Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The authors studied  the nanostructured superlattice coatings (NSCs)  properties by instrumented depth-sensing nanoindentation, The NSCs exhibit a superlattice structure with alternating TiAlSiNb-N/TiCr-CN bilayers, incorporating refractory metals Cr, and Nb,  which deposited onto 100Cr6 bearing steel substrates, achieving enhanced nanohardness values of approximately 25 GPa. A novel empirical methodology was used to extract stress-strain field (SSF) gradient and divergence representations from nanoindentation datasets. Analysis of load-displacement data from individual indentation tests revealed the rather complex, irregular oscillatory structure of the SSF within the coating under the incrementally loaded indenter.    These SSF gradient and divergence spatial oscillations were attributed to alternating strain-hardening and strain-softening deformation mechanisms within the near-surface layer during progressive loading.  The results showed that alternating cold work hardening and softening phases represent a general phenomenon in thin film/substrate systems subjected to incremental stress loading during nanoindentation.

The reviewers put forward the following suggestions.

1. It is suggested that specific descriptions of the experimental equipment and measurement accuracy be added in the methods section to improve the repeatability of the experiment.
2. It is suggested that further interpretation of the results be added in the discussion section, especially to conduct a more in-depth exploration of the mechanisms of the observed strain hardening and softening phenomena.
3. The conclusion can be further simplified, considering the inclusion of discussions on the limitations of the research and possible directions for improvement.

Author Response

Reviewer: 1. It is suggested that specific descriptions of the experimental equipment and measurement accuracy be added in the methods section to improve the repeatability of the experiment.

 

We thank the reviewer for the suggestion to describe the experimental equipment and measurement accuracy in greater detail. 

 

We have now added more detailed descriptions of the nanoindentation method, coefficient of friction calculations and data processing.

 

In section “2.3. Strain Gradient and Divergence Oscillation Analysis of the Stress–Strain Field Caused by Incrementally Loaded Indenter” we have now provided more detail on the bin-averaging approach used for calculating the baseline (fine structure) of the stress-strain field (SSF) gradient:

 

“To perform the Fourier analysis on the mean baseline component P’b(h), we used a bin-averaging low-pass filtering approach using a 2 nm bin width, which yielded a smoothly varying P’b(h) component. This signal processing technique segments data into fixed-width intervals, calculates the arithmetic mean within each interval, and uses these averaged values to represent the corresponding data segments. The bin-averaging approach effectively reduces random fluctuations while preserving the underlying mechanical response characteristics, even at low amplitudes.”

 

In section “2.4. Nanoindentation Hardness Testing Experiment” we have now added more details on the nanoindentation setup:

 

“The nanoindentation response of the nanostructured tribological coatings (NSCs), including load-displacement (P-h) curves, nano-hardness (H), and elastic modulus (E), was measured using the TriboIndenter system TI980 (Bruker Nano Surfaces, Minneapolis, MN, USA), equipped with a sharp diamond Berkovich indenter. Additionally, the Herzan™ AVI-200 S/LP active vibration isolation system was operated during the nanoindentation experiments. This system comprises a control unit and two rails positioned on either side of the granite base within an acoustic enclosure. Each rail contains four piezo-electric accelerometers that continuously monitor vibrations through an internal feedback loop. Vibration damping is achieved through a dual mechanism: four electro-dynamic transducers apply counteracting forces to attenuate low-frequency vibrations (0-200 Hz), while higher-frequency vibrations are passively dampened by the mass of the granite base in conjunction with the spring system integrated within the rails. To ensure comprehensive surface assessment, 10 positions were selected within the chosen indentation matrix for testing peak load, Pmax, and 10 load-displacement, P-h, loops were measured in load-interval (0, Pmax).”

 

In section “2.5. Tribological Tests of the NSC Samples” we have now added:

 

“Steady-state coefficient of friction (CoF) values were used to evaluate and compare the friction properties of different coatings. These steady-state CoF values were extracted from plateau regions within the CoF vs. time curves, defined as segments exhibiting stable friction behavior over a minimum sliding distance of twenty meters. To qualify as a plateau region, the coefficient of variation (relative standard deviation) of CoF values within each segment was required to remain below 10% for all tests. Test results are reported as mean CoF values ± standard deviation.”

