# Nanoindentation of Historic and Artists' Paints
## 4 Characterization of Artists' Paints
### Free Film Paint Samples
#### 4.1.4 Calibration and Cleaning of Sharp Indenter  
While 'pile-up' and roughness of the paint surface are two primary contributors to the discrepancy between the actual and theoretically predicted contact depths, improper calibration of the indenter shape as well as the contamination of the indenter tip can further impact this divergence. Typically, the shape of the Berkovich indenter is accurately defined with high precision and certified by the manufacturer. Nanoindentation defines the shape of the indenter with an area function, which describes the cross-sectional area of the indenter as a function of the distance from the apex. Such a function is routinely obtained using a calibration procedure developed by [PERSON] and [PERSON] [7; 18], which involves indenting a reference material with a known Young's modulus and Poisson's ratio to a range of depths. The most commonly used reference material is fused silica. The area function derived from this calibration procedure allows one to define the exact shape of the indenter that may be imperfect or worn at extremely small depths. However, due to the high stiffness of fused silica (Young's modulus of ~72 GPa), an indentation test with a maximum force available with most commercial nanoindentation instruments results in a contact depth no greater than 1 um (e.g., a maximum force of 100 mN results in a contact depth with fused silica of ~0.7 um). To test a realistic paint sample with a considerably rough surface, it is necessary to define the indenter shape at contact depths well beyond this instrumental limit. The three-dimensional shape of a pyramidal Berkovich indenter may be translated into an analogous two-dimensional conical indenter. This involves equating the triangular-shaped cross-section of the indenter at a given contact depth to a circle, and regarding the radius of the circle (\(a=\sqrt{A_{\mathrm{P}}/\pi}\)) as the equivalent contact radius of the indenter at that contact depth. An example of the two-dimensional shape function of a Berkovich indenter is given in Figure 7a. The equivalent contact radius (\(a\)) versus contact depth (\(l_{\mathrm{c}}\)) curve is fitted with a polynomial function in the form \(a=C_{1}h_{\mathrm{c}}+C_{2}h_{\mathrm{c}}^{1/2}\), where the first term describes the global pyramidal geometry of the indenter and the second term accounts for the rounding of the indenter tip. Such a function may be used to extrapolate the indenter shape, but only slightly beyond the contact depth range of calibration. When it is necessary to extrapolate the shape function far beyond the existing data, it may be more appropriate to use a linear function fitted to the linear portion of the data (i.e., \(h_{\mathrm{c}}\geq 200\) nm for this example, Figure 7b). To assess if the fitted calibration function adequately describes the shape of the indenter at several microns in contact depth, indentations may be performed on a bulk homogeneous material that is much more compliant than fused silica. In the GCI laboratories, a 9.5 mm thick polycarbonate sheet (Lexan) is used routinely for this task, with a resulting contact depth of ~5 um at 100 mN (depending on the loading condition used). At this depth, the substrate effect is nonexistent, and the reduced storage modulus measured with the CSM technique should remain constant over the entire depth range (excluding data collected at shallow depths influenced by surface roughness and tip imperfections). The results presented in Figure 7c show that the calibration function based on the applied procedure successfully extrapolates the indenter shape over the depth range necessary for testing realistic paint samples. Indentation on polycarbonate also serves as an effective method for cleaning the indenter. Soft and viscous paints readily contaminate the indenter tip, leading to systematic errors in successive measurements.