Scholarly article on topic 'Revealing the microstructure evolution in Cu-Cr alloys during high pressure torsion'

Revealing the microstructure evolution in Cu-Cr alloys during high pressure torsion Academic research paper on "Materials engineering"

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{"High pressure torsion" / "Cu-Cr nanocrystalline alloy" / "Dissolution process" / "X-ray diffraction" / "Transmission electron microscopy"}

Abstract of research paper on Materials engineering, author of scientific article — Jinming Guo, Julian Rosalie, Reinhard Pippan, Zaoli Zhang

Abstract Usually immiscible Cu-Cr compounds in equilibrium condition were mechanically processed via high pressure torsion with large and controlled strains. A systematical investigation on 57wt%Cu − 43wt%Cr was carried out to get insights into the microstructural evolution of Cu-Cr nanocomposites and their dissolution process, as well as to determine the solid solubility limit of Cu and Cr elements under severe deformation. Microstructural evolution was captured with grain refinement from micron-size down to less than 20nm as the increase of strains. A strain-saturated state in 57wt%Cu − 43wt%Cr bulk was achieved after 100 rotations deformation (effective strain 1360), with a stable grain size of 13.7nm and invariable hardness of 480–495 HV. Fine scanning of X-ray diffraction and sub-nanometer scale measurements of energy-dispersive X-ray spectroscopy showed that 32wt% Cu could be fully dissolved into Cr matrix, and conversely solubility of Cr in Cu was determined to be about 3wt% after an enough amount of deformation. The phase fraction change associated with Cu dissolution into Cr matrix during continuous deformation was captured and accurately calculated, indicating a negative exponential phase change mode. A phenomenological intermixing mechanism based on the kinetic competition between external forcing mixing and thermal-diffusion induced decomposition was proposed, which was well accordant with the phase evolution observed from experimental results.

Academic research paper on topic "Revealing the microstructure evolution in Cu-Cr alloys during high pressure torsion"

Author's Accepted Manuscript

Revealing the microstructure evolution in Cu-Cr alloys during high pressure torsion

Jinming Guo, Julian Rosalie, Reinhard Pippan, Zaoli Zhang

MATERIALS SCIENCE & ENGINEERING

Editor m chief: A Structural Materials: Properties, e.j. lavemia # % Microstructure and Processing

www.elsevier.com/locate/msea

PII: S0921 -5093(17)30474-4

DOI: http://dx.doi.org/10.1016/j.msea.2017.04.034

Reference: MSA34935

To appear in: Materials Science & Engineering A

Received date: 8 February 2017 Revised date: 5 April 2017 Accepted date: 7 April 2017

Cite this article as: Jinming Guo, Julian Rosalie, Reinhard Pippan and Zaol Zhang, Revealing the microstructure evolution in Cu-Cr alloys during hig pressure torsion, Materials Science & Engineering A

http://dx.doi.org/10.1016/j.msea.2017.04.034

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Revealing the microstructure evolution in Cu-Cr alloys during high pressure torsion

Jinming Guo, Julian Rosalie, Reinhard Pippan, Zaoli Zhang* Erich Schmid Institute of Materials Science, Austrian Academy of Sciences, 8700 Leoben, Austria

Corresponding author: zaoli.zhang@oeaw.ac.at

Abstract

Usually immiscible Cu-Cr compounds in equilibrium condition were mechanically processed via high pressure torsion with large and controllable strains. A systematical investigation on 57 wt.%Cu -43 wt.%Cr was carried out to get insights into the microstructural evolution of Cu-Cr nanocomposites and their dissolution process, as well as to determine the solid solubility limit of Cu and Cr elements under severe deformation. Microstructure evolution was captured with grain refinement from micron-size down to less than 20 nm as the increase of strains. A strain-saturated state in 57 wt.%Cu - 43 wt.%Cr bulk was achieved after 100 rotations deformation (effective strain 1360), with a stable grain size of 13.7 nm and invariable hardness of 480 - 495 HV. Fine scanning of X-ray diffraction and sub-nanometer scale measurements of energy-dispersive X-ray spectroscopy showed that 32 wt.% Cu could be fully dissolved into Cr matrix , and conversely solubility of Cr in Cu was determined to be about 3 wt.% after an enough amount of deformation. The phase fraction change associated with Cu dissolution into Cr matrix during continuous deformation was captured and accurately calculated, indicating a negative exponential phase change mode. A phenomenological intermixing mechanism based on the kinetic competition between external forcing mixing and thermal-diffusion induced decomposition was proposed, which was well accordant with the phase evolution observed from experimental results.

