Grain Growth in Nanosized Nickel Deformed in a Confining Environment

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C: Physical Processes in Nanomaterials and Nanostructures

Grain Growth in Nanosized Nickel Deformed in a Confining Environment Yuejian Wang, and Jianguo Wen J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b01142 • Publication Date (Web): 09 May 2019 Downloaded from http://pubs.acs.org on May 9, 2019

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The Journal of Physical Chemistry

Grain Growth in Nanosized Nickel Deformed in a Confining Environment

Yuejian Wang,*,† Jianguo Wen‡

†Physics ‡Center

Department, Oakland University, Rochester, MI, 48309

for Nanoscale Materials, Argonne National Laboratory, 9700 S Cass Ave. Lemont, IL 60439

*Email: [email protected]

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ABSTRACT: Stress-induced grain growths were observed in many nanosized metals and alloys. Correctly understanding this unique feature is critical in designing and tailoring proper nanostructures for particular applications in mechanically harsh environments, e.g. high-stress concentration, mechanical vibrations. Though extensive researches have been carried out on metals or alloys subjected to deformation, experimental studies on metals deformed in a confining environment are severely lacking. Nearly all of the previous investigations on this theme were carried out either through theoretical simulations or by using transmission electron microscopy (TEM) to probe grain variation in vacuo. In the present study, we employed a powerful high-pressure technique along with high energy synchrotron X-rays to monitor the grain size evolution in situ, in nanosized nickel deformed in a confining environment. Our experimental data demonstrate, for the first time, that grain sizes grow with the increment of the confining pressure. Since plasticity strongly depends on the grain size of a given material, understanding and controlling fundamental mechanisms leading to stress-assisted grain growth may pave a new route to improve the mechanical properties of nanosized materials by tuning confining environment within which the deformation is operated.

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INTRODUCTION Generally, we believe that under heating material’s constituent grains/particles tend to grow into bigger ones. However, heating is not the only measure to realize materials’ growth. At room temperature, without any heating, grain growth has been found in nanocrystalline (nc) metals and alloys when they were subjected to plastic deformation via various experimental methods, such as high-pressure torsion,1 uniaxial compressive deformation,2 nanoindentation,3 and tensile tests.4-5 Even rapid grain growth at cryogenic temperature conditions, observed from both molecular dynamics simulation6 and experiments7, suggests that besides thermally activated process plastic deformation is also able to induce the grain growth in nc metals. Meanwhile, as we know, the plastic deformation may crash/break the materials into fine particles, which is the basic mechanism for the production of nanopowders by using top-down approach, for example, ball milling and high-pressure torsion.8-9 Therefore, the question is which direction will go, grain diminishment or grain growth, during the plastic deformation? The answer is that the change in grain size during the plastic deformation depends on the grain sizes of the starting materials. Briefly speaking, the starting materials with coarse grains are apt to be broken down into smaller particles while the nanomaterials incline to grow into bigger ones under the influence of severe stress accumulated in the sample during the plastic deformation. However, the nanograins cannot grow without limit. For instance, under the high-pressure torsion condition, nc nickel (Ni) reaches a stable state with a grain size ranged from 100 to 170 nm.10 Although the mechanical characteristic, as well as the variation of grain sizes of nc metals during plastic deformation, have been studied extensively, as described in the above, all of those investigations were performed by using a single deformation mode, such as indentation, tensile, and high stress torsion. The performance of nanosized materials during a complex deformation

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process, e.g. compressive-tensile deformation at various confining pressures, has not been thoroughly explored. Deforming nanosized material at different confining pressures is a robust means to expose its features in a broader perspective. It may tell us the connection between the yield strength of a nanosized material and the confining pressure, as well as whether the confining pressure can push up the upper limit of the grain growth during the plastic deformation process. Answers to these questions are vitally important to understand the unique properties of nc materials applied in an extreme environment. The goal of the present study is to investigate the mechanical properties and the change in grain size in a nanosized metal cyclically deformed (compression and extension) under various confining pressures. We choose nanosized Ni as the tested material because this material has been well characterized by using a wealth of deformation methods.1-2, 11-12 Therefore, by comparing the results of the present study with literature, we can accurately determine the impact of confining pressure on the mechanical properties as well as the grain size of this material during the cyclic deformation. We employed high-energy monochromatic synchrotron X-ray to in-situ monitor the evolution of diffraction patterns of nanosized Ni during the deformation. Xray diffraction patterns, shedding light on the strain/stress development as well grain size change in a material under severe plastic deformation condition, is a well-known technique applied in many disciplines, such as physics, chemistry, geology, material science and engineering, and geology.13-19 Compared to other traditional deformation approaches, this technique is capable of minimizing the measurement uncertainty caused by the presence of porosity or other artificial defects in the sample.20-26

