OBRABOTKAMETALLOV MATERIAL SCIENCE Vol. 24 No. 3 2022 Fig. 6. Linear dependence of diffraction maximum position (222) of ZrN phase on sin2Ψ for samples of multilayer coatings deposited at different rotational speeds of table and substrate holder where 0 ctg , MPa/grad, 2(1 ) 180 ÌÏ E M (3) 2 (2 ) , grad (sin ) x K (4) Consequently, quantitative determination of the residual stress in the multilayer coatings requires determining angle Θ0 of the stress-free material from the 2ΘΨx – sin 2Ψ plot, where 2Θ 0 is the extrapolation of linear approximation 2ΘΨx – sin 2Ψ [20]. Coeffi cient KΔ is determined from the 2Θ Ψx – sin 2Ψ approximation line slope as shown by equation 4. Stress coeffi cient M was calculated according to equation 3 using the earlier obtained values of νML, E, Θ0. The residual stress magnitudes in the multilayer coatings were obtained using equation 2 (see Table 1). Similar to the previous stages, the residual stress magnitudes were obtained from XRD patterns in the vicinity of (200)CrN angle position at 2Θ = 44° (Fig. 7). Angle positions of the (200)CrN are represented in the 2ΘΨx – sin 2Ψ domain in Fig. 8. Finally, some data as well as residual stress magnitudes were shown in Table 2. Ta b l e 1 Calculated values for determining the residual stresses and the result of calculating the residual stresses in the plane of the surface of the multilayer coating samples for the ZrN phase Coating 2Θ0, ° Coeffi cient M, MPa/grad Coeffi cient K, grad Residual stress, MPa ZrN/CrN-0.5 70.754 ± 0.017 –2.393×103 0.003 ± 0.001 –6.437 ZrN/CrN-3.5 70.808 ± 0.026 –2.235×103 –0.010 ± 0.001 22.000 ZrN/CrN-8 70.851 ± 0.057 –2.599×103 –0.008 ± 0.003 19.65
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