Keywords

High pressure torsion, Cu-Cr nanocrystalline, dissolution process, X-ray diffraction, transmission electron microscopy,

1. Introduction

Severe plastic deformation (SPD) has been quite arrestive for the last two decades due to its superior advantages in fabrication of novel nanocrystalline bulk materials even out of "immiscible" composites [1], such as Cu-based binary systems [2,3] including Cu-Fe [4-8], Cu-Cr [9-12], Cu-Nb [13-15], CuTa [16] and Al-based systems including Al-Mg [17-21], Al-Zn [18,19], which possess a lot of excellent mechanical, thermal or electrical properties. Of the various SPD methods [1], for instance, equal-channel angular pressing [17,20,22], accumulative roll-bonding [23,24], high energy ball milling [25,26], bundling and drawing [13,14] and so on, high pressure torsion (HPT) is one of the most efficient mechanical alloying techniques where a disk is subjected to a high applied pressure and concurrent torsional straining [27-30]. In practice, this metal forming process provides an opportunity for achieving exceptional grain refinement in applicable bulk materials, often to the nanometer level. Due to the large grain refinement and chemical intermixing that occurs during processing, this technique poses another route to produce binary or even polynary alloys with very high mechanical strength.

Among non-equilibrium systems, Cu-Cr was widely investigated and thought as a promising alloys in potential applications. Sauvage et al. processed a Cu-Cr composite containing 43 wt.% Cr by high pressure torsion and found that the grain size of the unprocessed composite was reduced from 40 - 60 ^m to 10 - 20 nm after 25 revolutions of deformation under a pressure of 6 GPa [9]. It was found that super saturated solid solutions (SSSSs) of up to 15 at.% (17.7 wt.%) Cu in the body-centered cubic (bcc)

Cr phase were formed but no formation of SSSSs of Cr in the face-centered cubic (fcc) Cu phase was observed. Bachmaier et al. obtained similar results for grain refinement, hardness increase and the formation of Cu SSSSs in Cr matrix [10]. To date mechanical alloying of Cu-Cr system by either HPT process or ball milling, has given a solubility limit of Cu atoms into Cr of 15 at.%, which may limit the further improvement of comprehensive properties for bulk materials [9,26]. A detailed understanding of the relationship between the dissolution volume and applied strain is still lacking.

As already known, alloys fabricated from such "immiscible" systems at room temperature are non-equilibrium with metastable phases. Because the thermodynamic driving force for diffusion is dominated by the positive heat of mixing even for those systems with liquid miscibility, so that the thermo-diffusing atomic fluxes will generally proceed in the direction which causes chemical segregation and phase decomposition. For solid-state alloying, nanostructuring to alter the energetics of systems and external driving force are two key strategies to form a stable alloys from "immiscible" systems [4,31]. Kinetic models have been proposed to describe the alloying process as a competition between external forcing mixing during plastic deformation and decomposition due to thermal diffusion [32,33].

Motivated by the promising properties of high content of Cu dissolved Cu-Cr bulk nanocrystalline materials, a series of investigations were conducted on micrometer-sized staring bulk of nominal 57 wt.% - 43 wt.%Cr with different high-strained revolutions, from 25 rotations to even 1000 rotations in accordance with strain of 340 to 13600. Simultaneously, the concurrent phase fraction change accompanied with microstructure evolution during deformation was well calculated and it showed a negative exponential transition mode. Here a possible intermixing model was proposed based on above-mentioned kinetic model from the phenomenological point of view to describe the dissolution process in details, and it fitted well with experimental results.

2. Experimental

A commercial coarse-grained Cu-Cr bulk material was HPT deformed at room temperature with air cooling. The initial bulk material with nominal composition of 57 wt.%Cu - 43 wt.%Cr (volume and atom fraction of about 50%.) was produced by PLANSEE (Reutte, Austria). Left image in Figure 1 shows a backscattered electron image of the raw material with Cu (bright) and Cr (dark) particles having an average size of about 50 ^m distributed homogeneously. Disks with a diameter of 8 mm and an initial thickness of about 1.0 mm were HPT-deformed with different numbers of rotations N (N = 25, 50, 100, 300, 420, 1000) under a constant pressure of 7.3 GPa and a rotation speed of 0.4 rotation/min. The schematic diagram of HPT is shown in the middle image of Fig. 1 All data shown in this paper is either presented as a function of strain seq or given for a certain seq (radius r = 3.0 mm from the disk center), respectively. seq is calculated by equation (1) [10,27]

£eq = Tvf (1)

where r is the radial distance from center of the disk. t is the thickness of deformed sample. The thickness value t was taken as 0.8 mm for all samples.

X-ray diffraction (XRD) was conducted on all samples using Smartlab X-Ray Diffractor (Rigaku, Japan) with Cu Ka1 radiation = 1.540593 A). A series of Cu-Cr powder compacts were produced for use as external standards in XRD experiments. Commercially-available powders from Alfa Aesar (Karlsruhe, Germany) of Cu (Purity 99.9%) and Cr (Purity 99.9%) were mixed and then compacted with a pressure of 7.3 GPa for 10 seconds. One such powder compact (with a composition of 30 wt.%Cu - 70 wt.%Cr) was also subjected to HPT using a two-stage method. The detailed information for this two stages method can be found in Ref. [5].

