70 nm: The most unstable grain size in Cu prepared by surface mechanical grinding treatment

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70 nm: The most unstable grain size in Cu prepared by surface mechanical grinding treatment Xin Zhou, Xiuyan Li *, Ke Lu ** Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, 72 Wenhua Road, Shenyang, 110016, China

A R T I C L E I N F O

A B S T R A C T

Keywords: Nanograins Thermal stability Mechanical stability Atom free energy Copper Severe plastic deformation

The stability of Cu with different average grain sizes prepared by surface mechanical grinding treatment were investigated under the conditions of isothermal annealing and uniaxial tension. In both conditions, experimental results revealed that the stability of the grains decreased with the decrease of grain size when the grain size was above 70–75 nm, while the stability of the grains increased with the decrease of grain size when the grain size was below 70–75 nm. The grains of about 70–75 nm in size showed the worst stability in both thermal and mechanical conditions due to having the highest level of average atom free energy and their large amount of high energy grain boundary with large curvature. This size was very close to the calculated smallest size achievable by severe plastic deformation based on the grain refinement mechanism of dislocation evolution under present processing condition, at which both the highest density of dislocation and highest energy should be produced and induces poor stability. Below 70 nm, the deformation mechanism of nanograined Cu was transformed into a partial dislocation motion, which activated mechanically induced grain boundary (GB) relaxation accompanied by GB flattening and GB energy decrease and resulted in enhanced stability. This discovery offers the potential for developing nanograined metals with high strength and high stability.

1. Introduction Plastic deformation with large strain may result in the formation of ultrafine-grained (UFG) or nano-grained (NG) metallic materials, which exhibit enhanced strength compared to their coarse-grained counterparts [1,2]. Various severe plastic deformation processes, such as equal channel angular pressing [3], high pressure torsion [4], and accumulative rolling and bonding [5], have been developed for grain refinement in the past few decades [6]. During plastic deformation, a large number of grain boundaries (GB) accompanied by other crystal defects have been introduced into the materials and have provided a strong driving force for grain coarsening, resulting in the instability of NG metallic materials under mechanical or thermal stimulus [7]. The apparent grain coarsening temperatures of most NG pure metals are below 0.4 Tm (Tm is the equilibrium melting point) [8], which is clearly lower than the recrystallization temperature of the deformed coarse grained metals. In some NG metals, such as Cu, Ag, etc., grain coarsening occurs even at room temperature [9,10]. After grain coarsening, the strength of the materials has decreased significantly. Grain coarsening can also be triggered under various mechanical loading conditions in NG metallic materials, such as

tension, compression, fatigue and indentation, even at cryogenic temperatures, as proven by experiments and atomic simulations in many metals and alloys [11–16]. Grain coarsening easily occurs in the early stage of deformation and usually leads to strain localization and poor plasticity [17]. The poor stability of NG materials not only deteriorates their properties and use in applications but also hinders their processing by plastic deformation. The stability of metallic materials is determined by the stability of the GBs. GB stability is usually interpreted as the velocity of GB migration, which is controlled by the grain size (related to the curvature of the GB), GB energy and stored energy [18,19]. Generally, as the grain size decreases, the driving force for GB movement increases and the stability of the materials decreases. Other researchers have reported their experimental results regarding the stability of NG materials prepared by different processing techniques, these reports have proved the comment of “smaller grain size, less stable” [7,8], which brought a dark cloud over the prospects of the research and possible applications of NG metallic materials. In this work, we discovered that there was a most unstable grain size of Cu prepared by surface mechanical grinding treatment (SMGT), below

* Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (X. Li), [email protected] (K. Lu). https://doi.org/10.1016/j.nanoms.2020.01.001 Received 15 November 2019; Accepted 12 December 2019 Available online xxxx 2589-9651/© 2020 Chongqing University. Production and hosting by Elsevier B.V. on behalf of KeAi. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Please cite this article as: X. Zhou et al., 70 nm: The most unstable grain size in Cu prepared by surface mechanical grinding treatment, Nano Materials Science , https://doi.org/10.1016/j.nanoms.2020.01.001

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Table 1 The parameters used in the SMGT process for two types of samples. Materials

Types

v1 (rpm)

v2 (mm/min)

ap (μm)

d (mm)

Repeated times

D (mm)

T (K)

Cu

Straight rods Dog-bone rods

600

20

40

6

10

10 9

~77

(v1: rotating velocity of the sample; v2: sliding velocity of the tool tips; ap: the preset penetration depth of the tool tip into the sample surface each pass; d: diameter of the hemi-spherical WC/Co tool tip; T: processing temperature; D: diameter of the sample).

