3-D Raman spectroscopy measurements of the symmetry of residual stress fields in plastically deformed sapphire crystals Thomas Wermelinger, Cesare Borgia, Christian Solenthaler, Ralph Spolenak * Laboratory for Nanometallurgy, Department of Materials, ETH Zurich, Wolfgang-Pauli-Strasse 10, 8093 Zurich, Switzerland Received 19 February 2007; received in revised form 10 April 2007; accepted 13 April 2007 Available online 12 June 2007 Abstract The development of methods to characterize materials in three dimensions, such as tomography by X-rays, focused ion beam and electrons, has led to progress in the understanding of materials properties. Recently, even stress and deformation tensors could be mea- sured in three dimensions. Specifically the stress fields around indents in metals were studied by three-dimensional (3-D) X-ray stress microscopy. In this paper, we investigate the 3-D residual stress field around a microindent using confocal Raman microscopy with a lateral resolution of 300 nm and a depth resolution of 600 nm. The model system investigated was single crystalline sapphire, which was indented normal to its basal c(0 0 0 1) plane. A cross-section of the indent was studied by transmission electron microscopy to visu- alize the deformed microstructure. The major result is that the geometry of the indenter has no direct influence on the symmetry of the resulting residual stress field. Residual stresses directly depend on the crystal symmetry and the defect structures formed during inden- tation. Confocal Raman microscopy is a powerful method for analyzing 3-D stress fields and the corresponding defect structures (by peak width analysis) with a resolution in the submicron range. Ó 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Raman spectroscopy; Residual stress; Phase transformation; Microindentation; Ceramics 1. Introduction Novel applications in the microelectronics industry have intensified interest in sapphire as a substrate [1]. Various sapphire-based devices, such as fast neutron filters and high-pressure magnetic resonance cells, have been devel- oped. Specifically, the high strength and heat resistance of sapphire attracts a lot of attention. Therefore a pro- found knowledge of the mechanical properties is required. In this context, the deformation of sapphire has been extensively studied by several groups [1–12]. As a result, the deformation and fracture mechanisms of the sapphire single crystal are well known. In contrast, magnitude and distribution of residual internal stresses after plastic defor- mation, i.e. the properties of residual stress fields, still remain unclear. Since these stresses may cause failure, and hence affect the lifetime of devices, it is important to measure and to visualize them, ideally in three dimensions (3-D). At the moment, only a few methods are known to perform 3-D measurements with a resolution at or below the micrometer range. One method is 3-D X-ray diffraction microscopy, which has a resolution in the micrometer range [13]. Another is X- ray microbeam diffraction, which is an experimental option to measure the strain tensor with a submicrometer resolu- tion [14–16] in three dimensions. The 3-D distribution of the local crystalline phase, the texture and the elastic strain tensor can all be measured with a resolution below 1 lm. These instruments combine ultraintense synchrotron X- ray sources and advanced X-ray optics to probe crystalline materials. Only a few such systems are available world wide, and until now only a few such experiments have been performed to date. Consequently, alternative methods on the laboratory scale are needed. 1359-6454/$30.00 Ó 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2007.04.036 * Corresponding author. E-mail address: ralph.spolenak@mat.ethz.ch (R. Spolenak). www.elsevier.com/locate/actamat Acta Materialia 55 (2007) 4657–4665