Here we emphasize that the X-ray beam width for all the measurements in this work was limited to 2

mm using an incident slit, covering a large area of HPT deformed disk from radius of 2 mm to 4 mm as

shown in right schematic diagram of Fig. 1. The beam height was set to 1 mm, which indicates the

beam will be elongated in the X-ray reflection direction to 1.41 mm - 3.24 mm for scanning range of

40° - 100° and to 2.77 mm - 3.24 mm for 40° - 47° measurement. Therefore, the X-ray actually covered a large area of disk from radius of 2 mm to 4 mm, and its results can represent the average effect of HPT disk in macro-scale, rather than localized measurement. The X-ray scanning speed is 0.4 °/min with step of 0.02°.

Transmission electron microscope (TEM) and scanning transmission electron microscope (STEM) were used to characterize in details the microstructure of the deformed material. All microstructural investigations were undertaken at radius of 3.0 mm from the torsional axis of the HPT deformed disks (as shown in right schematic diagram of Fig. 1). The (S)TEM samples were cut from the HPT disks, and then mechanically thinned and polished to a thickness of about 50 ^m, followed by mechanical dimpling. Subsequently the samples were ion-milled using a Gatan Precision Ion Polishing System until perforation with voltage of 4 kV and angle of 4° - 6°. (S)TEM studies were carried out using a field emission gun transmission electron microscope (JEOL JEM-2100F, Japan) equipped with an imaging spherical aberration corrector and an Oxford INCA Energy TEM 200 energy-dispersive X-ray spectroscopy (EDXS) system. In STEM mode, high angle annular dark field (HAADF) detector with a spot size of 0.7 nm was used to record HAADF-STEM images. EDXS for nanoscale compositional analysis was also carried out in STEM mode. The chemical compositions obtained from EDXS were analyzed using commercial INCA system or DigitalMicrograph software. The electron beam was perpendicular to the shear plane of the disks for all microstructural investigations shown in this work. Vickers microhardness measurements were conducted on a Buehler Mircomet 5100 using a load of 500 g (HV0.5). Indents were made across the radii of the disks with a spacing of 300 ^m between the indents, and average values of six individual measurements with the same strain on deformed disks for each deformation condition are reported in this work. 3. Results 3.1 Phase evolution

Fig. 2a shows the X-ray diffraction (XRD) patterns of 57 wt.%Cu - 43 wt.%Cr raw material and deformed samples with different numbers of rotations. All the curves are normalized by the intensity of the highest peak, either (111)Cu or (110)Cr. For all HPT-deformed samples, the structure is a two-phase mixture of face-centered cubic (fcc) and body-centered cubic (bcc) structures. The relative intensity ratio between (111 )Cu and (110)Cr obviously changed with increasing number of rotations. The relative peak intensities for each phase matched well with standard polycrystalline diffraction peaks generated by the PowderCell programme. This means that grains of the HPT-deformed Cu-Cr alloys are randomly oriented and the influence of the texture on the X-ray can be neglected. If the grains of each phase are randomly oriented, quantitative estimation of phase fractions by XRD is feasible, based on the principle that the integrated intensity of diffraction peak for each phase in a mixture is proportional to the volume fraction of that phase [34,35]. In order to accurately calculate the integrated area of relevant peaks for each sample, the peaks of (111)Cu and (110)Crare separated from the measured curves by accurate fitting with residual value less than 2%. The relative intensity ratio of (111)Cu and (110)Cr is then calculated according to following equation (2):

Rcu = (2)

LU 'Cu+'Cr

where RCu represents the relative intensity ratio of Cu peak, and ICu as well as ICr means the integrated area of each corresponding peak after subtracting the background [36].

The results calculated for the relative intensity ratio of (111)Cu and (110)Cr are plotted in Fig. 2b. The

relative intensity ratio of (111)Cu decreased obviously from 0.71 for raw bulk material to 0.38 for the

sample deformed with 300 rotations. It then remained constant even the sample was deformed further

to up to 1000 rotations. From the relationship between relative intensity ratio and number of rotations

(and corresponding strain), the relative intensity ratio of (110)Cr increases quickly when the sample was

deformed in the first 100 rotations, and then this value tended to stabilize with the level around 0.62.

Fig. 2c shows the lattice parameters calculated from the fine scanning of (111)Cu and (110)Cr peaks,

using the relationship of that lattice constant equals to V2 times of the spacing of (110) plane and V3 times of the spacing of (111) regarding the structure as cubic phase. Generally, both of the lattice parameters of Cu phase and Cr phase are increased as the increasing of numbers of rotations. The dissolution of Cu and Cr atoms into each counterparts causes the expansion of each cubic lattice, which is in agreement with the lattice change reported for Cu-Cr alloys in the literatures [2,3].

