## 3 Results and Discussion
### Tribological Study of TiCrN Thin Films  
A conventional ball-on-disk machine was used to measure the COF and the sliding WR of thin films. It was observed that the coating volume loss is negligible as compared to the volume loss of the bare WC ball (counter body) [ASTM G-99]. Therefore, in the present investigation, the volume loss and WR of the bare WC ball were calculated for each set of tests to discover the better coating parameters. The scar is formed at the contact point between the sample and the bare WC ball. For sample T2, scars on both ball and sample are shown in Figures 6a and 6b, respectively. The scar on the ball is like a chord cut on a solid sphere with a diameter of 471.42 \(\upmu\)m, schematic is shown in Figure 6c. However, the observed scar on the thin film surface consists of a wear track of 424.24 \(\upmu\)m as shown in Figure 6b. Figure 6d depicts the relationship between the COF and sliding distance for each set of coating.  
After a sliding distance of 180 m, the COF value reaches its steady state. The image (Figure 6d) indicates that the initial COF is very low, increases slowly, and attains a steady state that is independent of the sliding distance. Special attention was given to evaluating the steady-state COF. The average COF value was found to be less as compared to the steady-state COF value. This may be due to the initial low value of the frictional force. As time progressed, the steady-state COF was achieved keeping the fact in mind that the coating was not completely absent from the substrate. The volume loss and scar depth of the bare WC ball were calculated by using the following formulae (Equations (2) and (3)) and represented in Figure 7.  
\[V=\pi\times h\times\frac{\left(3a^{2}+h^{2}\right)}{6} \tag{2}\]  
\[h=r-\sqrt{\left(r^{2}-a^{2}\right)} \tag{3}\]  
where V is the volume loss (in mm\({}^{3}\)), a is the radius of the scar on the WC ball (in mm), h is scar depth (in mm), and r is the radius of the WC ball (in mm). Wear torque is the product of the applied load on the ball and the sliding distance covered by the ball. Sliding distance and sliding velocity were calculated by using the following relations (Equations (4) and (5)):  
\[S=V_{\rm s}\times T \tag{4}\]  
Figure 5: Variation in modulus of elasticity and plasticity index values of samples.  
\[V_{s}=\frac{\pi\times D\times N}{60} \tag{5}\]  
where S is the sliding distance (in meters), V\({}_{s}\) is sliding velocity (in m/s), T is the test duration for each sample (in sec), D is the track diameter (in meter), and N is the speed of the disc (in rpm).  
Figure 6: SEM micrographs of the (**a**) scar on the WC (tungsten carbide) ball (counter body for sample T2) and (**b**) wear track on the sample T2. (**c**) Schematic of chord cut on a sphere. (**d**) Dependence of steady state friction on sliding distance.  
Figure 7: Scar diameter and scar depth of counter body (bare WC ball) used in the wear test for each sample.  
The WR of the ball for the respective coated sample was calculated by using the above-mentioned procedure. From Figure 8, it can be inferred that the WR of the counter body (WC ball) is highest (463 \(\upmu\)m\({}^{3}\)/Nm) for the T2 sample. From the results, it is observed that when there is a higher amount of wear loss on the ball surface, the better is the corresponding coating. It indicates that sample T2 is more resistant to wear than samples with other chromium contents. Consequently, this will be one of the criteria needed for optimizing a single-layer hard TiCrN coating for tribological applications. Figure 8 also presents a relationship between the ratio of Cr to Ti and COF. As the ratio of chromium to titanium increases, the COF is found to decrease. It is important to consider factors like hardness, elastic modulus, toughness, WR, and residual stress when selecting the optimal composition.