 

Please see Figures 1-2 below for more details on CoF measurements (figures not included in the final manuscript).

 

Figure 1. Friction curves vs time showing steady-state behavior. Top: friction force (N) vs. time. Bottom: Coefficient of friction (CoF) vs. time. In this example, the steady-state CoF value would be calculated from the data measured within the time interval 3000-5000 s.

 

Figure 2. Friction CoF-curve vs time, vs lap, and vs distance (m) showing steady-state behavior at several places. In this example, the steady-state CoF value would be calculated from the data measured after the run-in region, i.e., at a distance of about 100 m.

 

We have also added a section “2.6. Electron Microscopy Examinations of the NSC Samples” describing the electron microscopy equipment:

“2.6. Electron Microscopy Examinations of the NSC Samples

The morphology of the NSC sample structures was investigated with a scanning electron microscope (SEM) Lyra3 (Tescan, Czech Republic, Brno), equipped with an energy-dispersive X-ray spectrometer (EDS), AZtecCrystal (Oxford Instruments, United Kingdom). SEM and EDS measurements were performed using a beam-accelerating voltage of up to 30 kV and a beam current of 500 pA.”

 

In section “3.1. Preparation and Characterization of the NSC Film Samples” we have now provided further details on the nanoindentation test sites:

“Nanoindentation experiments were conducted using a TriboIndenter apparatus (model TI980) to generate load-displacement loops (LDLs). A total of 40 nanoindentation tests were performed on four NSC samples (Table 2) at a peak load of 8000 µN. For each NSC sample, an indentation matrix of 10 positions with controllable coordinates (Xi, Yi) was established on the sample surface through careful microscopic examination. Indentation sites were selected using optical microscopy to identify the smoothest possible surface areas and were spaced at least 4000 nm apart to prevent mutual interference between neighboring indentations. Each NSC sample underwent 10 indentation tests, yielding load-displacement data from the corresponding 10 LDLs, with each dataset containing 2600 measurement points acquired during successive loading, drift, and unloading segments. All experiments were conducted in a single session to ensure identical measurement conditions and enable reliable comparison between NSC samples.”

 

Reviewer: 2. It is suggested that further interpretation of the results be added in the discussion section, especially to conduct a more in-depth exploration of the mechanisms of the observed strain hardening and softening phenomena.

 

We thank the reviewer for the suggestion to expand the discussion and interpretation of our results.

 

In section “3.1. Preparation and Characterization of the NSC Film Samples” we have now added the following discussion regarding the results reported in Table 2:

 

“Elevated substrate temperatures during the PVD process significantly influenced the contact nanohardness of NSC samples. Maintaining substrate temperatures near 400°C, particularly in the range of 380-390°C, resulted in a substantial coating hardness due to improved microstructure, lowered residual stress-strain state, and superior interfacial quality between sublayers. Higher substrate temperatures promote increased adatom surface diffusion, enabling atoms to migrate more freely across the substrate surface and locate energetically favorable sites. This enhanced mobility leads to larger grain formation and denser film structures. In contrast, substrate temperatures below 300°C (not reported here) are insufficient for significant surface diffusion, resulting in limited adatom mobility and consequently higher defect densities and more porous microstructures. The substrate temperature thus critically determines the balance between adatom mobility and shadowing effects during film growth.  

Additionally, the enhanced nanohardness observed in NSC samples could be attributed to multiple strengthening mechanisms, including grain refinement, solid solution strengthening, and precipitation hardening. Grain refinement contributes to mechanical strengthening through the Hall-Petch effect, whereby grain boundaries serve as effective barriers to dislocation movement. Solid solution strengthening occurs through the incorporation of refractory elements (Cr and Nb) into the host lattice, which creates lattice distortion fields that impede dislocation motion. Precipitation hardening arises from the formation of fine, hard precipitates that act as obstacles to dislocation propagation. Although a detailed investigation of these mechanisms lies beyond the scope of this study, their relative contributions are likely influenced by the superlattice architecture, elemental composition, and processing parameters.”

