26.2.5 Determination of the Contact Pressure and Indentation Strain To facilitate the analysis of the experimental data, it is necessary to convert the indentation force (specific to the experimental set-up) to the more “generalized” parameter of average contact pressure. The mean contact pressure pi at the indentation force Fi (at which a Raman image was recorded) was calculated using the following equation: pi ¼Fi= π ac,i 2 ð26:1Þ where ac,i is the radius of the circle of contact at the force Fi. The contact radius ac,i was determined at a specific indentation force according to the approach employed by Weppelmann et al. [18]. ac,i ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffifi R 2 i Ri hp,i 2 q ð26:2Þ where Ri is the effective radius of indenter tip curvature and hp,i is the plastic deformation at the indentation force Fi. The plastic deformation hp,i at the indentation force Fi was calculated with the following equation: hp,i ¼hi δi 2 ð 26:3Þ wherehi is the total displacement andδi is the elastic deformation at the indentation forceFi. The elastic deformationδi at the indentation force Fi was calculated with the following equation: δi ¼hi hr,i ð26:4Þ where hi is the total displacement andhr,i is the residual displacement at the indentation forceFi. The values for Fi, hi andhr,i were determined from the force displacement data recorded during the indentation test. The indentation strain εi was estimated using the following equation: εi ¼hi=t ð26:5Þ where hi is the indentation depth at the indentation force Fi and t is the film thickness. As can be seen from the calculated values for pi and εi given in Table 26.2, the strain increases significantly with greater indentation forces, whereas the average contact pressure changes only slightly. 26.3 Results and Discussion Figure 26.1 shows two Raman spectra, one of which is taken outside the contact zone between indenter probe and sample and the other inside the contact zone under the first contact load. The spectrum taken outside the contact zone is representative of the pristine SoS featuring three peaks. Peak 1 observed at 522 cm 1 is associated with first-order phonon of the dc phase of Si [19, 20]. The peaks located at 378 cm 1 and418cm 1 (peaks 2 and 3) can be assigned to theEg andA1g modes of the sapphire substrate, respectively [21]. In the center of the contact region, significant changes in the Raman spectrum of the SoS sample were observed: Peak 4 appeared in the spectrum at 535 cm 1 and formed a shoulder on the righthand side of the dc peak. Peak 5 emerged at around 370 cm 1 forming a shoulder on the left-hand side of the sapphire Eg mode. As neither of those peaks seems to be associated with the dc Si structure or sapphire, their presence is a manifestation of phase transformation processes in the contact zone at the first contact load (pi: 5.8GPa, εi: 0.25). The contact pressure of Table 26.2 Values for average contact pressure pi and indentation strainεi calculated from the indentation data at indentation forces Fi, atwhich Raman images were collected Image 1 Image 2 Image 3 Image 4 Fi (mN) 44 83 122 201 pi (GPa) 5.8 6.3 6.4 6.4 εi 0.25 0.38 0.51 0.72 198 Y.B. Gerbig et al.
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