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(a)

(b)

Figure 1. TEM characterization of the starting samples. a) the typical TEM image of the powdered samples. b) high-resolution TEM image showing that one particle contains several grains. EXPERIMENTAL METHODS The tested material, nanosized Ni powders were prepared by a ball-milling method.27 The TEM image, Figure 1a, shows that the grain size of the starting powdered materials is about 30-50 nm. Also, the image, Figure 1b, illustrates that one particle may accommodate a number of grains with disoriented lattice orientation and separated by grain boundaries. Considering the great ductility and flexibility of nickel, under compression, the powders may condense into a piece of bulk material, and thus the intimate contacting between particles facilitates the grain boundary migration and thereafter the grain growth. The deformation experiment was conducted via using a D-DIA apparatus, in conjunction with monochromatic synchrotron radiation ( = 0.1907 Å), at the GSECARS beamline 13-BM-D of the Advanced Photon Source, Argonne National Laboratory. The detail description of the experimental setup and the sample cell assembly, as shown in Figure 2a, has been published elsewhere.28 The compression process includes two stages: the hydrostatic compression (confining pressure) and then the deviatoric compression (differential pressure). Like the regular DIA, in D-DIA, one hydraulic actuator loads force along the vertical axis to push the six anvils

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moving symmetrically towards the center of the sample chamber to compress the sample hydrostatically. After the desired hydrostatic condition (confining pressure) is realized, the pair of anvils driven by two independent actuators (differential rams) shorten (compressive) or lengthen (tensile) uniaxially the sample alone the vertical direction, causing the differential strain/stress in the sample. We used four sintered diamond anvils, which are X-ray transparent and allow us to observe the entire diffraction Debye rings over the 360o detector azimuth range, perpendicular to the incident beam. Prior to the experiment, the distance between the sample and the charge-coupled device (CCD) detector as well as the detector orientation relative to the incident beam were calibrated using a CeO2 standard. The data were collected from a cylindrical sample subjected to two shortening-lengthening deformation cycles under confining pressures of ~2GPa and ~4GPa, respectively, hereafter referred to as the deformation cycle 1 and cycle 2. The deformation behavior of the sample was evaluated by calculating the macroscopic and microscopic strains accumulated in the tested material deformed under different confining pressures. Based on those data, we are able to identify the effect of confining pressure on the material’s plastic deformation as well as the grain growth. (e)

(f)

ng agi e m I lat P

ted ac y r f f a Di X-r (b)

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Anvil

vi l An ed itt m y s an ra Tr X-

vi l An

g sin c u ns o F Le

Anvil

ic at

t Sli

or irr M

om hr oc -ray n o X M

e pl le m Sa emb s as

D CC

m Ca

a er

Figure 2. a), scheme of the D-DIA synchrotron facility including the radiographic CCD camera. b)-d), digital radiographs of nanosized Ni under compressive deformation. Images display the 6


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sample b) before deformation, c) deformed with a total strain of 12.75%, d) deformed with a total strain of 19.71%. e), A typical CCD image recording diffraction Debye rings of the sample during the shortening process. f), representative unrolled diffraction pattern converted from regular Debye rings using software TWO2ONE by integrating data over 10o steps. The distortion of diffraction lines is induced by the differential stresses created during the deformation. The macroscopic or total strain, total, in the sample was calculated from the change in the sample length during the deformation, namely total=(l0-l)/l0, where l0 is the reference length of the sample while l is the sample length during the deformation. Typically, we choose the sample length at the beginning point of the 1st cycle deformation as the reference length. The sample length in pixels was measured from the radiography of the sample collected during the deformation by using an X-ray fluorescent CCD camera, as shown in Figure 2b-d. 2000 1800

111

1600 1400 Counts

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1200 1000

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600 400 200 4.0 4.4

4.8 5.2 5.6 6.0 6.4 6.8 7.2 7.6 8.0 8.4 8.8 9.2 2 (Degree)

Figure 3. An example of the determination of a single peak position by GSAS package. The 2θ scanned X-ray patterns were converted from Debye rings using TWO2ONE software by integrating the azimuth angle over 10o internals. The determined peak position was used to calculate the lattice strain at each azimuth angle via equation (1).

