## 3 Instrumented Indentation  
Instrumented indentation (more commonly referred to as micro- or nanoindentation depending on the loads employed and depths of indentation), which involves an indenter of defined geometry being driven into the surface of a material under load before subsequent unloading, is essentially not dissimilar from a conventional hardness test. However, it differs from conventional hardness testing, which is determined from measurements of the residual indent dimensions. In instrumented indentation, by contrast, the loads and depths are continuously recorded during an indentation cycle to generate a load-depth curve, from which the hardness can be obtained. The load-depth curve also enables other properties to be determined. For example, \(E_{r}\), the reduced, or contact, modulus (from which elastic modulus may be calculated if the Poisson's ratio of the material is known), can be obtained from the initial portion of the unloading curve. A number of methodologies have been developed to measure mechanical properties from load-depth data, the most widely used being that of [PERSON] and [PERSON] [21]. A range of indenter geometries have been used for nanoindentation studies. The most widely used is the Berkovich indenter, which is in the form of a three-sided diamond pyramid. One notable advantage of the Berkovich geometry is that it is easier to produce an indenter in which the three sides of the pyramid meet at a single point [22], which enables it to be used to indent materials to very small depths. In contrast, with a Vickers (square pyramid) indenter, the four sides often do not converge at a single point, which can introduce errors in hardness measurements at small depths [23]. Cube corner indenters can also be used, although the smaller face angle (the angle between the indentation vertical axis and the indenter faces) of a cube corner indenter is only 35.3\({}^{\circ}\) (c.f. 65.3\({}^{\circ}\) for a Berkovich indenter) which can result in different deformation behaviour [24]. Nevertheless, they may be used to measure hardness and elastic modulus, although they can be more fragile than other indenter types; they are also prone to wear more rapidly [23]. As well as pyramidal indenters, spherical indenters are also used, one advantage being the ability to study the stress-strain behaviour of the material (e.g., yield stress and strain hardening exponent). Instrumented indentation therefore enables the measurement of mechanical properties from components which cannot be measured by more conventional test methods (e.g., tensile or compression tests), although it does not eliminate the need for such tests. Instrumented indentation has been used to measure the mechanical properties of a wide range of bulk materials: see, for example, [25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36]. In instrumented indentation (hereafter referred to as nanoindentation) the range of loads used are typically between 1 \(\mu\)N and 500 mN, while the indent depths are usually in the range of 5 nm to 5 \(\mu\)m. The upper end of these ranges therefore overlaps with the lower end of the range covered by conventional microhardness testing. Owing to the localised nature of nanoindentation, tests conducted at lower loads (<10 mN) and depths (<1 \(\mu\)m) enable the properties of coatings and other surface films (e.g., oxide layers) as well as individual constituents in multi-phase materials to be obtained. One such example was that of [PERSON] and [PERSON] [37], who used nanoindentation to obtain the properties of various rare earth intermetallic compounds in tin (Sn)-based solders. In order to overcome the difficulty of accurately locating individual indents on particular features, the measurements can be set up to perform a set of indentations equally spaced in a grid (shown in schematic form in Figure 1[38]) to obtain a map of the mechanical properties across the area of interest.