OBRABOTKAMETALLOV MATERIAL SCIENCE Vol. 25 No. 2 2023 multilayer coating, obtained at a substrate holder rotation speed of 0.5 rpm, are presented according to the known Equation (1) [20]. The calculation of CLTE was performed using Equation 2 for each temperature point presented in Table 1. The X-ray diffraction pattern (Fig. 3) shows the reflections (111) of the CrN and ZrN phases of the multilayer coating in the selected temperature range. The dependence of the lattice parameter on the temperature is shown in Fig. 4, a. The graph shows that the lattice parameter of the coating materials (CrN and ZrN) increases, indicating an increase in material volume, which occurs according to a linear law with some error. The dependence of the lattice parameter on the exposure temperature is shown in Fig. 4, b. a b Fig. 4. Dependence of the crystal lattice parameter of the ZrN/CrN multilayer coating phases on temperature – a; dependence of the changes in the crystal lattice parameter (Δa) of the phases of the ZrN/CrN multilayer coating on temperature – b Equation 2 is applied as follows. Obviously, Figure 4b is a modified graph shown in Figure 4a, such that Δa = aT - a0, where aT is the lattice parameter at a higher temperature (in the case of Figures 4a, b, the highest values on the linear segments: 50–550 °C), and a0 is the lattice parameter at the beginning of the linear segments (in the case of Figures 4a, b, the lowest values on the linear segments: 50–550 °C). That is, for the heating range from 50 °C to 550 °C, the CLTE (β) of the ZrN phase of the multilayer coating will be calculated as: 6 1 4, 6145 4,5965 7,83 4,5965(550 50) 10 ZrN - - - β = ⋅ = - Ê . For the linear heating range from 50 °C to 550 °C, the lattice constant (β) of the CrN phase of the multilayer coating will be calculated as: 6 1 4, 2516 4, 2426 4, 2426 4 (550 50 24 10 ) , CrN - - - ⋅ β = = - Ê . Equation 2 can be represented graphically as a dependence of the change in the lattice parameter (Δa) on the temperature of exposure, as shown in Fig. 4, b. The slope of the tangent in this case is the rate of change of the lattice parameter value (nm) per 1 °C during heating. The thermal expansion coefficient (TEC) over the entire temperature range of exposure from 50 °C to 650 °C will be positive for both phases of the multilayer coating: 2.28249×10-14 K-1 for the CrN phase and 3.54878×10-14 K-1 for the ZrN phase. Fig. 5 shows the dependence of the FWHM of the (111) reflections of the CrN and ZrN phases on the temperature of exposure. Based on the possibility of the occurrence of microstrains with an increase in the FWHM value, it can be concluded that the increase in microstrains is possible in the temperature range
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