###### Abstract
Based on the analysis of the research results, a mathematical model was developed that allows for predicting the formation of Ti-Al intermetallic compounds depending on the spatial arrangement of the sample relative to the plasma flows [9]. The stable fcc phase (Ti,Al)N is formed as a result of a solid-phase reaction at a high nitrogen concentration, while aluminum atoms are replaced in large quantities by titanium atoms in the (Ti,Al)N solid solution [10]. A high hardness of the (Ti,Al)N coating (31.4 GPa/3200 HV) is observed at an Al/(Ti + Al) ratio of 60% [11]. The maximum hardness of the (Ti,Al)N coating is observed at the Al/Ti atomic ratio of 11:10 [12]. In this study, the ratio of the elements was changed by increasing the cathode arc current ratio I\({}_{\rm Al}\)/I\({}_{\rm TI}\) from 0.31 to 0.73, while the Al/Ti atomic ratio linearly increased from 0.49 to 1.29. When comparing (Ti,Al)N coatings with the Ti/Al ratios of 50/50 and 72/28, it was found that the maximum hardness of the coating was achieved at the Ti/Al ratio of 50/50 [13]. The properties of Ti\({}_{1-x}\)Al\({}_{x}\)N coatings were compared, where x = 0, 0.1, 0.3, 0.5, 0.6, 0.7, 0.8, 0.9 and 1.0 [14]. It was found that with an increase in the Al content to x = 0.6, the coating hardness increases (up to \(\sim\)3200 HV), but with a further increase in the Al content, the hardness begins to decrease. With an increase in the Al content to x = 0.6, the lattice parameter decreases, but with a further increase in the Al content (x \(\geq\) 0.7), the active formation of the hexagonal phase AlN is observed [15; 16]. Depending on the deposition conditions and the type of equipment, the active formation of the hexagonal phase can begin at x > 0.52 [17] and at x > 0.7 [15; 16]. With an increase in the Al content to x > 0.6, a columnar crystalline structure is not formed, while a decrease in the grain size is observed [15; 18]. At an Al content of 0.5 \(\leq\) x \(\leq\) 0.66, the AlN phase is formed along the grain boundaries of (Ti,Al)N [18]. In this case, with a coating composition of 20 at.% Ti, 25 at.% Al and 55 at.% N, a superhard structure (hardness up to 47 GPa) can be formed, consisting of (Ti,Al)N grains (a size of about 30 nm) oriented in one direction, which are surrounded by an amorphous or nanocomposite c-AlN phase. Nitrogen pressure has an insignificant effect on the Al content in the coating [19]. An increase in nitrogen pressure from 0.66 to 6.60 Pa (5-50 mTorr) led to a slight change in the Al content within 3 wt.%. The corrosion resistance of CVD TiN and TiAlN coatings in 3.5 wt.% NaCl solution was studied [20]. (Ti,Al)N coatings were deposited using TiCl\({}_{4}\) precursors and AlCl\({}_{3}\) precursors. The Al/Ti ratio was changed by changing the precursor ratio. It was found that with an increase in the Al content, the corrosion resistance first increases and then begins to decrease. The coating obtained with the AlCl\({}_{3}\)/TiCl\({}_{4}\) ratio = 24/12 had the highest hardness in combination with the best corrosion resistance. Therefore, when using the PVD method, there are three ways to change the ratio of elements in the coating:  
* Using alloy cathodes with different ratios of elements. This method is very labor-intensive and requires significant financial costs. Suitable only for mass production when a large number of cathodes of a standard composition are used. * Changing the arc currents of the cathodes. This method is quite effective, but allows for varying the ratio of elements in the coating only in a limited range due to the fact that at an arc current below the limit value, it is impossible to form a plasma flow, and at too high arc current values, a significant phase of microparticles is formed [1; 2; 3; 21]. * Changing the spatial position of the sample relative to the plasma flows. This method assumes a static position of the samples during the coating deposition process.