To investigate the relationship between relative intensity ratio and dissolution of Cu, namely, how much percentage of Cu has been dissolved into Cr matrix after different numbers of rotations, XRD spectra of blended powders with different ratios of x wt.%Cu - (1-x) wt.%Cr (x = 5, 15, 35, 65, 85) were measured to calculate the relative intensity ratio changes of (111)Cu and (110)Cr peaks with different compositions. The XRD measurement curves and calculated ratios were plotted in Supplementary Fig. S1a and Fig. S1b respectively. The curve in Supplementary Fig. S1b was used as a reference in this work to calculate the quantity of each phase in the deformed alloys. Table 1 shows the percentage of residual Cu phase in the first row and the already dissolved percentage of Cu phase in the second row. Finally, after HPT deformation with 300 rotations or even higher, 32 wt.% (27.8 at.%) Cu can be fully dissolved into the Cr phase bcc structure. The confirmation results with blended powders of 30 wt.%Cu - 70 wt.%Cr will be addressed later to show the accuracy of calculation out of this method.

3.2 Microstructure characterization

Figs. 3a-f show the TEM bright field images of Cu-Cr samples deformed with different numbers of

rotations. The average grain size can be observed to be decreased as the increasing of numbers of

rotations. For all the samples deformed by HPT, grains are equiaxed and randomly distributed, and

with almost spherical shape. This also facilitates statistic measurement of grain size regarding the grain

as a sphere and the diameter of the sphere is the calculated grain size [17]. It is worth noting that the

average grain size in the central part of HPT deformed disk with 25 rotations is in the order of 100 nm

to 200 nm based on the TEM images. Theoretically, the grain size in the center of HPT disk should be the same with starting bulk material in micron scale in ideal case if the torsional axis is in perfect condition without deviation and the perforation of TEM sample is small enough and in the exact center of HPT disk. In practice, the center of HPT disk may be also slightly deformed due to the little deviation of torsional axis [29,37,38]. Anyway, it will not affect the results mentioned in this work. For other edge part samples, the average grain size is quickly decreased to the order of 10 - 20 nm rather than amorphization reported in 30Cu-70Cr alloy generated by ball milling [39].

Fig. 3g shows the grain size distribution of Cu-Cr alloys deformed with different numbers of rotations. Fig. 3h shows the change of average grain size with an error bar of standard deviation. The average grain size of sample deformed with 25 rotations is 19.5 nm with a relatively wide distribution compared with the sample deformed with 300 rotations with average grain size of 13.7 nm and narrower distribution. The grain size change indicates that grain refinement was finished in the initial stage of deformation. Due to the nearly same volume amount of Cu and Cr in this composition of 57 wt.%Cu - 43 wt.%Cr, grinding of each part during HPT deformation is easy to proceed in spite of the large difference of hardness between Cu and Cr, rather than swimming in some compositions with large proportion of Cu and little part of Cr.

Fig. 4 shows the high resolution TEM (HRTEM) images of HPT deformed 57 wt.%Cu - 43 wt.%Cr alloy with 100 rotations. Fig. 4a shows three adjacent grains of Cu and Cr with different zone axes. The grain in right side is Cu with fcc structure and on the zone axis of [011] which is parallel to the incident electron beam while the bottom-left grain is chromium with bcc structure and on the zone axis of [001]. In this image, (110)Cr plane of Cr grain is strictly parallel to (111)Cu plane of Cu grain, which is the typical matching relationship of bcc and fcc structure with {110}bcc//{111}fcc [13,40,41]. In the top-left corner, the grain is not well on zone axis, but {111} Cu planes can still be distinguished from the results of spacing measurement. Fig. 4b shows a grain of Cu with fcc [001] zone axis. Form this image,

(200)cu, (220)cu and (020)cu can be observed here according to Fast Fourier Transform (FFT) in upper-left corner derived from the area marked with white frame. For the FFT image, except the main spots indexed with the zone axis of [001]fcc, there are some tiny spots close to the central spot. After checking the interplanar spacing represented by these spots, oxides of CuO, Cu2O and Cr2O3 can be recognized with structure of monoclinic, cubic and hexagonal structure respectively [42,43]. (011)CuO, (101)CuO, (110)Cu2O and (110)Cr2O3 have been indexed in the FFT. Fig. 4c shows a typical small angle grain boundary between two Cr grains with matching plane of (110). From FFT images calculated from the white frames of both left and right part, these two Cr grains both possess bcc structures with zone axis of [111]. Compared with clear atom columns of right Cr grain, the left image doesn't show distinct interplanar planes except (110)Cr plane, even though all spots with zone axis of [111]bcc in FFT can be observed. This may be caused due to a tiny in-plane tilt of (110) plane in left grain. At grain boundary, dislocations can be observed directly marked in the white circles. Based on HRTEM image, this grain boundary can be deduced to be a typical symmetrical tilt boundary with a splitting angle of 13.3°. The

relationship of spacing d and distance between two dislocations fits well with s in 6 = ^ [14]. One

should note that at the bottom right of this image which is marked with a white ellipse, there is one part of right grain which shows planes almost on [001]bcc zone axis. But the rest part of right grain crossed the white dash line shows obvious [111]bcc zone axis. This coexistence of two subareas with zone axes of [111]bcc and [001]bcc inside one Cr grain should be due to the deformation-induced local transition from <001>-oriented bcc structure to <111>-oriented lattice, which is similar as phase transition in bcc molybdenum caused by in-situ straining [44]. Fig. 4d shows an atomic-scale twin boundary with a zone axis of fcc [011]. At the top-right part of the image, there are some areas with different contrast and latticed shape (Moiré fringes), probably due to the grain overlapping.