 

In the newly created section “3.2. Scanning Electron Microscopy Examinations of the NSC Film Samples” we have now added the following discussion regarding the electron microscopy results:

 

“Several interconnected mechanisms could explain the observed morphological pattern. The atomic shadowing effect during PVD deposition, where sputtered material flux arrives at the substrate at oblique angles rather than normal incidence, can result in preferential growth directions. Some regions receive greater flux and grow faster, leading to an undulating or rippled structure that becomes further amplified by self-shadowing, which reinforces surface roughness. 

Additionally, strain-driven surface instabilities may contribute to the undulating pattern. The bilayered {TiAlSiNb-N/TiCr-CN}n superlattice structure introduces internal stress variations due to alternating composition, creating strain gradients across sublayers. Surface undulations can develop to relieve compressive stresses, potentially representing an example of the Asaro-Tiller-Grinfeld instability [29,30,34], where surface perturbations grow due to anisotropic stress relaxation. 

The undulating pattern with nanometer-scale wavelengths indicates that limited surface diffusion plays a significant role. Because adatom mobility is restricted, roughness increases over time through kinetic roughening. Low-temperature deposition or high deposition rates can enhance this effect, reinforcing the undulating pattern. Finally, the bilayered superlattice nature of the NSC films may contribute to periodic growth modulation. 

In summary, we propose a NSC growth model based on competitive columnar growth mechanisms balanced against strain-driven instability factors. Initially, PVD growth begins with fine nucleation, forming separate grain-island structures. Atomic shadowing contributes to local thickness variations, with columnar growth dominating the initial stages. As alternating TiAlSiNb-N/TiCr-CN sublayers are deposited, strain accumulates at their interfaces. This accumulated strain induces periodic wavelength-modulated structures. Since adatom mobility remains limited, kinetic roughening reinforces the undulation. The self-organized morphology suggests anisotropic diffusion-driven instability. 

The morphological anisotropy described above likely produces direction-dependent tribological behavior [42-44]. When tribological contact occurs parallel to undulation ridges, the surface offers reduced resistance, functioning similarly to rails and potentially decreasing friction and wear in that direction. Conversely, sliding perpendicular to these undulations requires greater energy to overcome topographical barriers, resulting in higher friction coefficients and increased abrasive wear. Furthermore, the periodic surface roughness (with average wavelengths of 49-52 nm in our samples) may promote stick-slip motion at nano- and microscale contacts. These undulations can interact with asperity dimensions or lubricant molecular sizes, significantly affecting friction dynamics. In dry or boundary lubrication regimes, such unidirectional undulations may provide additional benefits by channeling lubricants along specific directions, enhancing hydrodynamic lubrication along preferred paths while restricting flow in others.” 

 

Regarding the observed strain hardening and softening oscillations, we have now written in the “Conclusions” section as follows:

 

“The undulating fine structure of the P’/h-profile captures a low-pass filtered, smoothened response of the NSC film samples to the indentation process, thus reflecting the overall trend of the strain-hardening and strain-softening phenomena over a larger length-scale. It can be viewed as representing the quasi-equilibrium mechanical response of the material, and as such it is influenced by the inherent micromechanical properties of the nanostructured NSC film samples, for example: (i) elastic–plastic transition, with the undulations of the strain gradient fine structure marking transitions from elastic deformation to plastic flow; (ii) material heterogeneity, with variations in the fine structure likely correlating with structural features such as grain boundaries or sublayer interfaces; (iii) strain accumulation during progressing loading.  

Superimposed on the fine structure are the high-frequency hyper-fine structure oscillations captured by the detrended strain gradient Pd'(h), which carry information about deformation instabilities and sub-surface material behavior. They can be seen to correspond to localized events within the evolving stress–strain field, such as (i) strain-hardening cycles manifesting as periodic increases in resistance, likely from dislocation interactions or barrier effects at microstructural interfaces, and (ii) strain-softening cycles manifesting as drops in resistance, possibly due to local yielding, microvoid formation, microcracks or sublayer delamination. The spectral analyses of these oscillations revealed that their dominant wavelengths shift to shorter scales with increasing depth, which underscores the transition from coarse, surface-dominated deformation to finer-scale, bulk-driven mechanisms deeper in the film.”

Reviewer: 3. The conclusion can be further simplified, considering the inclusion of discussions on the limitations of the research and possible directions for improvement.

