## 1 Introduction  
Nanoindentation has become a standard non-destructive technique to measure mechanical properties of materials and their phases at the submicron scale, especially when standard methods such as tensile, three-point-bending, and other tests cannot be used. The technique is successfully applied in industry and research, and is used to characterize metals, ceramics, minerals, thin films and coatings, polymers, composites, natural materials, biological tissues, and many more [1; 2; 3; 4; 5; 6]. To guarantee the validity of results, a set of empirical rules were established. Those include the 10% rule for indentation depth on coatings and thin films, 5% surface roughness, 1 degree for surface tilt and alignment [7], as well as spacing between the indents. In the literature about nanoindentation, a distance of at least 30 times the maximum indentation depth is suggested to avoid interference for Vickers and Berkovich tips in real tests [8; 9]. The validity of those rules was investigated to some extent experimentally and in combination with finite element analysis (FEA). Probably the most investigated is the 10% rule. A systematic experimental study of mechanical properties dependence on indentation depth of soft and hard coatings on various substrates showed that the rule very much depends on the properties of the substrate [10]. The validity of this rule was further investigated with the help of FEA studies [11; 12]. The finite element method combined with nanoindentation experimental data became a popular technique to support the investigation of the mechanical behavior of materials. [PERSON] et al. [13] used nanoindentation with a conical indenter to investigate the failure properties of a DLC/steel system. Finite element simulation under the ideal situation was applied to acquire coating fracture and interfacial bonding strengths as well as evolutions of failures in the coating-substrate system [13]. A deconvolution method was proposed to develop elastic modulus of thin films in a film-substrate bilayer system. This method optimized the load-displacement (P-h) cycle obtained from a finite element nanoindentation model towards the experimentally measured curve [14]. The relationship between the shape of the normalized loading P-h cycle and the indenter tip rounding radius was investigated through theoretical analysis and FEA [15]. [PERSON] et al. [16] studied the effects of crystallographic orientation, indentation speed, indentation depth, and indenter size for pure aluminum using both nanoindentation and the finite element method. The stress-strain behavior of ferrite and austenite in a commercial 2205 duplex stainless steel had been explored by both experimental and FEA methods in [17]. A proposed reverse algorithm with spherical indentations was confirmed by the load-displacement curve to simulate the deformation and load resistance for SiC in nanoindentation process using finite element method [18]. Another technique is proposed to combine the results of continuous stiffness measurements with spherical indenters, Hertzian theory and Berkovich nanoindentations to obtain load-displacement of indentation curves to their corresponding indentation stress-strain curves [19]. The technique was implemented to fused silica, aluminum, iron and single crystals of sapphire and ZnO. The effects of roughness on the reduced modulus of contact was explored using 3D FEA modeling to map the apparent modulus on a real rough surface as measured by atomic force microscopy [20]. Very limited work was done on finding the optimal indent spacing. When investigating bulk materials with large surface areas, to have large spacing between indents is not so important. The spacing becomes a problem when small volumes of materials with specific features have to be measured.