copper layer was electro-deposited onto the processed surface of the Cu samples to avoid possible damage during sample preparation. The SEM and TEM foil samples were prepared by cutting, mechanical thinning and a final electropolishing or ion thinning. The electrolyte used for electropolishing was composed of 25% alcohol, 25% phosphorus acid and 50% de-ionized water. In order to identify the grain size distribution along the depth, we measured the average grain size from the TEM images. Specifically, we acquired images of the cross-sectional and longitudinal samples and recorded the corresponding distance of each image away from the surface as their depth. Then, we divided the images into groups according to their depth and measured the interception length of the short axis of grains in each group. After that, the average grain size based on the number fractions of each group were obtained by Gauss fitting. Every value of the average grain size was averaged for more than 300 grains. The density of dislocation in typical layers of the as-prepared samples were estimated by X-ray diffraction (XRD) using a Cu-Kα ray with a scanning step of 0.02 in the 2Θ range of 30–100 . The influence depth of the X-ray was approximately 10 μm. The stored energies of the NGs with different average grain sizes were measured by the use of a PE differential scanning calorimeter at a heating rate of 40 K/min. Each sample was scanned twice for an accurate measurement of the exothermal enthalpy released during the grain coarsening process. The Vickers hardness distributions along the depth were measured using a Qness Q10 Aþmicrohardness tester. The maximum load of the

this size, the stability of the NGs unexpectedly improved, rather than worsening, as the grain size decreased. 2. Experiments 2.1. Materials and methods Commercial, pure Cu rods (99.97 wt %) were used in this investigation, they were annealed at 723 K for 2 h to form fully recrystallized equiaxial grains. The rods with a diameter of 10 mm and the dog bone shaped bars with a gauge diameter of 9 mm and a length of 20 mm were processed by surface mechanical grinding treatment (SMGT) [20] at cryogenic temperature. The straight rod samples were used for thermal tests and the dog bone shaped samples were used for tensile tests. The specific SMGT processing parameters for the two types of samples are listed in Table 1. Several passes of the SMGT were processed in order to achieve a thick and uniform gradient NG surface layer. The surface of samples was smooth (Ra ¼ 0.3 μm) and no cracks were detected. 2.2. Structural analysis The cross-sectional and longitudinal microstructures of the asprepared, as-annealed and as-tensioned samples were characterized using a FEI Verios 460 scanning electron microscope (SEM) and a FEI Talos F200X transmission electron microscope (TEM). First, a pure

Fig. 1. (a) A typical cross-sectional SEM image of the gradient NG Cu; (b) The distribution of Vickers hardness in the top 1100 μm layer; (c) The average grain size distribution along the depth in the top about 150 μm layer, error bars indicate the standard error of average grain size and the depth range for measurement. 2

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Fig. 2. (a, b, c) Typical bright-field TEM images of NGs at ~5 μm, ~30 μm and ~110 μm deep from the treated surface of the gradient NG Cu samples. (d) Typical XRD curves in the top about 10 μm layer, around 30–40 μm layer and around 100–110 μm layer in the gradient NG Cu samples.

measurement was 25 g, and the holding duration was 10 s.

DepthC ¼ eεt =2 Depth0 ;

2.3. Thermal stability test

where DepthC is the corrected depth, Depth0 is the measured depth from TEM observation, and εt is the true strain of the position for TEM observations.

A tube furnace with a protective Ar atmosphere was used for the isothermal annealing treatment, the temperature control accuracy of the furnace is about 2 K. The as-prepared samples were annealed at every preset temperature, namely 373, 393, 413, 433, 453, 473, 523, 573 and 623 K (holding for 30 min at each temperature), then air-cooled down to room temperature for SEM and TEM observations. The thermal stability of Cu as a function of the grain size was analyzed according to the structural changes in the Cu samples after the annealing treatment.

(1)

3. Results 3.1. Microstructure of gradient nanograined Cu A typical cross-sectional microstructure of the gradient NG pure Cu bar prepared by SMGT is shown in Fig. 1a. According to the measurement of the grain size from TEM images, the average transversal grain size in the topmost layer was 40  10 nm with an aspect ratio of about 1.7. As the depth increased, the grain size increased gradually, the average transversal grain size at about 150 μm depth was 200 nm, and the grain size distribution in the top approximately 150 μm layer is displayed in Fig. 1b. The deformed coarse grained structure adherent on the deformation-free core in the depth span of 150–500 μm, which was verified by the hardness distribution, as shown in Fig. 1c. The Vickers hardness averaged for the top 20 μm layer was 1.8 GPa (the hardness in the topmost layer was as high as 2.0–2.1 GPa, which was measured directly in the treated cambered surface) and decreased along with the depth increased, and the hardness of coarse grained core is 0.7 GPa. The morphology of the NGs of different average grain sizes in the top layer can be seen in the TEM images, as shown in Fig. 2 (a, b, c). GBs in the topmost layer (0–5 μm depth) were flattened and plenty of twins were