 

We thank the reviewer for the opportunity to improve the Conclusions section. We have now adjusted our Conclusions as follows:

 

“This study investigated the nanomechanical behavior of TiAlSiNb-N/TiCr-CN superlattice coatings fabricated via HiPIPMS, combining empirical nanoindentation analysis with a novel gradient-divergence framework. These coatings exhibited distinctive multilayer architecture reflected in both mechanical performance and deformation response. 

We demonstrated that Meyer's power law, historically developed for bulk materials, can be extended for thin films providing a semi-universal mathematical model across macro-, micro-, and nanoscale indentation tests. The evolution of the Meyer exponent n with indentation depth captures the transition from surface-dominated to bulk-like deformation and directly links to the SSF gradient beneath the indenter, offering a robust framework for comparing materials and capturing deformation behavior changes across scales. 

We applied a simple empirical method to extract and analyze stress-strain field (SSF) gradient and divergence representations from nanoindentation load-displacement datasets measured regarding nanostructured tribological coatings (NSCs). The total strain gradient P’/h-profiles and divergence P”/h-profiles were calculated from load-displacement P/h-curves as normalized non-dimensional derivatives. By using this gradient-divergence approach, we revealed reproducible, depth-dependent oscillations across all samples, interpreted as alternating strain-hardening and strain-softening events related to local structural heterogeneities. 

The undulating fine structure of the P’/h-profile captures a low-pass filtered, smoothened response of the NSC film samples to the indentation process, thus reflecting the overall trend of the strain-hardening and strain-softening phenomena over a larger length-scale. It can be viewed as representing the quasi-equilibrium mechanical response of the material, and as such it is influenced by the inherent micromechanical properties of the nanostructured NSC film samples, for example: (i) elastic–plastic transition, with the undulations of the strain gradient fine structure marking transitions from elastic deformation to plastic flow; (ii) material heterogeneity, with variations in the fine structure likely correlating with structural features such as grain boundaries or sublayer interfaces; (iii) strain accumulation during progressing loading.  

Superimposed on the fine structure are the high-frequency hyper-fine structure oscillations captured by the detrended strain gradient Pd'(h), which carry information about deformation instabilities and sub-surface material behavior. They can be seen to correspond to localized events within the evolving stress–strain field, such as (i) strain-hardening cycles manifesting as periodic increases in resistance, likely from dislocation interactions or barrier effects at microstructural interfaces, and (ii) strain-softening cycles manifesting as drops in resistance, possibly due to local yielding, microvoid formation, microcracks or sublayer delamination. The spectral analyses of these oscillations revealed that their dominant wavelengths shift to shorter scales with increasing depth, which underscores the transition from coarse, surface-dominated deformation to finer-scale, bulk-driven mechanisms deeper in the film. 

Our results demonstrate how gradient-divergence analysis adds substantial interpretive power to nanoindentation, offering insight into subsurface mechanical phenomena otherwise obscured by conventional metrics. The methodology is broadly applicable to architected coatings where microstructural complexity governs mechanical performance. 

Future work should integrate advanced in-situ characterization techniques—particularly coupling nanoindentation with in-situ SEM or TEM—to directly visualize underlying deformation mechanisms corresponding to the observed SSF gradient oscillations, enabling real-time tracking of dislocation activity, interface yielding, and microcrack formation. Computational modeling including FEM simulations with crystal plasticity and atomistic modeling should simulate indentation responses in superlattice coatings, incorporating layer-specific properties to reproduce oscillatory behavior and link the SSF gradient-divergence features to specific micromechanical processes. These efforts will advance predictive design of next-generation tribological materials with architecture-dependent mechanical signatures.”

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

May,23,2025

Manuscript ID: coating-3671192-peer-review-v1

 

Dear Editor,

 

I reviewed the manuscript titled “Nanoindentation response analysis of thin nanostructured nitride/carbonitride coatings based on transition metals using strain gradient-divergence approach”.

 

This work introduces the strain gradient-divergence method, a new analytical approach to nanoindentation, to investigate micromechanical behaviors, particularly strain hardening and strain softening, in nanostructured superlattice coatings. These coatings consist of alternating TiAlSiNb-N and TiCr-CN bilayers reinforced with refractory metals (Nb, Cr) and deposited using advanced HiPIMS (High Power Pulsed Magnetron Sputtering). MAnuscriptte investigates the mechanical and tribological performance of these films and develops a rigorous methodology to extract microstructural information from nanoindentation data.