3.3 Hardness measurements

To check the mechanical properties, hardness of Cu-Cr alloys deformed with different numbers of rotations was measured systematically as shown in Fig. 5. The inset shows the enlarged hardness results with relatively low strain range of 0 - 1800. Generally, the increment of hardness as a function of strain can be divided into 3 stages. The hardness value increased as the increasing of strain quickly in the initial stage of deformation with a lower strain less than 400. Here the fast increasing of hardness was due to the combination of contributions of grain refinement and formation of solid solutions. According to the calculation of dissolution process, about 18 wt.% Cu was dissolved into Cr matrix when the given strain was about 400 (equivalent to the strain of position at radius of 3 mm deformed with 29 rotations). But the average grain size was reduced fast from more than 150 nm to less than 20 nm. When the strain reached about 400, the hardness value increased to about 440 from the initial value of about 280 for the center point of HPT disk deformed with 25 rotations correlated with the average grain size of about 158 nm. For the second stage when the strain increased from 400 to about 4000 (equivalent to the strain of position at radius of 3 mm deformed with 294 rotations), about 9% of hardness value was improved from 440 to 480. From the calculation of grain size, the average grain size was reduced to about 19.5 nm when the sample was deformed with 25 rotations. The equivalent strain at the radius of 3 mm for the sample deformed with 25 rotations was about 340. Then as the increase of strain, the grains were only slightly refined within the range of 13.7 - 19.5 nm. But the dissolution of Cu into Cr matrix was finally improved from 18 wt.% at the strain of 400 to about 32 wt.% at the strain of 4000. So for the second stage of relative small increment of hardness, the main contribution for the 9% improvement of hardness should come from the formation of solid solution of bcc structure of Cu-Cr composite. Simultaneously, we can roughly deduce that in the initial stage of deformation the main contribution of hardness increasing should come from the grain refinement due to the large increasing of hardness with about 57% increment. For the third stage, when the strain reached about 4000, the dissolution of Cu into Cr got saturated which was consistent with the stabilization of

hardness value. The hardness value was invariable within the range of 480 - 495 HV even the sample was deformed with extremely high strain to 16000 which had never been tried before. For the solubility limit, total 32 wt.% Cu can be dissolved into Cr matrix. The grains were also refined uniformly with average size of 13.7 nm after deformation with large strains. So the maximum of dissolution and grain refinement caused the highest hardness value of about 495 for 57 wt.%Cu - 43 wt.%Cr composites obtained by mechanical alloying.

3.4 Verification experiments of blended powders of 30Cu-70Cr and melted bulk of 95Cu-5Cr

As mentioned in the experimental part, nominal 30 wt.%Cu - 70 wt.%Cr composition was deformed using powders as raw material with two stages method. Fig. 6 shows the fine scanning XRD curve measured from the edge part of the disk of 30 wt.%Cu - 70 wt.%Cr deformed with 50 rotations at the second stage. The measured curve only displayed one broadened peak. But due to the slightly unsymmetrical shape of the peak, the fine fittings of (111)Cu and (110)Cr were carried out to separate the measured curve. The overall fitted curve (red) accorded well with the measurement result (black), meaning good accuracy of fitting. Then the relative intensity ratio of (111)cu can be easily calculated based on the fitting result. Referring to Supplementary Fig. S1b (the relationship between relative intensity ratio of (111)Cu and weight percentage of Cu phase in blended powders), about 3 wt.% (2.5 at.%) Cu can be identified as residual phase in the composite. That is, about 27 wt.% Cu in the composite was successfully dissolved into Cr matrix after the second stage of deformation with 50 rotations. As described in Ref. [5], the total strain after two stages HPT deformation, should be multiplication of strain of each stage. For the first stage of this sample, the strain is about 40 calculated from equation (1) considering 8 mm of the sample thickness and 9 mm of the distance at radius. For the second stage, the strain at the radius of 3 mm with 50 rotations is about 680. So theoretically the total strain at point of 3 mm far away in radius should be 27200. The reason for that 3 wt.% residual Cu was still detected according to XRD in the deformed composite even after deformation with strain of 27200,

is that, the starting materials were powders rather than melted bulk material like 57 wt.%Cu - 43 wt.%Cr. The 30 wt.%Cu - 70 wt.%Cr is extremely hard due to the large fraction of Cr, the processing anvils were easily damaged during deformation, so no higher strain was tried. Anyhow, current XRD result is sufficient to show that at least about 27 wt.% Cu can be dissolved into Cr by HPT method although the needed strain is different due to the difference of starting materials.

