OBRABOTKAMETALLOV MATERIAL SCIENCE Vol. 25 No. 2 2023 well as the coefficient of thermal expansion (CLTE) for each phase at all stages of the heating temperature range. Based on the obtained data, a dependence of the lattice parameter (a) for each phase of the multilayer coating on the temperature of exposure was constructed for each stage of the heating temperature range of the sample with a multilayer coating, as well as the dependence of the change in the lattice parameter (Δa) and graphical determination of the CLTE using the last coefficient of thermal expansion. Quantitative determination of the crystal lattice parameter (a) was carried out after approximation and determination of interplanar distances (d) using equation 1 [20]: 2 2 2 a d H K L = ⋅ + + , (1) where d is the interplanar distance [Å]; H, K, L are the Miller indices of the analyzed reflection. Based on the calculated crystal lattice parameters of the multilayer coating components using equation 1, it is possible to calculate the linear coefficient of thermal expansion (CLTE) of each component of the multilayer coating separately using equation 2: , a a T ∆ β = ∆ (2) where β is the CLTE (K-1); a is the crystal lattice parameter in nm; Δa is the change in the crystal lattice parameter in nm when the sample with the multilayer coating is subjected to a temperature change (ΔT [K]). To assess the temperature at which microstresses may occur, the full width at half maximum intensity (FWHM) of the coating phases was plotted against temperature. As it is known from literature [21] that the magnitude of microstresses is directly proportional to FWHM, comparing the FWHM of at least two samples with multilayer coatings allows for conclusions to be drawn about the degree of microstresses present in multilayer coatings. Results and discussion The heating was carried out in an air medium on a holder with a platinum heating element. The initial state of the multilayer coating material was characterized by obtaining an X-ray diffraction pattern at a temperature of 30 °C. In our case, for the CrN and ZrN coating phases, the X-ray diffraction pattern registration range was 31–48 2Θ. Figure 2 shows an array of X-ray diffraction patterns obtained at a heating rate of 5°C/min, by the asymmetric scanning method using synchrotron radiation transformed into monochromatic radiation with a wavelength of 1.54 Å, during the heating ZrN/CrN-coated samples in the temperature range from 30 °C to 750 °C. The array consists of 71 projections of X-ray diffraction patterns obtained from both the substrate surface and the layers of the deposited multilayer coating, where each projection of the diffraction pattern represents a gradation of pseudo-color, shown in Fig. 2, indicating the intensity of the obtained signal during the X-ray diffraction pattern construction. Such data visualization is convenient for a qualitative analysis of phase transformations. The graphs presented in Fig. 2 (a, b) allow assessing the final stage of phase transitions in multilayer coatings. In the case of the CrN/ZrN coating applied at a table rotation speed of 0.5 rpm, the coating phase completely disappears at 575 °C, while the CrN/ZrN multilayer coating applied at a table rotation speed of 8 rpm completely loses its phase only at 635 °C. Fig. 3 shows selected X-ray diffraction patterns from the array shown in Fig 2. The temperature interval, initial and final points of temperature exposure are chosen for the sake of readability of a smaller data array and considerations of the end of phase transformations. As shown in Fig. 2, coating phases in multilayer coatings completely disappear after 650 °C, and it is advisable to limit the temperature range from 30 °C to 650 °C. In Table 1, the calculated values of interplanar spacing (d, Å), the width of the reflection at FWHM (in degrees), as well as the lattice parameter of the crystalline structure for the components of the CrN/ZrN
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