In this study, a new empirical method for calculating GGF gradient and divergence from nanoindentation data has been developed, thus contributing to the literature. This "gradient-divergence" approach is more sensitive than classical nanoindentation analyses in determining local structural heterogeneities within the coating. Thanks to this method, nanoindentation has become a diagnostic tool that can detect dynamic deformation processes (e.g., successive hardening and softening stages) beyond the mere measurement of average hardness. In terms of Depth-Dependent Analysis of Micromechanical Behavior, the study has shown that the dominant oscillation wavelengths decrease as the load depth increases, revealing how the material behavior changes from the surface to the depth. This analysis shows for the first time in such detail the direct effect of the multilayer structure of the coatings (e.g., superlattice periods) on the nanoindentation response.

 

By examining the effect of superlattice structures, it was shown that oscillation frequencies are directly related to these structural periods in these coatings with superlattice periods in the range of approximately 17–21 nm. This shows that nanoindentation can be used not only as a mechanical measurement tool but also as a microstructural analysis tool.

 

Although Meyer's power law (P = C*h^n) is a classically used model, in this study, new conceptual approaches are presented by relating the coefficient n to the "strain gradient" for the first time. Thus, a physical meaning is given to this parameter and the interpretation of nanoindentation data is deepened.

 

Other studies have also investigated the hardness and elastic modulus values of thin film coatings by nanoindentation. Similarly, mechanical property changes related to load depth, such as the indentation size effect (ISE), have been investigated in many studies. Multilayer nitride/carbonitride coatings have high hardness, low coefficient of friction and good wear resistance, which is consistent with previous studies.

This study makes a significant contribution to the literature by presenting a new method based on strain field gradient/divergence that further utilizes nanoindentation data for mechanical microstructure analysis. At the same time, establishing a direct link between the mechanical response and superlattice structures at the nanoscale is one of the significant differences between this study and previous studies. This structure offers an important innovation, especially in understanding the local mechanical responses of thin film coatings in detail. The developed method has transformed the nanoindentation technique from a mere hardness measurement tool to a microstructural analysis and deformation dynamics investigation tool. In addition, for the first time in the literature, the hyperfine structures extracted from nanoindentation data have been clearly associated with the mechanical reflections of the layered structure.

 

A material system consisting of multilayer superlattice films with alternating nitride (TiAlSiNb-N) and carbonitride (TiCr-CN) phases was developed.

 

A HiPIMS deposition technique with mosaic-type targets was used, which enabled uniform deposition of multielement coatings.

 

The substrate, 100Cr6 bearing steel, was coated with ~5.3–5.8 μm thick films.

 

The use of high-intensity plasma to precisely control multilayer architectures and achieve improved hardness (~25 GPa) and elastic modulus (~340–415 GPa) is a novelty.

The introduction of P'/h (strain gradient) and P”/h (strain deviation) profiles to determine subsurface mechanical oscillations and deformation cycles is innovative.

 

This manuscript contributes to a significant advance in nanoindentation-based mechanical analysis, providing multi-scale insight into thin film behavior by a mathematically elegant yet physically grounded method. The integration of Fourier spectral techniques, advanced PVD processing and classical mechanics theory provides a strong foundation for further research and industrial applications in wear-resistant coatings.

 

The paper is suitable for acceptance in Coating journal after major corrections are made with the addition of a few deficiencies I saw.  It provides a new analytical framework and includes solid experimental data, but still needs major revisions to meet the standards of respected scientific journals The additions and corrections I suggested are as follows:

 

 1.⁠ ⁠It was concluded that the oscillations observed in P'/h and P”/h profiles are due to dislocations, grain boundaries or substrate interfaces; however, TEM and AFM were not used to confirm this. It is important to include TEM and AFM images and their interpretations.

 

 2.⁠ ⁠Limited material comparisons have been made. Comparisons with conventional PVD coatings, amorphous carbon films, other superlattice systems, and similar systems are required. Limited material comparisons make it difficult to evaluate relative performance improvements.