2.4. Mechanical stability test The mechanical stability of Cu with different grain sizes was measured under a loading condition of uniaxial quasi-static tensile test to fracture, which was performed on an Instron 5982 testing machine with a constant strain rate 1.5  103 s1 at room temperature. We took the sample cut from a uniformly deformed section with a true strain about 0.27 as the research object. The correlation between mechanical stability and average grain size was evaluated through the grain size variations of different initial grain sizes (corresponding to different depths in the asprepared samples) in the longitudinal section of samples before and after tension. Due to the shrinkage of the samples’ cross-sections after tension, the depths of the tensioned samples were corrected by applying the formula 3

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of severe plastic deformations [25–30], and it also conforms to the general trend that the smaller grain size was, the less stable the grains were. When the grain size was below a critical size (approximately 70 nm in the annealing experiment), the grain coarsening temperature increased remarkably rather than dropping continuously. In other words, the lowest grain coarsening temperature appeared at grain sizes near 70 nm. The TEM and SEM images of grains with typical average grain sizes in the as-prepared NG Cu sample and the sample annealed at 523 K are shown in Fig. 4.

3.3. Size dependence of the mechanical stability in Cu Uniaxial quasi-static tension was used for the investigation of the effects of grain sizes on the mechanical stability of Cu prepared by SMGT. After tension, the NG surface layer deformed uniformly along with the coarse grained core without any surface cracking or delaminating [31]. Obvious grain coarsening was recognized in the NG surface layer of tensioned sample as compared to the microstructure of the as-prepared sample. The degrees of relative grain size change (ΔD/D0) measured by TEM in the NG and UFG Cu after tension in this experiment are plotted as the function of the initial average grain size (Fig. 3b). Mechanically induced grain coarsening in pure Cu began at a grain size of nearly 200 nm and increased as the grain size decreased from 200 nm to around 75 nm, the degree of the relative grain size change of the grains with an initial average grain size of about 75 nm was as high as 60%. The finding that mechanical stability is dependent on grain size is in agreement with the reported data [13,32,33] and also conforms to the trend of “smaller grain size, less stable.” However, a deviation from the trend appeared at grain sizes of approximately 75 nm, below this size, mechanically induced grain coarsening was suppressed gradually as the grain size decreased. The degree of relative grain size change in the top layer of the sample with initial grain sizes of about 40 nm was less than 20%. The peak of the mechanically induced grain coarsening occurred at grain sizes of approximately 75 nm. The TEM images of grains of the typical average grain size in the as-prepared gradient NG Cu sample and the tensioned sample are shown in Fig. 4.

Fig. 3. (a) Grain size dependence of the normalized instability temperature (TGC/Tm) in NG and UFG Cu prepared by different severe plastic deformation processes, error bars are the variation range of measured instability temperature and the average grain size span. (b) Grain size dependence of the measured relative grain size change (ΔD/D0) in NG and UFG Cu prepared by severe plastic deformation, error bars indicate the typical variation ranges of ΔD/D0 and the standard deviations of D0.

inside the grains (Fig. 2a), while the boundaries of the grains in subsurface layer were very curved. The intragranular inhomogeneous contrast in the subsurface layer indicated that there were many dislocations, while there seemed to be less in the top layer. However, as measured by XRD, the dislocation densities in different layers in the depth range of 0 to around 110 μm are comparable. The estimated dislocation density in the NG layer was (1.95  0.5)  1015 m2 (ρ ¼ 16:1  ε2 =b2 ) [21], which is consistent with that measured in NG Cu prepared by equal channel angular pressing or dynamic plastic deformation [22,23]. The typical XRD curves in three different layers of Cu are shown in Fig. 2d. No contamination in the surface layer was identified beyond several tens of nanometers due to the low processing temperature, which has been described in previous work [20,24].

