Journal of Alloys and Compounds 425 (2006) 429–435 Analysis of ISE in microhardness measurements of bulk MgB 2 superconductors using different models U. K ¨ olemen ∗ Department of Physics, Faculty of Science and Arts, Gaziosmanpa¸ sa University, 60240 Tokat, Turkey Received 2 January 2006; accepted 29 January 2006 Available online 10 March 2006 Abstract The indentation load–displacement curves of the MgB 2 sample are drawn by different peak load levels ranging from 300 to 1500 mN. Micro- hardness values are calculated from loading–unloading curves. The results show that the hardness values exhibited peak load dependence, i.e., indentation size effect (ISE) on intermetallic MgB 2 superconductors. The peak load dependence is analyzed by using the Meyer’s law, the Hays–Kendall approach, the Elastic/Plastic Deformation model, the Proportional Specimen Resistance model (PSR), and the Modified PSR mod- els. As a result, Modified PSR model is found to be the most effective one for microhardness determination of intermetallic MgB 2 superconductor. © 2006 Elsevier B.V. All rights reserved. Keywords: Superconductors; Mechanical properties; Indentation size effect (ISE) 1. Introduction Mechanical properties of superconductors are intimately con- nected to other properties like physical, structural, and electrical properties to determine the performance of devices prepared from the solids. For example, elastic constants of magnesium diboride are important from fundamental point of view because, they determine phonon spectrum responsible for superconduct- ing Cooper’s electron pairs. It is also important for design and fabrication of composite superconductors where metal compo- nents, presumably metal wires or tubes bear the load while they support superconducting current. Consequently, there is an inter- est in assessing the mechanical properties of superconductors. Among the various experimental techniques for the determina- tion of the mechanical properties, hardness testing is frequently used to assess the mechanical properties of solids in the form of bulk samples [1–5]. Vickers microhardness test is one of the convenient methods to estimate the mechanical properties of materials. On the other hand, depth sensing (or dynamic) microindentation method that is used in this study offers great advantages over the conventional Vickers microhardness testing [6–10]. ∗ Tel.: +90 356 252 15 82/3099; fax: +90 356 252 15 85. E-mail address: ukolemen@gop.edu.tr. Recently, Vickers microhardness testing has been applied to different kind of materials (superconductors, ceramics, semi- conductors, thin films, polymers, and alloys) [1,11–16]. It is revealed that some materials exhibit an increase in the hardness with decreasing load (indentation size effect, ISE) while others undergo a decrease in the hardness with decreasing load (reverse indentation size effect, RISE). Undoubtedly, the existence of ISE or RISE may hamper or preclude plausible hardness measure- ments. Furthermore, using a load dependent hardness number in material characterization may result in some unreliable con- clusions. Much work has been performed to explain the origin of the ISE. Several possible explanations focused on a number of phe- nomena including work hardening during indentation [17,18], load to initiate plastic deformation [19], indentation elastic recovery [17,20], mixed elastic–plastic deformation response of material [21], size of dislocation loops formed during inden- tation [22], strain gradients associated with dislocations [23], and indenter–specimen friction resistance of the specimen [24]. Recent reviews about the ISE [2,10,25] show that, despite all these mechanisms being considered, the cause of ISE is still a topic of debate and needs to be clarified. The aim of this study is to describe the ISE in intermetallic MgB 2 superconductor by using depth sensing indentation tech- nique and to determine the most suitable model for the estimation of true hardness value. 0925-8388/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2006.01.075