Available online at www.sciencedirect.com Journal of the European Ceramic Society 28 (2008) 2213–2220 Analyzing indentation stress–strain response of LaGaO 3 single crystals using spherical indenters Siddhartha Pathak a,∗ , Surya R. Kalidindi a , Christine Klemenz b , Nina Orlovskaya c a Department of Materials Science and Engineering, Drexel University, 3141 Chestnut Street, LeBow 344, Philadelphia, PA 19104, USA b Advanced Materials Processing and Analysis Center, University of Central Florida, Orlando, FL 32816, USA c Department of Mechanical, Materials, and Aerospace Engineering, University of Central Florida Orlando, FL 32816, USA Received 5 September 2007; received in revised form 22 January 2008; accepted 8 February 2008 Available online 2 April 2008 Abstract In this work, a new approach to spherical nanoindentation analyses has been described and utilized to study the anisotropy of mechanical properties for (1 0 0) and (0 0 1) LaGaO 3 single crystals. Unlike sharp indenters, indentations by spherical indenters permit the nanoindentation load–displacement curve to be converted more reliably into indentation stress–strain curves. Using a new definition of indentation strain, we present indentation stress–strain curves that are relatively insensitive to the radii of the indenters. These curves allow the modulus of the sample to be evaluated from the elastic loading segment, instead of the common practice of approximating it from the elastic unloading segment. These measurements indicate that the (1 0 0) LaGaO 3 single crystal has a higher modulus and a higher hardness compared to the (0 0 1) sample. © 2008 Elsevier Ltd. All rights reserved. Keywords: Nanoindentation; Perovskites; Mechanical properties; Hardness; Modulus; LaGaO 3 1. Introduction Mechanical properties of the lanthanum gallate-based per- ovskites have received limited attention with most of the reports being concentrated on the polycrystalline ceramics 1 which yields only average properties. 2 In our previous work, 3 the anisotropy in the mechanical properties of (1 0 0) and (0 0 1) LaGaO 3 single crystals (the indentation direction being perpen- dicular to the (1 0 0) and (0 0 1) planes) was studied with respect to their micro-hardness, fracture toughness and crack propa- gation behavior when indented with sharp indenters (Vickers and cube corner indenter). Sharp indenters produce much higher stress and strain in the vicinity of contact which results in produc- tion and propagation of well defined cracks around the hardness impression. 4 Although this feature enables the determination of fracture toughness, 5 it is a major drawback in studying the elas- tic behavior of the material. On the other hand, the stress field for a spherical indenter is well defined and does not exhibit the stress singularities inherent in the sharp indenters. This makes the spherical indenters an attractive option in that they enable ∗ Corresponding author. Tel.: +1 267 243 9492; fax: +1 215 895 6760. E-mail address: sp324@drexel.edu (S. Pathak). one to follow the entire evolution of damage modes from ini- tial elasticity, the initiation of plasticity at a critical load (yield behavior in the form of elastic limit) to full plasticity. 6 An added advantage in using spherical indenters is that they can be used to generate indentation stress–strain curves, using certain idealizations. 7,8 LaGaO 3 has been shown to be orthorhombic (o) Pnma at ambient temperature 9 and to undergo a first order phase transi- tion to a rhombohedral (r) R ¯ 3c structure at 145 ◦ C. 10 Pressure can also control the relative stability of these two phases. 11 Increase in pressure should reduce the volume of the cell. In the case of LaGaO 3 , the volume of the high temperature r phase is smaller than the low-temperature o phase. Thus at room tem- perature, the r phase is stabilized under higher pressure while releasing the pressure stabilizes the o phase. It has been shown that at the hydrostatic pressure of 2.5 GPa the r structure exists at room temperature with small amount of residual o phase. 11 Above 2.5 GPa, only the r R ¯ 3c phase was reported. Upon pres- sure release at 1.83 GPa the reversible transition occurred and predominantly o Pnma phase together with a small amount of the r R ¯ 3c phase was found. At pressures below 1.83 GPa, only the o Pnma phase was reported. In this article, the calculation and analysis of indentation stress–strain curves obtained during nanoindentation by spheri- 0955-2219/$ – see front matter © 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.jeurceramsoc.2008.02.009