Determination of average X-ray strain (AXS) on TiN hard coatings using cos2αsin2ψ X-ray diffraction method

•A parameter average X-ray strain (AXS) was proposed in this study.•AXS was measured by cos2αsin2ψ method at several rotational angles.•AXS can improve the accuracy of X-ray stress and XECs of thin films.•The concept of AXS was by increasing sampling volume to reduce data fluctuations.

For stress measurement on thin films and coatings using X-ray diffraction (XRD) methods, the uncertainty is commonly acknowledged to be from elastic constants. However, the uncertainty can be due to the statistical fluctuation of strain measured by XRD. In this study, we proposed a method where the average X-ray strain (AXS) was determined using cos2αsin2ψ XRD technique at several rotational (ϕ) angles to improve the accuracy of the measurement of X-ray stress or X-ray elastic constants (XECs). The major concept was to increase sampling volume by measuring X-ray strain at multiple rotational angles. TiN hard coating on Si (100) substrate was selected as the model system, where the residual stress was determined by laser curvature technique and the accompanying lattice strain was measured by cos2αsin2ψ method. The average effective elastic constant (AEXEC) could be attained by substituting the residual stress into the slope of AXS vs. cos2αsin2ψ plot. The AEXEC was served as an indicator to validate the AXS measurement. By substituting AEXEC in conventional sin2ψ XRD stress measurement, the deviation of the result from the stress obtained by laser curvature method was less than 7%, indicating that AXS effectively reduced the uncertainty in XECs and thus increased the accuracy of stress measurement. The concept of increasing sampling volume was also confirmed using synchrotron X-ray source, where the statistical fluctuation in X-ray strain could be further reduced by performing the measurement at all azimuthal direction. The experimental results showed that the uncertainty on XEC measurement by sin2ψ method was less than 10%, if sufficient sampling volume was provided. Furthermore, using AXS and elastic constant measured by nanoindentation (ENIP) to calculate X-ray stress, the stress deviation from that by laser curvature method could be substantially reduced even down to 3% with sufficient sampling points. Therefore, AXS may serve as a convenient parameter, when combining with ENIP, in X-ray stress measurement, by which residual stress of hard coatings comparable to that by laser curvature method can be obtained without using XECs.