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The microscopic or lattice strains were derived from the distortions of X-ray Debye rings, as shown in Figure 2e, recorded by a CCD detector during the deformation. The approach of data analysis is similar to that described in the reference.29 As shown in Figure 2f, the twodimensional (2D) diffraction Debye rings were converted into conventional one-dimensional diffraction patterns by binning the data at 10o azimuth intervals using the software Two2One.29-30 Then the peak positions were determined by using GSAS package (Figure 3).31 Lattice strains were calculated following the equation: ε(φ, hkl)=[do(φ, hkl)-d(φ, hkl)]/ do(φ, hkl)

(1)

Where φ is the azimuth angle, and do(φ, hkl) and d(φ, hkl) are the d-spacings of peak positions at the reference point and at a given deformation condition, respectively. By neglecting the lattice preferred orientations, the lattice strains were then fit to the following equation ε(φ, hkl)= εh(hkl)-εd(hkl)(1-3sin2 φ)

(2)

to obtain the hydrostatic lattice strain, εh(hkl), and the differential lattice strain, εd(hkl), induced by the differential/deviatoric stress (Figure 4). The differential stress t is defined by t=σ1- σ3, where σ1 and σ3 are, respectively, the principal stresses in the vertical (φ=0o/180o) and horizontal (φ=90o/270o) directions applied to the sample during the deformation. The differential stress can be inferred by t(hkl)=εd(hkl)E(hkl), where E(hkl)is the elastic constant along a given (hkl) direction.32 0.010 0.005

Peak 111

Peak 200 0.005

0.000

Lattice strain

0.000 Lattice strain

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-0.005

-0.005

-0.010 0.06% 0.43% 1.45% 6.38% 12.75% 19.71%

-0.010

-0.015

0

60

120

180 240 Azimuth (Degree)

300

0.06% 0.43% 1.45% 6.38% 12.75% 19.71%

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Figure 4. Measured lattice strain ε(ø, hkl) as a function of azimuth angle ø for peaks 111 and 200 of nanosized Ni shortened in cycle 1. The hydrostatic lattice strains and differential lattice strains are determined by fitting these lattice strains to equation (2).

RESULTS AND DISCUSSION The differential stress derived from the lattice plane of (111) versus the total strain in cycle 1 is illustrated in Figure 5a. The sample experiences a uniaxial deformation including shortening and lengthening alone the vertical direction perpendicular to the incident X-ray path. The flow curve in Figure 5a shows the deformation stages including compressive elastic loading, plastic deformation with a large amount of hardening and then a slight softening, elastic unloading, tensile loading, and plastic deformation with a lasting softening. From the curve, we clearly see two yielding points in the elastic loading stage, one for micro/local yielding at which the local contact zone between nanograins is yielding, and the second one for macro/bulk yielding at which the entire nanograin, as well as the whole sample, becomes yielding. The similar phenomenon was observed in other metal and ceramic materials.21-22 The corresponding compressive yielding strengths, determined from points B and C in the flow curve, are 0.27, and 0.37 GPa, respectively. These yielding strengths are much smaller than the value of 2.35 GPa, derived from the broadening of X-ray peaks collected from energy-dispersive synchrotron radiation under tri-axial deformation conditions.33 The different research approach plus the different sample deformation condition perhaps induce the discrepancy in these values. Beyond the bulk yielding, the materials enter the plastic deformation stage with a significant stress increase versus total strain and then slightly softening (CDE part in the flow curve). The similar trend was also observed in previous investigation.33 From the maximum reached total strain 0.23,

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the materials start to elastic unloading, during which differential stress drops to zero, whereas the total strain decreases to 0.22. During this run cycle, the material has been changed permanently without any chance to be recovered fully. Therefore, during this loading and unloading, we observed an evident hysteresis on the flow curve. Thereafter, the material is deformed under tensile mode, which includes two yielding points (H and L points on the curve), 0.45 and 1.22 GPa, for micro/local and macro/bulk yielding strength respectively. We can see a substantial increase in the yielding strength compared to those values determined from the compressive stage. The repeatedly compression/extension and hardening/softening as well as loading/unloading process may be the reason for this increase. Beyond the bulk yielding point, the materials are plastically deformed with a softening (LMN part on the flow curve) instead of hardening detected in the compressive stage. 1.2

1.6

1.0

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0.8 G

A O

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-0.2 -0.4

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-0.6 -0.8 -1.0 -1.4

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Differential Stress (GPa)

B

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-1.2

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B

1.0

0.4 0.0

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0.6 0.4 0.2 0.0

A

F

-0.2 -0.4 H

-0.6 -0.8

M

L

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-1.0

-1.6

E

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L

-1.2 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13

Total percent strain


Figure 5. Deformation flow curves of the sample at ~2 GPa and ~4GPa, respectively. The deformation behavior of nanosized Ni in cycle 2, as shown in Figure 5b, is substantially different from that at ~2GPa. First of all, in the compressive stage, we only see one yielding point (point B on the flow curve) with a yielding strength about 1.1 GPa, which is about three times greater than the yielding strength determined from the shortening in cycle 1. However, the 10