The dissolution limit of Cu into Cr was determined based on HPT deformation of 57 wt.%Cu - 43 wt.%Cr. The same method was used on the composite of 95 wt.%Cu - 5 wt.%Cr to determine the solubility limit of Cr into Cu. Fig. 7 shows the XRD curves of the bulk material and deformed samples with 50 and 100 rotations. All the curves were normalized by (111 )Cu. The melted bulk material was thinned down by rolling, so the sample showed partial (200) texture. After HPT deformation, the texture disappeared and the Cr peak obviously decreased. Compared to the curve measured from the sample deformed with 50 rotations, the intensity of Cr peaks from 100 rotations deformed sample reduced further but these peaks still can be observed. After referring to Supplementary Fig. S1b, about 2 wt.% of Cr phase was left, which meant about 3 wt.% (3.6 at.%) Cr has been successfully dissolved into Cu matrix to form fcc structure. This result is consistent with the value of Cr solubility in Cu of 4 at.% (3.3 wt.%) in Cu-Cr thin films deposited by molecular beam epitaxy [45].

4. Discussion

4.1 Chemical composition verification

To verify the exact compositions of HPT deformed Cu-Cr alloys, we performed sub-nanometer scale EDXS measurements on the samples deformed with different strains. Fig. 8 a shows one HAADF-STEM image of 57Cu-43Cr alloy deformed with 25 rotations where the dark areas are Cr grains and the bright areas represent Cu grains. Systematical line-scan of EDXS measurements can be implemented across Cu and Cr grain boundaries. Fig. 8b and Fig. 8d show the HAADF-STEM images of 57Cu-43Cr alloys deformed with 25 rotations and 100 rotations respectively. Fig. 8c and Fig. 8e

show the weight percentage concentration profiles measured across Cu and Cr grains along the white arrowline showed in STEM images Fig. 8b and Fig. 8d respectively. The spacing between two measurement ponits for EDXS line-scan is 1.4 nm with a electron probe size of 0.7 nm. All EDXS measurements shown here were obtained at the extremely thin area of edge part to insure no overlapping of grains (beam broadening effect is negligible). For sample deformed with 25 rotations, the concentration profile in Fig. 8c obviously shows that in Cr grains the average amount of Cu is about 19.6 wt.% (16.6 at.%), while in the Cu grain side, the dissolved Cr amount is about 3.8 wt.% (4.6 at.%). When 57Cu-43Cr was deformed with 100 rotations, the concentration profile in Fig. 8e shows that about 30.5 wt.% (26.4 at.%) of Cu stoms has been dissolved into Cr grains, simultaneously Cu grains contain about 3.9 wt.% (4.7 at.%) Cr dissolved inside. In addition, 10 point measurements at respective Cu and Cr grains were performed in the sample deformed with 100 rotations to confirm the results, as showed in Supplementary Table S1. The average amount of Cu atoms in Cr grains is about 30.6 wt.% (26.5 at.%) and Cr amount dissolved into Cu grains is about 4.1 wt.% (4.9 at.%), which is fully consistent with the results showed in EDXS line-scan. Compared with the results showed in Table 1, the dissolved amount of Cu into Cr should be 17.5 wt.% (14.8 at.%) and 28.5 wt.% (24.6 at.%) when the samples were deformed with 25 rotations and 100 rotations respectively according to the XRD method. The results obtained from different methods have a little difference, but with the same change trend, that is, larger strains cause higher dissolution amount. The main reason of this small difference may be due to the different scales of these two methods. Anyway these results are quite convictive information to understand the strain-dependent dissolutions of 57Cu-43Cr systems.

4.2 Dissolution process of HPT deformed Cu-Cr alloys

As mentioned in introduction part, for the dissolution process of alloys generated by mechanical alloying, there were many discussions about the non-equilibrium state from different points of view. Ma et al. [31,46] and Martin [47] have discussed the dissolution process quantitatively in non-

equilibrium state to determine the largest solubility (For details, see discussion in Supplementary). Even though the phenomenological model in their work is relatively rough and based on the ball milling process, but it can empirically explain the increase of solubility due to the external forcing. But this description cannot intuitionally tell the dissolution process of the alloys under continuous deformation. Actually some literatures reported the alloying process could be a competition between mixing under sustained external forcing and decomposition due to thermal diffusion [31,32,46-48]. Based on our experimental results, we have proposed an empirical formula to mimic the details and influencing parameters of dissolution process based on our experimental data [49]. The idea of thermodynamics-related diffusion was employed to describe the inverse flow of dissolved solute atoms during deformation. In our previous work [49], the thermodynamic diffusion flux Jth was deduced with a relationship of applied strain seq (Equation (3) in literature [49]):

Jth _ Jf _iek(r-£eq) (3)

Eq. (3) shows that Jth is a negative exponential function of applied strain seq, where k and t are coefficients, and Jf means external forcing mixing flux. So it will increase as the increasing of strain, but with an approaching value. Two boundary conditions should be considered for this equation. First,

when £eq is 0, Jth should equal to 0, which means Jf _ ^ekT. Second, when seq ^ Jth _ Jf, that

is, the approaching value is Jf and the system has arrived a balanced state with equivalent speed between forcing mixing and thermodynamic diffusion.