 

 3.⁠ ⁠Extensive use of mathematical representations without corresponding material characterization (e.g. TEM, cross-sectional SEM) to verify the origins of oscillations (e.g. grain boundaries, interface roughness) is a shortcoming. Should be improved.

 

 4.⁠ ⁠Some results (e.g. Meyer's law exponent "n") are expressed but not interpreted in physical detail beyond their relation to the strain gradient. Should be elaborated.

 5.⁠ ⁠The figures are detailed but more interpretive sentences should be added in the text.

 

 6.⁠ ⁠Reference list needs updating, is inadequate. Does not adequately support new claims. Lacks recent citations and cross-field substantiation, needs to be significantly expanded to include both classical theory and current research.

 

7. There is an addition of numbers 40,41 in the references section. Literature 40 and 41 are not included in the text. It should be deleted.

 

8. References should be corrected according to the journal's rules.

 

9.⁠ ⁠There are grammatical errors and spelling mistakes. The sentence structure is too passive, more active structures should be used.

 

 10.⁠ ⁠The phrasing is moderate. It can be improved by reducing redundancies.

 

 11.⁠ ⁠The grammar is mostly correct but there are gaps. Some articles have incorrect usage, which introduces agreement errors.

 

 

Sincerely yours

 

Comments on the Quality of English Language

The English of the manuscript needs to be corrected.

There are grammatical errors and spelling mistakes.

The sentence structure is too passive, more active structures should be used.

The phrasing is moderate. It can be improved by reducing redundancies. The grammar is mostly correct but there are gaps. Some articles have incorrect usage, which introduces agreement errors.

 

 

 

Author Response

Reviewer: 1. ⁠It was concluded that the oscillations observed in P'/h and P”/h profiles are due to dislocations, grain boundaries or substrate interfaces; however, TEM and AFM were not used to confirm this. It is important to include TEM and AFM images and their interpretations.

 

We thank the reviewer for the opportunity to expand our description of the structural properties of the nanostructured coatings. We have now added a table characterising the superlattice structure of the coatings (Table 1) as well as electron microscopy measurements.

 

We have now written:

 

“The cross-field configuration of the corresponding mosaic-type MSTs, combined with the rotating carousel of the substrate holder, enabled identification of the superlattice structure based on the PVD process technological parameters. Specifically, since the total coating thickness, t, is always measured after completion of the PVD process, an approximate superlattice structure can be calculated using process parameters such as deposition duration and the number of substrate holder carousel revolutions (Table 1). Additionally, by considering the sputtering yields of individual chemical elements (e.g., Ti ~0.5-0.8; C ~0.1-0.3; Cr ~0.6-1.0; Nb ~1.0-1.4), one can estimate the thickness of each sublayer, t₁ and t₂, from the total bilayer thickness, tb = t₁ + t₂, based on the average sputtering yields of the respective MSTs.”

Table 1. Characterization of the superlattice periodic structure of the NSC samples.

 

To characterise the structural properties in further detail, we have now added a section “3.2. Scanning Electron Microscopy Examinations of the NSC Film Samples” and have written:

 

“The SEM plan view micrograph study of the bilayered nitride/carbonitride superlattice NSC film samples revealed a one-directional undulating anisotropic morphology pattern as surface roughness waving. The wavelengths of the undulations span between 1.28 and 81.35 nm, while the average wavelength was 49.85 nm for the NSC-1 sample. The narrow bands run through the entire SEM image height of about 1360 nm (VFW parameter). Thus, the fine-grained nodule-like morphology pattern contains very pronounced narrow bands, which could be characterized as having a very high aspect ratio of more than 27:1. The one-directional undulating surface pattern suggests that the coating morphology is governed by a combination of atomic-scale self-organization mechanisms, strain effects, and directional growth influences (Figures 1-2). The observed one-directional undulating morphology pattern was not sensitive to substrate temperatures within 350-400 °C range.”

 

Figure 1. Surface texture analysis of the NSC-1 sample (top panel): (a) SEM micrograph plan-view of the rectangle X*Y-selection; (b) surface 3D-roughness profile of the same selection in grayscale units averaged along Y-axis; (c) 3D-surface plot of the X*Y-selection in arbitrary units produced by ImageJ software. Fracture analysis of the NSC-1 sample (bottom panel): (d) SEM micrograph cross-sectional view; (e) coating’s bilayered superlattice structure with the period of about 17-18 nm; (f) fracture 3D-surface plot in arbitrary units produced by ImageJ software. Scale bars correspond to 200 nm. SEM analysis revealed an anisotropic one-directional undulating surface roughness pattern with spatial wavelength distribution between 1.28 and 81.35 nm, and an average value of 49.85 nm. 

