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Relationship Between Hardness and Dislocation Processes in a Nanocrystalline Metal at the Atomic Scale

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Relationship Between Hardness and Dislocation Processes in a Nanocrystalline Metal at the Atomic Scale PHYSICAL REVIEW B 83, 224101 (2011) Relationship between hardness and dislocation processes in a nanocrystalline metal at the atomic scale Frederic Sansoz* School of Engineering and Materials Science Program, The University of Vermont, Burlington, VT 05405, USA Kevin D. Stevenson School of Engineering, The University of Vermont, Burlington, VT 05405, USA (Received 18 February 2011; revised manuscript received 25 March 2011; published 9 June 2011) By combining atomic force microscopy (AFM) and large-scale molecular dynamics (MD) simulations, we examine at comparable scales the atomistic processes governing nanohardness in electrodeposited nanocrystalline Ni with a mean grain diameter of 18.6 nm under confined contact deformation. Notably, this mean grain diameter represents the “strongest” size for Ni and other nanocrystalline materials where both crystal slip and grain-boundary deformation processes are intertwined to accommodate plastic flow. Accurate hardness measurements were obtained from shallow nanoindentations, less than 10 nm in depth, using an AFM diamond tip. We show evidence that the controlling yielding mechanism in the peak of hardness as a function of penetration depth corresponds to the emission of partial dislocations from grain boundaries. However, MD simulations also reveal for this grain size that the crystalline interfaces must undergo significant sliding at small penetration depths in order to initiate crystal slip. The strong interplay between intergranular and intragranular deformation processes found in this model nanocrystalline metal is discussed and shown to considerably reduce the local dependence of nanohardness on the initial microstructure at this scale, unlike past observations of nanoindentation in Ni electrodeposits with larger grain sizes. These new findings therefore constitute an important step forward to understanding the contribution of nanoscale grain-boundary networks on permanent deformation and hardness relevant for nanoscale materials and structures. DOI: 10.1103/PhysRevB.83.224101 PACS number(s): 62.25.−g, 62.20.Qp, 61.72.Ff, 61.72.Mm I. INTRODUCTION smaller than 850 nm in Ni electrodeposits, Yang and Vehoff37 have observed that the permanent displacement jump caused Mechanical strength in polycrystalline materials like metals by the nucleation of new dislocations decreased, and the is known to increase monotonically with the inverse square nanohardness increased, with decreasing grain size. Because root of grain size due to the classical Hall–Petch effect.1,2 the grains were large compared to the contact size, they argued Nanocrystalline materials with grains less than 50 nm in that new dislocations interacted directly with only adjacent diameter, however, possess a distinctive mechanical behavior grain boundaries. For nanoscale contacts, however, such pro- compared with coarse-grained polycrystals. Remarkably, this cesses become highly complex and stochastic, and therefore type of material exhibits a peak in elastic limit and hardness more difficult to verify experimentally, because the distance under deformation at a critical grain size, defining the so-called 3,4 between indentation site and the closest interface is mostly “strongest” size. This phenomenon has been understood for random and the mean contact pressure at yield point depends some time in bulk nanostructures in terms of the dominant on both the crystal orientation and the local grain boundary mode of plastic deformation at the atomic scale. Both model structure.38,39 Also, the above model breaks down when the experiments and atomistic computer simulations have proved contact zone becomes larger than the mean grain diameter, that a fundamental shift from grain-boundary-assisted crystal particularly in the nanoindentation of nanocrystalline materials slip to grain-boundary-localized deformation, such as grain- with grains less than 20 nm in diameter.40 As a result, coopera- boundary sliding and migration, takes place during grain tive deformation processes involving grain boundaries such as 5–30 refinement in nanocrystalline materials. Understanding the dislocation emission,13,36,41 twinning,42,43 grain rotation, and influence of nanoscale grain-boundary networks on nanohard- stress-assisted grain coarsening23,26,29,44–46can simultaneously ness in atomic-scale contacts is therefore increasingly impor- act to accommodate plastic flow during nanoindentation. How- tant for synthesizing thin films and nanoscale devices with ever, among all deformation processes at play, the fundamental improved resistance to contact deformation and failure. mechanism that predominantly controls materials