The external forcing flux Jf keeps constant during deformation, while the thermodynamic decomposition flux Jth shows a negative exponential increasing trend. When the sample is deformed with high strains, the back-diffusion flux increases close to the level of forcing flux due to the large amount of net Cu solute atoms, so the dissolution of Cu atoms into Cr matrix gets saturated (Refer to

Fig. 3 in literature [49]). So the final percentage of Cr phase R c r which involves the integration of net flux J can be also given in a negative exponential increasing, as shown in equation (4):

R c r = C-A-e~ eo'£ e i (4)

where A and C are positive constants. In Fig. 2b, the experimental data of Cr phase percentage in the deformed alloys was well fitted by negative exponential formula. The equation (4) derived from our diffusion model accords well with previous fitting formula in Fig. 2b. Namely, C = 0.60566, A = 0.30727 and o = 0.01583.

Here a model without consideration of the solid solution in equilibrium condition was proposed to describe the dissolution process in non-equilibrium state due to the negligible solubility for the "immiscible" Cu-Cr alloy even at eutectic melting temperature of 1075 °C [2]. The final equation (4) is in consistent with the experimental results perfectly to describe the dissolution process. Even though the exact implications of constants A, C, o and k were not given yet, but it doesn't affect the understanding of dissolution process from the phenomenological point of view with this model. Based on previous discussion of solubility of already balanced system from the standpoint of energetics, these parameters should be related to enthalpy and chemical potential of the system. One may have a query that if so called "backflow" diffusion of solute atoms is such significant, why the supersaturated solid solution does not decompose when HPT was removed? Straumal et al. interpreted the reason was due to low bulk diffusivity without HPT [18]. Sauvage et al. discussed in specific conditions of the HPT process the diffusion coefficient would increase for four orders of magnitude compared with that under the condition without strain [8], basing on the calculation result of that the vacancy migration energy might be lowered by 30% even subjected to a compressive strain of 5% [50]. According to these explanations, the relatively stable phases after HPT may be attributed to that the solute atoms are "frozen" in the bulk and cannot reach the grain boundaries.

This model can be extended to phenomenologically explain the deformation process in other fcc-bcc "immiscible" systems, such as Cu-Fe and Cu-Mo systems. However, two points should be noted: First, for this phenomenological descriptions it is assumed that the phase boundary area is always constant during the process. Actually, in the initial stage of deformation, the refinement is much faster than the supersaturation process, hence, the refinement produce numerous boundaries during the deformation. Our result showed that the grains were refined quickly down to 19.5 nm even with the deformation of 25 rotations, and only a slight refinement to 13.7 nm occurred when the sample was further deformed with 100 rotations. So our proposed model simplified the dissolution process by treating the boundary area unchanged, without consideration of boundary area increasing due to grain refinement in the starting stage of deformation. Second, flux changes of thermodynamic back-diffusion are only caused by the strain-dependent accumulation of net Cu solute atoms, not by the difference of diffusion coefficient. Our previous investigation on the atomic-scale intermixing of HPT deformed Cu-Cr alloy has confirmed that Cu diffusion coefficient only has a small variation at different temperatures [51]. So here the employment of unchanged diffusion coefficient should be reasonable from empirical point of view.

5. Conclusion

57 wt.%Cu - 43 wt.%Cr was HPT deformed with controllable strains, especially with extremely high strains. Finally, nanocrystalline alloy was formed with average grain size less than 20 nm and good homogeneity. Comprehensive characterization methods, including XRD, (HR)TEM, STEM and EDXS were employed to systematically capture and characterize the phase fraction change, nanostructures and sub-nanometer scale compositions. The derived negative exponential intermixing mode was discussed in detail based on the proposed kinetic model. The main conclusions can be summarized as follows:

1. Phase evolution and the extended solubility of Cu-Cr system under HPT process were determined. The dissolution-induced phase change was driven by continuous deformation. The phase fraction change of as-deformed Cu-Cr alloy showed an obvious negative exponential trend. This work showed that about 32 wt.% (27.8 at.%) of Cu can be fully dissolved into Cr matrix to form bcc structure using HPT method. Only about 3 wt.% (3.6 at.%) Cr can be dissolved into Cu phase even the sample was deformed with 100 rotations.

2. The grain refinement of 57 wt.%Cu - 43 wt.%Cr sample was finished almost at the starting stage. When the sample was deformed with 25 rotations, the average grain size was decreased dramatically from micron-scale to less than 20 nm. Only a slight further refinement to average size of 13.7 nm occurred even the sample was deformed to 100 rotations.

