather complex electric resistivity and tensile stress responses in terms of the activity of several distinct processes triggered at different temperatures during heating (Fig. 9). Although it was possible to follow the progress of the microstructure evolution during the electropulse heating by the in-situ X-ray measurements, it is difficult to discuss the kinetics of individual recovery processes. In spite of the rather large heating rates used (reaching ~3500 o C.s -1 in case of the P= 10 W/ 0.18 s treatment), the processes seem to be still fast enough to follow the prescribed T(t) profile. Nonetheless, the fact that individual responses shown in Fig. 7 do not follow same path upon heating is thought to be experimental evidence suggesting that the intrinsic kinetics of individual processes does matter. The heating rate is even much higher (~50000 o C.s -1 ) in case of the shorter P= 125 W treatments used in the earlier ex-situ experiments [18,[START_REF] Delville | [END_REF]. In this case, the intrinsic kinetics of the recovery processes evidently plays a much more important role (note Fig. 8 in [START_REF] Delville | [END_REF]).

Although the same processes take place also during conventional heat treatments in a furnace, there are significant differences which need to be emphasized. First is the very fast rate of temperature increase during the FTMT-EC treatment leading most likely to extreme overheating during the short pulse FTMT-EC treatment. The overheating selectively affects individual processes having different intrinsic kinetics. Second is the mechanical stress action on the processes which can be partially controlled in the FTMT-EC treatment by applying suitable external constraint. Third is the possible direct action of passing electrons [START_REF] Conrad | [END_REF] on the individual processes as point defect mobility [34], recrystallization [START_REF] Conrad | [END_REF]35] as well as plastic deformation [START_REF] Conrad | [END_REF]36,37]. We did not particularly elaborate the possible role of direct effects of the electric current so far. The peak electric current densities used in the present experiments are in the range 10 4 -10 5 A.cm -2 . According to the literature, it seems that the major effect of the electric current (continuous or pulsed current with densities larger than 10 3 A.cm -2 ) on the recrystallization is an enhancement of the recrystallization rate in early stages resulting in finer recrystallized grain size [START_REF] Conrad | [END_REF]35]. Subsequent grain growth is, however, enhanced as well. Electric current applied during plastic deformation does not alter the physical deformation mechanism but mainly reduces the thermal component of the flow stress causing a significant increase in plastic strain rate at given temperature [START_REF] Conrad | [END_REF]36,37]. In contrast to the earlier literature studies, where DC pulsed or AC electric current were employed under quasistatic thermomechanical conditions commonly together with external environmental heating, this work deals with physical processes occurring during ultrafast heating performed by a single short DC electric pulse of controlled power P(t). The enhancement of recrystallization and plastic strain rates by electric current is crucial particularly for the short pulse experiments where the used current densities are higher. We assume that all the three above mentioned FTMT-EC specific features (fast heating rate, dynamic recrystallization under varying Naformátováno: Doprava Naformátováno: Angličtina (USA)

stress and direct effects of the electric current) affect dramatically the formation of the polygonized/recrystallized nanograin microstructures in the FTMT-EC treated NiTi wires. Although further research is necessary to recognize mutually their individual effects, there seems to be a possibility to use the special FTMT-EC treatments to produce NiTi wires having special microstructures and special functional properties not achievable with the furnace treatments.

Although the heating time may seem to be a free parameter of the FTMT-EC method (similar functional properties of the wire can be obtained in treatments using pulse t _2 = 12 ms as well as 1 hour), in fact, it is not. The thinner is the wire, the less efficient is the Joule heating since more heat is lost into the environment due to the larger surface to volume ratio of the thinner wire. This can be beneficially compensated by using shorter electric pulse. Note that, although the same energy is supplied to the wire in the P= 2 W/ 0.9 s and P= 10 W/ 0.18 s treatments, only the latter treatment is sufficient to develop superelasticity. The maximum reached wire temperature is about twice as large in the latter treatment (Fig. 1). At the same time, the heating rate 3500 o C/s employed in the 10 W/ 0.18 s treatment is about 10 times larger than that used in the 2 W/ 0.9 s treatment. The larger heating rate is more effective in suppressing the slow processes and gives rise to the smaller temperature gradient from the wire core to the surface. This possibly affects the homogeneity of the formed nanosized microstructure in the wire. It should be noted that heating rates approaching 50000 o C/s were used in sequential FTMT/EC treatments reported in [18,[START_REF] Delville | [END_REF].

Finally, the electric current density is larger in case of the shorter treatments, which according to Conrad [START_REF] Conrad | [END_REF] further increases the kinetics of the processes with all consequences discussed above.

There are basically two practical ways how to perform the FTMT-EC treatment of the as-drawn NiTi wire leading to the desired microstructure and functional superelastic properties. Either the parameters of the electropulse treatment (P, t_ 2 , and constraint resulting in the desired T(t), ρ(t) and σ(t) -see (Fig. 6)) are determined from a preliminary series of experimental tests [START_REF] Pilch | Proc. of the ESOMAT[END_REF][START_REF]Patent applications[END_REF]. This is used for shape setting of wire segments embedded in structures or integrated in hybrid textiles. Or, as an alternative option, it is possible to heat treat continuous NiTi filaments during respooling while controlling the supplied electric power in a closed loop with respect to the change of the electric resistance of the filament caused by the heat treatment [START_REF]Patent applications[END_REF]. This is particularly useful for heat treatment of continuous NiTi filaments prior to their textile processing.