hardness at Past models of plastic yielding during the nanoindentation this scale is not fully understood. Furthermore, the relationship of polycrystals are based on the nucleation and propagation between experimental nanohardness and underlying molecular of dislocations and their interaction with surrounding grain processes remained largely unexplored in this type of material. boundaries beneath penetrating tips. A typical sequence In this paper, using a combined experimental and compu- of plastic flow consists of the homogeneous nucleation of tational approach at the atomic scale, we report on accurate dislocations under the contact zone and their glide through nanohardness measurements and microstructure evolution in the indented crystal.31,33 This process is followed by either slip electrodeposited nanocrystalline Ni under confined contact arrest or dislocation absorption by neighboring interfaces.34–37 deformation with an atomic force microscopy (AFM) diamond By performing nanoindents in the center of individual grains tip. A salient feature of the present investigation is the 1098-0121/2011/83(22)/224101(9)224101-1 ©2011 American Physical Society FREDERIC SANSOZ AND KEVIN D. STEVENSON PHYSICAL REVIEW B 83, 224101 (2011) combination of AFM nanoindentation experiments and large- vertical Z range of 6.11 μm. A sapphire AFM cantilever with scale molecular dynamics (MD) simulations, which made a specifically designed cube-corner, single-crystal diamond it possible, to our knowledge, for the first time to attain tip (both the cantilever and the tip were assembled by Micro comparable scales of analysis in terms of grain size and Star Technologies, Huntsville, TX) was used to perform the contact zone-size during spherical nanoindentation. Also, AFM imaging and nanoindentation on the electrodeposited Ni the electrochemical environment during material synthesis specimen. A finite element analysis was used to determine the has been optimized in order to produce a fully dense Ni normal spring constant of this cantilever,48 which was found microstructure with a critical grain size at the maximum of equal to 906 N m−1. The area function of the tip and the hardness. In the following sections, we show clear evidence radius of curvature at the tip apex were obtained by scanning that a peak of hardness as a function of penetration depth the probe over a TGT1 Si grating made of 750-nm-high is observed, and we elucidate the dislocation processes inverted Si tips, and by analyzing the resulting image with controlling this phenomenon for very shallow indentations the tip detection feature in the software Scanning Probe less than 10 nm in depth. Furthermore we demonstrate that Image Processor (Image Metrology, Denmark). Calibration the nanohardness of nanocrystalline Ni electrodeposits at to obtain quantitative nanohardness measurements from AFM depths larger than 2.5 nm is not significantly affected by local nanoindentation was performed with a fused quartz specimen differences in microstructure despite the stochastic nature of following the force-matching method described elsewhere.48 confined deformation in nanoscale grain-boundary networks. The indentation hardness H was estimated from Fmax II. METHODS H = , (1) Ac A. Material synthesis where Fmax is the peak load applied by the diamond tip and Direct-current (dc) electrodeposition of pure Ni was per- A is the corresponding projected area of contact based on the ◦ c formed on a polished Si (100) wafer at 50 C under constant area of the residual impression after unloading. To determine −2 current density (18 mA cm ) until the deposit was about Ac accurately, we first measured in situ the residual depth hc 40 μm in thickness.47 The anode material was a 99.9945%- of the permanent indentation after unloading by noncontact − purity Ni foil. The bath consisted of Ni sulfamate (400 g L 1) topographical AFM imaging with the diamond tip. Second, h − c with a small amount of Ni chloride (10 g L 1) and boric was substituted into the tip area function established above. − − acid (30 g L 1)2.0gL 1 of Ni carbonate were used to raise Here it was assumed that the difference between contact depth the pH value by increments of 0.2. The Ni carbonate was and residual depth is negligible for shallow indentations in Ni. mechanically agitated in the bath for 30 min. At the desired pH, the entire solution was vacuum filtered through a 1.3- μm paper C. MD simulations filter to remove any Ni carbonate precipitates. Conversely, amidosulfamic acid was used to lower the pH if necessary. MD simulations were conducted using Large-scale The pH investigated in this study was equal to 4.5. We added Atomic/Molecular Massively Parallel Simulator49 with an 2mLL−1 of dipolar surfactant (NP-M2 antipitting agent) embedded-atom method interatomic potential for Ni from to decrease the surface tension of the solution and release Mishin et al.50 Two films
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