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yielding strengths measured in the tensile stage, around 0.22 GPa (point G on the flow curve) and 0.45 GPa (point H on the flow curve), respectively, are significantly smaller than the ones detected in cycle 1, along with a work hardening (HLM part on the flow curve) instead of a work softening beyond the yielding point. All these observations suggest the confining pressure is a key factor for tuning the mechanical property of the nanomaterials. 0.16

0.23

0.22

Peak Width (degree)

0.15

Peak Width (degree)

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0.14

0.13

0.21

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0.12 -0.008

0.17 -0.006

-0.004

-0.002

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0.006

-0.008

-0.006

Differential Strain

-0.004

-0.002

0.000

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0.006

Differential Strain

Figure 6. Widths of peaks 111 and 200 as a function of differential strains. In Figure 6a, the deformation proceeds along the direction of A-B-C-D-E-F-G-H-I-G-J-K. The vertical line passing through the zero-strain point represents the reference state in which the peak width contribution from microstrains could be looked as zero (ignoring the instrumental effect). The decrease in widths of peak 111 suggests that the grain-growth apparently occurred with the increase of the confining pressure. Figure 6b shows that the trend of width change in peak 200 is the same as that in Figure 6a. As we know that the observed X-ray diffraction profile is a convolution of integrated effects of instrument response, grain size, micro-strains due to stress heterogeneity, lattice deformation, and dislocation density at a given pressure-temperature condition.21-22, 25 Grain growth and/or differential strain annihilation inside material could result in diffraction peak sharpening, given

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the instrument-related broadening is independent on the sample’s pressure and temperature. Therefore, the evolution of peak shapes of X-ray profiles enable us to find the change in grain size in the material deformed at different confining pressures, as it has been used in other studies.4, 12 Figure 6a shows the full widths at half maximum (FWHMs) for peak 111 as a function of differential strain in the run cycles. Again, we plausibly presume the instrumental contribution to the peak broadening is constant throughout the deformation, so the differences between the peak widths at the identical differential strains could be attributed to the grain size effect. In other hands, at certain conditions, if the peak widths and differential strains are exactly the same, the grain sizes at these conditions are indistinguishable. We measured the FWHMs along the direction of principal stress σ3, because σ3 is smaller than σ1 in magnitude and thus gives less effect to the X-ray peak width. In Figure 6a, a bar passing through the zero-differential strain was drawn. Along the reference bar, the peak widths contributed from differential strains are equal, so a narrow peak suggests the coarse grains in the sample. Under careful scrutiny, we can find the change in grain size at each deformation stage. At the compression stage from A to B, the straightly narrowing trend of peak widths suggests the continuous grain growth taking place in the sample based on the facts that compression causes higher strain density and supposedly, in turn, leads to broader peaks. This grain growth continued until the differential strain reached the value of 0.1361 (point B in Figure 6a), and then the peak began to widen (B to C in the inset in Figure 6a). It indicates that there exists an upper bound for the compression-induced grain growth in cycle 1, which is consistent with the observation in reference 1. During the lengthening process from C to D illustrated in Figure 6a, the peak sharpening, meaning the partial reversibility of peak broadening, may be attributed to the release of the microstrains built up during the compression stage since for nanosized

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materials the mechanism of deformation is controlled by grain boundary (containing a significant fraction of atoms in a grain) mediated process rather than the regular nucleation and motion of dislocation.11-12 The sections of lengthening D-E-F in the cycle 1 and shortening from F to G in the cycle 2 form an enclosed triangle, except that at the reference bar G is below D. It means, in that loop, the variations of peak width is mainly due to the creation of nonuniform microstrains during the sample’s tensile stage and the release of strains in the shortening process, in addition to a minor portion of peak broadening with respect to the grain growth. In the further deformation at the cycle 2, the shortening section of G-H-I and lengthening section from I to G form an enclosed triangle, and the two points H at reference bar are exactly coincident, which suggests that in these deformation processes there is no neat grain growth or strains accumulation taking place in the sample. The change in peak width is merely induced by the strain generation and annihilation. The tensile part G-J-K in cycle 2 is relatively parallel to the part D-E-F in cycle 1. Overall, the peak widths drop down from A to G during the compression-lengthening run cycles as the sample environment got more severely constraint. The similar trend was also observed in the other peak profiles, such as peak 200 (Figure 6b). Therefore, in an overall view, during the two cycles of compression and tensile test, the peak becomes narrower, suggesting a grain growth taking place during the deformation. Furthermore, the grain growth is strongly correlated to the confining pressure, which is able to further coarsen the grains. The mechanism leading to the grain growth during deformation in nc metals or alloys has been extensively explored through theoretical modeling6, 34-36and experimental approaches.1, 3-5, 37-38

