# Grain Orientation and Hardness in the Graded Interlayer of Plasma Sprayed W on CuCrZr
## 3 Results and Discussion
After correction from instrumental contribution, the total broadening \(\beta_{T}\) of each peak is basically the sum of two terms, namely the size of coherently diffracting domains (\(\beta_{D}\)) and of the micro-strains (\(\beta_{\varepsilon}\)):  
\[\beta_{T}=\beta_{D}+\beta_{\varepsilon}=\frac{K\lambda}{D\cos\Theta}+2 \varepsilon\tan\Theta \tag{1}\]  
where \(D\) is the domain size (in this case grain size), \(\varepsilon\) is the average micro-strain, \(\Theta\) is the Bragg angle, \(\lambda\) is the wavelength, and \(K\) is a constant (=0.89). Figure 8: Cu (220) peak (**a**) and W (211) peak (**b**) collected in different positions in the interlayer. To make the comparison of the peak broadening easier, peaks were suitably shifted to occupy the same central position. As shown in Figures 3 and 4, the value of D in both the metals (W and Cu) is of the order of some microns. Thus, the contribution to peak broadening due to the size of coherently diffracting domains (\(\beta_{D}\)) can be neglected and \(\beta_{T}\approx\beta_{c}\). Therefore, the average micro-strain \(\varepsilon\) was directly determined from \(\beta_{T}\) and the dislocation density \(\zeta\) calculated by means of the Williamson-Smallman equation [25]:  
\[\zeta=\frac{\Xi\varepsilon^{2}}{k_{0}b^{2}} \tag{2}\]  
where \(\Xi\) = 16 is a constant, b is the modulus of the Burgers vector (0.2556 nm for Cu, 0.2735 nm for W), and \(k_{0}\cong 1\) is a factor depending on dislocation interaction. The dislocation density of Cu is similar in all the examined zones and its value is \(\approx\)3 \(\times\) 10\({}^{13}\) m\({}^{-2}\), whereas that of W slightly decreases, moving from zone 3 (6 \(\times\) 10\({}^{14}\) m\({}^{-2}\)) to zone 5 (2 \(\times\) 10\({}^{14}\) m\({}^{-2}\)). Figure 9 shows the typical load-displacement nano-indentation curves measured inside Cu (a) and W (b) splats in different positions of the interlayer. Figure 9: Some representative nano-indentation curves measured inside Cu (**a**) and W (**b**) splats in different positions of the interlayer. The distances of the imprints from the CuCrZr substrate are indicated in the figures. Nano-indentations were performed in the interlayer region along line paths from the substrate to the W coating. At the interlayer, it was shown that through the applied load of \(P_{Max}\) = 8000 uN, the indentation tip reached a penetration depth ranging 300-380 nm in Cu. On the other hand, the penetration depth was halved (to approximately 200 nm) in W.  
Figure 10 displays a plot of the hardness H of Cu and W measured across the interlayer from the CuCrZr substrate to the W coating. The deposited Cu exhibits a near-constant hardness (\(H\) = 2.2 \(\pm\) 0.2 GPa) up to a distance of 800 um from the substrate; the hardness then starts to rise continuously with a parabolic-like trend until it reaches a value of 3.9 \(\pm\) 0.2 GPa near the W coating. Correspondingly, the hardness trend of the deposited W is significantly different. In this case, the hardness continuously increases from 3.8 \(\pm\) 0.3 GPa in the vicinity of the CuCrZr substrate up to 9.9 \(\pm\) 0.1 GPa at the opposite edge of the W-Cu deposition interlayer zone. A critical aspect of these tests was represented the by nano-indentations taken at the boundary between Cu and W splats; these measures gave rise to false results that needed to be discarded. Since microscopic inspection does not always guarantee a reliable identification of these occurrences, the curves corresponding to tests carried out at Cu-W boundaries were identified from the abrupt slope change in the loading stage, which is not present in the curves obtained by indenting homogeneous areas (Cu or W). In fact, the slope change occurs when one tip, which at the beginning of indentation penetrates into one of the two metals, starts to interact with the other. A more detailed explanation of the method is reported in [19].