Measurement of Crystal Lattice Rotations under Nanoindents in Copper
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Measurement of Crystal Lattice Rotations under Nanoindents in Copper
Kirsten K. McLaughlin, Nadia A. Stelmashenko, Stephen J. Lloyd, Luc J. Vandeperre and William J. Clegg Department of Materials Science and Metallurgy, University of Cambridge, Pembroke Street, Cambridge, CB2 3QZ, UK. ABSTRACT A technique is described to measure the rotations of the crystal lattice in the deformed region around a nanoindent from volumes smaller than 3 × 10-5 µm3. To demonstrate this method, a copper crystal has been indented on its (001) face to depths of 500 and 1300 nm. Cross-sections of nanoindents were prepared for transmission electron microscopy by focused ion beam milling, and rotations were measured about the [001], [010] and [100] axes using convergent beam electron diffraction. INTRODUCTION The hardness of a small indent is often greater than that predicted using continuum plasticity [1,2]. This is normally attributed to the greater density of dislocations required to accommodate the strain gradient as the indent depth decreases [3,4], although theories based on the rate of energy dissipation have also been suggested [5]. Experimental study of these ideas remains difficult and limited to atomic force microscope (AFM) measurements of plastic zone sizes [6-8], or to in-plane transmission electron microscopy (TEM) of dislocation patterns [9,10]. The former gives no sub-surface information, while studies of dislocation patterns are difficult due to the high dislocation density under the indenter [9]. One possibility for experimental confirmation is to measure the rotations of the crystal lattice, which are caused by the accumulation of an excess of dislocations of a particular sign [11]. These rotations can be measured quantitatively in different regions of the plastic zone. Yang et al. [12,13] were able to measure rotations from volumes of about 1 µm3, but other work has shown that there are variations on a smaller scale [9]. The aim of this work is to demonstrate a technique that measures the lattice rotations in smaller volumes than has been possible thus far. EXPERIMENT A (001) single crystal of copper was mechanically polished to 0.25 µm and indented using a Berkovich tip (Nanotest 600, Micromaterials) to give 500 and 1300 nm deep nanoindents. Electron-transparent cross-sections were made parallel to the [010] axis using the trench technique by focused ion beam milling, as described elsewhere [14]. No bending of the foil was observed in the last stages of milling and the final thickness was about 200 nm. Convergent beam electron diffraction (CBED) patterns were obtained by TEM (Philips CM30), operating at 300 keV. An example of an on-axis and a rotated CBED pattern can be seen in Figure 1.
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Figure 1. (a) CBED pattern on the [100] axis, unrotated. Plates are taken at several exposures and nested so detail from different intensities can be seen. The dark area at the bottom of the pattern is due to overhang from the trench. (b) CBED pattern of rotated and tilted crystal. This crystal has been rotated clockw
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