By far, two models have been proposed, grain boundary sliding/migration3-6, 38 and grain

rotation.36-37, 39 Indeed, which model plays a major role in the deformation-induced grain growth? The answer to this question depends on the grain sizes.40 In the review article,40 the authors

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claimed that when grains are larger than 100 nm, the grain growth is mainly triggered and driven by the grain boundary migration, while grain rotation taking part in the grain growth when grain sizes below 100 nm. However, other studies show that these two models work simultaneously without a sum zero relation.34 For example, molecular dynamics modeling demonstrates that the grain growth in nanocrystalline Ni wires is realized by grain boundary sliding coupled with grain rotation. Another study based on energy analysis reveals that the mechanism behind grain rotation in nc is the grain boundary migration.39 Notwithstanding the discrepancies existing among these explanations for the stress-induced grain growth, it was found that in nc materials with grain size less than a critical value, the deformation is controlled by grain boundarymediated process rather than the conventional nucleation and motion of lattice dislocation in coarse-grained materials.7, 12 Obviously, there is a transition of deformation mechanism from intragranular to intergranular as grain size is reduced to below the critical value. All these theories, however, are facilitated to interpret the observations of stress-induced grain growth in nc materials under deformation without any confining pressure. The role of the confining pressure in regard to the stress-driven grain growth has to date not been explored. The present study shows that during a single run cycle the grains grow with an upper limit, but viewing the entire two cycles under two different confining pressures, the further grain growth with the increase of confining pressure occurs. Therefore, the confining pressure is favorable for the grain growth, in which both thermodynamics and kinetics are perhaps gotten involved. In point of view of thermodynamics, the grain growth is a consequence of the material’s intrinsic tendency to lower its surface/interfacial energy. For example, oil droplets dispersed in water would spontaneously favor merging into a big one, because of the following reasons: i) low surface energy means the enhanced thermodynamic stability; ii) surface energy is negatively

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proportional to the surface area; iii) the surface area substantially decreases during the droplet fusing process. We can imagine that if a force is uniformly applied to the entire system of oil droplets plus water, the droplet growth would proceed more rapidly. The grain growths in solid materials unlikely occur naturally and spontaneously, because of the prevention from the grain boundaries and defects. It requires either injecting energy through a heating process or doing work onto the system via an external compression to overcome the energy barrier for grain growth. During the grain growth, the grain boundary migration and grain rotation as well as grains merging into bigger ones result in the shrink in the sample’s total surface area, and so does the total surface energy. Therefore, overall the deformation from the external compression decreases the surface energy and thereby induces the grain growth. From the perspective of kinetics, the confining pressure may accelerate the grain boundary motion and/or grain rotation leading to larger grains.

CONCLUSIONS In summary, high energy synchrotron X-ray beamline combined with a high-pressure D-DIA apparatus was used to investigate the mechanical properties as well as grain size change in nanosized Ni deformed under compression-tensile cycles with different confining pressures. As observed before, the grains grow during the deformation. Meanwhile, for the first time, it was found that the grain growth is also correlated to the confining pressure, in a short, higher confining pressure leading to greater grains. The mechanism of the grain growth includes two portions: the grain boundary sliding and the grain rotation. The mechanical properties, such as yielding strength and working hardening/softening beyond the yielding point, are impacted by the confining pressure. The repeated deformation may largely change the relative positions of

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atoms, dislocations, grain boundaries, and thus alter the entropy of the entire nanocrystalline system, so the material demonstrates the varied mechanical features at different confining pressures.

Acknowledgment Portions of this work were performed at GeoSoilEnviroCARS (The University of Chicago, Sector 13), Advanced Photon Source (APS), Argonne National Laboratory. GeoSoilEnviroCARS is supported by the National Science Foundation - Earth Sciences (EAR 1634415) and Department of Energy- GeoSciences (DE-FG02-94ER14466). This research used resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC02-06CH11357. TEM work was performed at the Center for Nanoscale Materials, a U.S. Department of Energy Office of Science User Facility, and supported by the U.S. Department of Energy, Office of Science, under Contract No. DE-AC02-06CH11357. Part of the research was supported by the Faculty Research Grant of Oakland University, Michigan, USA.

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