3. Hardness value of 480 - 495 was obtained when the deformation rotations reached 100 rotations or even higher. At the starting stage, the fast increasing of hardness mainly comes from the grains refinement. For later stage, the slight increment is mainly due to increased amount of dissolution of Cu atoms into Cr matrix.

4. Kinetic dissolution model was proposed in this work based on the idea of that final solubility was determined by the competition of external forcing mixing and thermodynamic decomposition. The obtained negative exponential formula fits well with our experimental data. From this model and equation, it is easy to know the relationship between dissolved Cu solute amount and applied strain, which facilitates the understanding of dissolution process.

Acknowledgements

We gratefully acknowledge the financial support by the Austrian Science Fund (FWF): No. P27034 -N20. Peter Kutlesa, Gabriele Moser, Herwig Felber and Silke Modritsch at Erich Schmid Institute of

Materials Sciences, Austrian Academy of Sciences, are gratefully acknowledged for their help with the HPT, TEM and metallographical samples preparation.

Appendix A. Supplementary data

Supplementary data related to this article is attached.

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Fig. 1. Schematic diagram of HPT deformation. The left part shows EBSD image of raw bulk material

of 57 wt.%Cu - 43 wt.% Cr.

Fig. 2. (a) XRD patterns of 57 wt.%Cu - 43 wt.%Cr raw material and as-deformed samples with

different numbers of rotations. (b) Relative intensity ratio changes of (111)Cu and (110)Cr with different numbers of rotations. (c) Lattice parameters of Cu and Cr phase calculated from (111)Cu and (110)Cr

diffraction peaks.

(a) N = 25_Center £eq = 0

W ' RWp

nn»rr [fill

riwT»

(d) N = 100_Edge

£eq =1360

(e) N= 300 Edge £eq = 4080

8 12 16 20 24 28 32 ono/ 8 12 16 20 24 28 32

OU /err

N = 10OEdge £-eq=1360 Mean: 13.72 nm

N = 300 Edge

\ ¿eq= 4080

1 ^ Mean: 13.76 nm

1 1 111

12 16 20 24 28 32

Grain Size (nm)

12 16 20 24 28 32

1000 2000 3000 4000 Strain

Fig. 3. TEM bright field images taken at the same magnification (images a - e), and high magnification image of edge part of deformed sample with 300 rotations (image f). For the TEM sample made from the center part of HPT deformed disk with 25 rotations, the perforation of TEM sample was exactly in the center of HPT disk. For all the TEM samples made from the edge part of HPT deformed disks, the perforation of TEM samples were exactly at the radius of 3 mm of HPT disks. (g) Histogram

distributions of grain size statistics of Cu-Cr alloys deformed with different numbers of rotations. Each histogram was based on measurements of a minimum of 100 grains. (h) Average grain size values of samples deformed with different numbers of rotations with error bar of standard deviation.

ff /V fcc(1ll

bee [001]

(c)l (200)'

I • (iiinui

fee (111)

-fee (200)

^¿WwMffÂ

Fig. 4. HRTEM images of 57 wt.%Cu - 43 wt.%Cr alloys after HPT deformation with 100 rotations. (a) Three adjacent grains of Cu and Cr with different zone axis. (b) Cu grain with fcc structure on zone

axis of [001]. (c) Small angle grain boundary in two Cr grains with matching plane of (110)bcc. (d) Twin boundary in atomic scale in nano-size with zone axis of [011]fcc.

X 400 to

g 350 ~0

0 2000 4000 6000 8000 1000012000140001600018000

Strain

Fig. 5. Hardness measurements of Cu-Cr alloys deformed with different numbers of rotations. The inset shows the enlarged hardness results with a strain range of 0 - 1800.

26 (°)

Fig. 6. XRD curve of fine scanning in range of 40° - 47° for the sample of 30 wt.%Cu - 70 wt.%Cr

deformed with 50 rotations at the second stage.

Bulk Material 50 Rotations 100 Rotations

20 (°)

Fig. 7. XRD curves in range of 40° - 66° for the raw bulk material and samples of 95 wt.%Cu - 5

wt.%Cr alloy deformed with 50 and 100 rotations.

Fig. 8. HAADF-STEM images of HPT deformed samples of 57Cu-43Cr alloy: (a, b) 25 rotations. (d) 100 rotations. Concentration profiles of EDXS line-scan measurements across Cu and Cr grains along the white arrowline showed in STEM images: (c) 25 rotations. (e) 100 rotations.

Table 1 Residual percentage of Cu phase and dissolved percentage of Cu phase after different numbers of rotations.

Rotations N = 25 N = 50 N = 100 N = 300 N = 1000

Residual Cu (wt.%) 35.5 31.1 24.5 21.0 21.2

Dissolved Cu (wt.%) 17.5 21.9 28.5 32.0 31.8