Conclusions

Functional superelastic properties of the NiTi wires can be precisely set using non-conventional heat treatment by pulsed electric current. The treatment is performed using a single electric pulse with controlled electric power P(t) applied to the wire which is prestrained in axial direction in environmental chamber. In contrast to the conventional furnace treatment, this method allows for precise control of the rise of the wire temperature T(t) and tensile stress σ(t) during fast heating (3500 o C/s). This enables to control the progress of the recovery and recrystallization processes during heating responsible for the fast evolution of the microstructure and presize setting of the functional superelastic properties of the treated wire.

A unique combined in-situ experiment was carried out in which evolution of the parameters of the synchrotron X-ray diffraction profile (intensity, position, area and width of the {011} austenite reflection), tensile stress and electrical resistance of the wire were simultaneously recorded during the heat treatment by the pulsed electric current. The obtained in-situ results provide direct experimental evidence on the internal strain (stress) and density of defects in the microstructure evolving during the fast heating from 20 o C to 700 o C. This evidence has been used to describe the progress of the dynamic processes responsible for the microstructure evolution during the heating.

Based on this knowledge, an interpretation of the experimentally recorded variation of the tensile stress and electric resistance of the treated wire is proposed.

Fig. 1 :

 1 Fig. 1: Microstructures and superelastic functional properties of thin NiTi wires evolving during sequential P= 125 W / 1, 2, 3…18 ms electropulse heat treatment (data taken from [21]). Microstructures found by TEM in 8, 12, 14, 18 ms treated wires (left) and their cyclic tensile stress-strain curves (right) -10 cycles in position control at room temperature.

Fig. 2 :

 2 Fig. 2: FTMT-EC treatment by controlled electric power pulse P(t): a) parameters describing the pulse shape, b) calculated temperature profiles T=T(t) achieved in pulses with parameters P = 2, 3, 4, 5, 6 W; t_ 2 = 0.9 s and P = 10 W, t_ 2 = 0.18 s, c) power, voltage, current, temperature, force and electric resistance varying during 6 W treatment of an already 6W heat treated NiTi wire, d) reversible evolution of electric resistance and tensile stress with temperature during the heat treatment described in (c).

Fig. 3 :

 3 Fig. 3: a) Setup of the in-situ high speed synchrotron X-ray experiment during the heat treatment by electric current. The FReLON camera reading was optimized for high speed data acquisition (only part of the detector -strip of 2048 × 64 pixels -was used to increase the time resolution to ~10 ms); b) The evolution of the {110} austenitic peak measured during heat treatment experiments P= 10 W/ 0.18 s.

Fig. 5 :

 5 Fig. 5: Quantitative phase analysis of the diffraction patterns to determine the evolution of the integrated intensity, position and width (FWHM) of the {110} austenitic peak (in red): diffraction pattern of NiTi powder (a) and NiTi cold-worked wire before (b) and after (c) heat treatment. Figuresd-gshow diffraction pattern evolution with time recorded during the electric pulse treatments with 2 W (d), 3 W (e), 6 W (f) and 10 W (g). In the case of the P= 6 W/ 0.9 s treatment there is missing data due to the fact that the wire moves out of the X-ray beam.

Fig. 6 :

 6 Fig. 6: Evolution of electric power, temperature, tensile stress and electric resistance of NiTi wires during FTMT-EC treatments with different power / pulse time (left) and resulting superelastic response of the treated wires at room temperature with superimposed in-situ electric resistivity records (right).

Fig. 7

 7 Fig. 7 Evolution of the tensile stress (upper figures) and the electrical resistivity (lower figures) with time (a) and temperature (b) measured in treatments with P= 2, 3, 4, 5, 6 W/ 0.9 s and 10 W/ 0.18 s

Fig. 8 :

 8 Fig. 8: In-situ X-ray diffraction experiments -evolution of the tensile stress (a,b) and electric resistivity(c,d) intensity (e,f), radial strain (peak position) (g,h), FWHM (peak width) (i,j) and integrated intensity (k,l) of the austenite {110} reflection with time (left) and temperature (right) during heat treatments using P= 2, 3, 6 W / 0.9 s and 10 W/ 0.18 s. The start and finish of the temperature rise are denoted by dashed lines.

  Temperature range I Reverse martensitic transformation & residual stress relaxation 20 o C -500 o C II Polygonization & defect annihilation & crystallization from amorphous 200 o C -550 o C III Recrystallization & plastic deformation 350 o C -700 o C IV Grain growth & plastic deformation > 600 o C

Fig. 9 :

 9 Fig. 9: Combined in-situ tensile stress (2), electric resistivity (3) and X-ray diffraction results (radial strain (4), FWHM (5), peak intensity (6)) recorded during the P =10 W/ 0.18s treatment plot together in dependence on a) time, b) temperature.

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Acknowledgments

The authors acknowledge the support of this work by EC within the integrated project AVALON (NMP2-CT-2005-515813), support of ESRF for performing the in-situ synchrotron experiment (MA-358) and support from Czech national research projects AV0Z10100520, IAA200100627.