Figure 2. SEM micrographs of plan-view (top panel) and cross-sectional view (bottom panel) of the NSC film samples NSC-2, NSC-3, and NSC-4. Scale bar correspond to 200 nm for all the NSC samples. All the NSC samples under investigation revealed anisotropic coating morphology that represents itself as a one-directional undulating surface roughness pattern. The coating’s bilayered superlattice period was estimated at around 17.9, 18.3, and 17.1 nm for the NSC-2, NSC-3, and NSC-4 samples, respectively. The fracture-view micrographs, in addition to the multilayered superlattice structure, contain remains of the crystalline Ti-adhesion layer at the bottom of the images. All NSC film samples exhibited very similar undulating roughness and superlattice structure profiles. 

 

“Several interconnected mechanisms could explain the observed morphological pattern. The atomic shadowing effect during PVD deposition, where sputtered material flux arrives at the substrate at oblique angles rather than normal incidence, can result in preferential growth directions. Some regions receive greater flux and grow faster, leading to an undulating or rippled structure that becomes further amplified by self-shadowing, which reinforces surface roughness. 

Additionally, strain-driven surface instabilities may contribute to the undulating pattern. The bilayered {TiAlSiNb-N/TiCr-CN}n superlattice structure introduces internal stress variations due to alternating composition, creating strain gradients across sublayers. Surface undulations can develop to relieve compressive stresses, potentially representing an example of the Asaro-Tiller-Grinfeld instability [29,30,34], where surface perturbations grow due to anisotropic stress relaxation. 

The undulating pattern with nanometer-scale wavelengths indicates that limited surface diffusion plays a significant role. Because adatom mobility is restricted, roughness increases over time through kinetic roughening. Low-temperature deposition or high deposition rates can enhance this effect, reinforcing the undulating pattern. Finally, the bilayered superlattice nature of the NSC films may contribute to periodic growth modulation. 

In summary, we propose a NSC growth model based on competitive columnar growth mechanisms balanced against strain-driven instability factors. Initially, PVD growth begins with fine nucleation, forming separate grain-island structures. Atomic shadowing contributes to local thickness variations, with columnar growth dominating the initial stages. As alternating TiAlSiNb-N/TiCr-CN sublayers are deposited, strain accumulates at their interfaces. This accumulated strain induces periodic wavelength-modulated structures. Since adatom mobility remains limited, kinetic roughening reinforces the undulation. The self-organized morphology suggests anisotropic diffusion-driven instability. 

The morphological anisotropy described above likely produces direction-dependent tribological behavior [42-44]. When tribological contact occurs parallel to undulation ridges, the surface offers reduced resistance, functioning similarly to rails and potentially decreasing friction and wear in that direction. Conversely, sliding perpendicular to these undulations requires greater energy to overcome topographical barriers, resulting in higher friction coefficients and increased abrasive wear. Furthermore, the periodic surface roughness (with average wavelengths of 49-52 nm in our samples) may promote stick-slip motion at nano- and microscale contacts. These undulations can interact with asperity dimensions or lubricant molecular sizes, significantly affecting friction dynamics. In dry or boundary lubrication regimes, such unidirectional undulations may provide additional benefits by channeling lubricants along specific directions, enhancing hydrodynamic lubrication along preferred paths while restricting flow in others.” 

 

Reviewer: 2.⁠ ⁠Limited material comparisons have been made. Comparisons with conventional PVD coatings, amorphous carbon films, other superlattice systems, and similar systems are required. Limited material comparisons make it difficult to evaluate relative performance improvements.