3.4. Size dependence of the stored energy The stored energy of NGs with different average grain sizes were measured using a PE Differential Scanning Calorimeter (DSC) equipment and the heat flow curves are shown in Fig. 5a. The grain coarsening onset temperatures (To) of three samples with different average grain size ranges were comparable at about 420 K, because the three samples all contained plenty of grains with sizes close to 70–75 nm, which are most unstable. Considering the heating rate of 40 K/min, the onset temperatures agreed well with the results measured in isothermal annealing experiments (Fig. 3a). The grain coarsening peak temperatures (Tp) of the sample with average grain sizes of 40–65 nm were located at 500 K and 680 K respectively, and the end temperature (Te) was approximately 700 K, which was consistent with the finding that plenty of grains with sizes close to 40 nm can be stable even at 623 K during isothermal annealing. The exothermic peak of the sample with an average grain size range of 70–120 nm is relative gentle because the sample may contained many grains with sizes below and above 70–75 nm due to the structural fluctuations in the sample prepared by SMGT, and Te was about 660 K. The Tp and Te of the sample with average grain sizes that ranged from 90 to 140 nm were 515 K and 590 K. The value of the stored energy of NGs calculated from the exothermic peak increased from 2.55  0.3 J/g to 2.78  0.5 J/g as the average grain size range reduced from about 90 to 140 nm to 70–120 nm. However, the values of the stored energy decreased to 2.40  0.2 J/g as the average grain size range further decreased to about 40–65 nm.

3.2. Size dependence of the thermal stability in Cu The correlation between the grain size and the thermal stability of Cu was examined through a series of annealing experiments. When the annealing temperature reached 393 K, grain coarsening occurred first in the layer with an initial grain size span of about 70–110 nm. With increased annealing temperature, grain coarsening occurred in both the layer with larger initial grain size and the layer with smaller initial grain size. The range of initial grain size where grain coarsening occurred expanded with the annealing temperature increased. The grain size dependence of grain coarsening temperatures found in our sample, as well as in the literature [25–30], is depicted in Fig. 3a, one can see that the grain coarsening temperature decreased along with the grain size decreased in the submicron grains in this experiment, which is in accordance with the other data about Cu processed by various techniques 4

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Fig. 4. Typical bright-field TEM images and a SEM image of grains in the specific depth layer with initial grain size of ~50 nm (a, b, c) and ~100 nm (d, e, f) in the gradient NG Cu samples. (a, d) are from the as-prepared sample, (b, e) are from the sample annealed at 523 K for 30 min, and (c, f) are from the tensioned sample with a true strain of 0.27.

Fig. 5. (a) Typical heat flow curves of NG Cu prepared by SMGT with different average grain size range measured by DSC. (b) Average atom free energy in Cu samples with different average grain size and average atom free energy at their grain boundary regions.

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4. Discussion

ds G ffi KM α  ; b σm

Based on our thermal and mechanical experimental results, the most unstable grain size in Cu prepared by SMGT was approximately 70–75 nm. As reported before [24,31], below approximately 70 nm the deformation mechanism of NG Cu is transformed from a full dislocation motion into a partial dislocation motion according to the dislocation multiplication model of Frank-Read source, this induces the GB relaxation of NGs accompanied by GB flattening and GB energy dropping. These effects lead to the enhanced stability of NGs below 70 nm. However, above sizes of approximately 70 nm, dislocation motion is the dominant deformation mechanism, and this leads to the accumulation of stored energy in the form of dislocation and GB. To evaluate the atom free energy level in NG samples with different average grain sizes, we calculated it based on the measured stored energy of NGs in three different layers. The formula we used was Qatom ¼

Q ; NA  m=MCu

in this case, σ m is the highest possible stress, G is the shear modulus and α is a numerical constant, typically of the order of 0.5. K is of the order of 10, M is about 3, and b is Burgers vector. σ m could be regarded as the maximum flow stress during processing. Considering high strain rate and cryogenic temperature in the sample processing for our experiments, σ m could be estimated as follows. According to the literature [38], the yield stress of Cu at 77 K is about 1.6 times higher than Cu at 298 K, which is also consistent with our experiments [39], so the yield stress at 77 K can be estimated as 1.6σy-298K (σy298K ¼ 0:113 þ 3:453=d1=2 GPa) [40]. In addition, the yield stress at high strain rate can be deduced by the use of σ the exponent of strain rate sensitivity, m ¼ dln dln_ε , which is usually around 0.04 to 0.07 for NG Cu [41,42]. Thus, σ m at the processing condition of our experiment was

σ m ¼ 1:6  σy298K  emðln_εlnε_0 Þ ;

(2)

Q  QTotaldis; ; NGB

ds G ¼ KM α  ; 1:6  σy298K  emðln_εlnε_0 Þ b

(7)

we used m ¼ 0.04–0.07, ε_ and ε_0 were 104 s1 and 103 s1, respectively, and G was 48 GPa. It worked out that the smallest achievable grain size is 71.32–154.43 nm. This implied that the saturated level of dislocation in the deformation condition of SMGT should be produced as the grain was refined to that size, at which size the grains possessed the highest stored energy and were most unstable. Such values are close to the size of the grains that were most unstable in our experiments.

(3)

5. Conclusion

where QTotal-dis. is the total energy in the form of dislocation and NGB is the number of atoms at the GB region. According to the energy of the dislocation per unit length (Qdis. ¼ 5  109 J/m) reported in literature [34], the total energy of the dislocation per unit mass in the surface layer of the as-prepared samples can be estimated as QTotaldis: ¼ Qdis:  ρdis: =ρCu ;

(6)

in which ε_ is the strain rate during the process of SMGT (103-104 s1) [43], and ε_0 can be treated as the strain rate during the process of quasi-static tension. The smallest achievable grain size can be calculated by the following formula:

in which Q is the measured stored energy per unit mass, NA is the Avogadro constant, and MCu is the molar mass of Cu. The calculated average atom free energy in samples with average grain size range of 40–65 nm, 70–120 nm and 90–140 nm were 1.58  0.13 meV, 1.83  0.33 meV and 1.68  0.20 meV, respectively, as shown in Fig. 5b. The average atom free energy increased as the grain size decreased from 90-140 nm to 70–120 nm, but obviously decreased when the grain size range was 40–65 nm. That's to say, the highest average atom free energy of the NGs led to the wrost stability. Also, considering the vital role of the GB energy as the driving force of GB migration, we could estimate the average atom free energy at the GB region by applying the formula QGBatom ¼

(5)

In summary, we found the most unstable grain size of Cu during the conditions of annealing and tension during this study, which was approximately 70–75 nm. The experimental results showed that the thermal and mechanical stability of Cu decreased as the grain size decreased when the grain size was above 70–75 nm, this is attributed to the accompanying increase of free energy and the amount of GB. However, when the grain size was below approximately 70–75 nm, the thermal and mechanical stability of Cu increased as the grain size decreased. Such an abnormal stability trend was brought about by the decrease of GB energy and GB flattening caused by mechanically induced GB relaxation. The worst stability occurred in grains whose sizes were close to 70–75 nm, this is ascribed to their highest average atom free energy and high grain boundary energy.

(4)

in which ρdis. and ρCu are the dislocation density and the density of Cu (ρCu ¼ 8.9 g/cm3). If we take the width of the GB as the spacing of three (111) planes, the average atom free energy at the GB region can be estimated. As seen in Fig. 5b, the average atom free energy at the GB region reduced slightly from 47.71  12.05 meV to 44.33  16.12 meV as the grain size decreased from 90-140 nm to 70–120 nm, and decreased sharply to 17.13  3.22 meV as the grain size decreased to 40–65 nm. The slightly reduced atom free energy at the GB region in the sample with an average grain size range of 70–120 nm can be ascribed to the wide range of grain size distribution and the structural fluctuation of the sample prepared by SMGT. Thus, the average atom free energy at the GB region might be comparable when the grains with size above 70–75 nm, which is in accord with the literatures [27–29]. As the grain size decreased, the amount and curvature of the GB increased, and this increased the driving force of the GB migration and contributed to the poor stability. When the grain sizes were below approximately 70 nm, the average atom free energy at the GB region greatly decreased and the GB became flattened (Fig. 2a), leading to the enhanced stability. Based on the grain refinement mechanism of dislocation evolution [35,36], we can calculate the saturated grain size under present processing condition. Considering the dynamic equilibrium of dislocation multiplication and annihilation, there is a smallest achievable grain size (ds), which can be estimated by using the following formula [37]:

Acknowledgements This work has been supported by the Ministry of Science and Technology of China (Grant Nos. 2017YFA0204401 and No. 2017YFA0700700), the Chinese Academy of Sciences (Grant No. ZDYZ201701), and the Liaoning Revitalization Talents Program (Grant No. XLYC1808008). References [1] M.A. Meyers, A. Mishra, D.J. Benson, Prog. Mater. Sci. 51 (2006) 427–556, https:// doi.org/10.1016/j.pmatsci.2005.08.003. [2] R.Z. Valiev, Y. Estrin, Z. Horita, T.G. Langdon, M.J. Zehetbauer, Y.T. Zhu, Mater. Res. Lett. 4 (2016) 1–21, https://doi.org/10.1080/21663831.2015.1060543. [3] R.Z. Valiev, T.G. Langdon, Prog. Mater. Sci. 51 (2006) 881–981, https://doi.org/ 10.1016/j.pmatsci.2006.02.003.

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