 

We thank the reviewer for the opportunity to expand our discussion on comparisons with other types of coatings. We have now adapted our Introduction section to include more details and references about other related coating types, and further justify the design of the TiAlSiNb-N/TiCr-CN coating system under investigation:

 

“Nitride/carbonitride superlattice coatings outperform both amorphous carbon films and conventional monolayers in tribological applications. Their alternating nanolayers enhance hardness by strengthening interfacial bonding and hindering dislocation movement, resulting in superior mechanical properties compared to amorphous carbon, which lacks long-range order [1,2]. While amorphous coatings can achieve high hardness, they are brittle. In contrast, superlattice architectures combine low friction with excellent wear resistance, as their layered structure distributes stress and enables controlled deformation under harsh conditions [3–9]. 

This study focuses on the nanomechanical behavior of a TiAlSiNb-N/TiCr-CN bilayer system developed via High-Power Ion-Plasma Magnetron Sputtering (HiPIPMS) [10]. The selected elements and multilayer design aim to enhance hardness, toughness, thermal stability, and wear resistance. A modified, non-stoichiometric multilayer structure, TiAlSiMe₁-N/TiMe₂-CN, has emerged as a promising candidate for next-generation self-healing nanostructured coatings, combining low friction with ultra-high wear resistance [4,11-13]. Here, Me₁ and Me₂ denote refractory metals. This strategy addresses the limitations of pure hard carbon coatings, such as high residual stress, poor adhesion to steel substrates, and low thermal stability [1,2]. 

 

Several nitride/carbonitride reference systems illustrate key superlattice effects. TiN/CrN superlattices exhibit hardness peaks and toughness maxima at specific bilayer periods (e.g., with wavelength Λ ≈ 6 nm) [14,15]. Their deformation involves grain boundary sliding in TiN and densification in CrN, with better corrosion resistance than TiN/VN [16]. CrN/NbN systems offer high hardness and thermal stability, leveraging Nb—also present in the current system—for improved cutting tool protection [17]. TiN/VN superlattices achieve extreme hardness (~55–56 GPa) but suffer from poor oxidation resistance [15,16]. TiAlN-based multilayers (e.g., TiAlN/VN, TiAlN/CrN) combine hardness and wear resistance with Al- or Si-enhanced oxidation stability. For instance, TiAlN/VN reaches ~38 GPa hardness and may form lubricious V₂O₅ at high temperatures, though oxidation resistance may decline if Al forms mixed oxides like AlVO₄ [18,19]. High Entropy Nitride (HEN) coatings represent a newer class of multicomponent nitrides forming stable solid solutions despite compositional complexity. Examples include (AlCrTaTiZr)N and HEN-based multilayers such as TiNbZrTaN/CrFeCoNiNx [20].

The TiAlSiNb-N/TiCr-CN superlattice developed here is a complex, quinary/ ternary multilayer system that merges traditional superlattice engineering with high-entropy principles. Some key features and advantages of the proposed current system include: (i) Compositional synergy: Al and Si enhance hardness, thermal stability, and oxidation resistance in TiAlSiNb-N; Nb contributes via grain refinement and solid solution strengthening; Cr in TiCr-CN improves wear resistance, while the carbonitride layer modifies friction and wear particle behavior; (ii) Hybrid design: the system blends superlattice mechanics (e.g., interfacial strengthening) with multicomponent layer chemistry, echoing high-entropy alloy design to achieve a balanced performance; (iii) Performance: with a reported hardness of ~25 GPa (cf. Results and Discussion), the system may not match the hardest superlattices but offers a superior combination of durability, damage tolerance, and potential for tribo-film formation (e.g., SiOx), especially under high-temperature conditions. Thus, the TiAlSiNb-N/TiCr-CN system design integrates compositional and structural strategies to achieve a robust, synergistic balance of strength, toughness, and tribological performance.”

 

 

Reviewer: 3. Extensive use of mathematical representations without corresponding material characterization (e.g. TEM, cross-sectional SEM) to verify the origins of oscillations (e.g. grain boundaries, interface roughness) is a shortcoming. Should be improved.

 

We thank the reviewer for the opportunity to provide additional material characterization. Analogously to our response above to Comment 1, we have now added more details in section “3.2. Scanning Electron Microscopy Examinations of the NSC Film Samples” (please see above our response to Comment 1).

Reviewer: 4.⁠ ⁠Some results (e.g. Meyer's law exponent "n") are expressed but not interpreted in physical detail beyond their relation to the strain gradient. Should be elaborated.

 

We thank the reviewer for the opportunity to provide further discussion and interpretation about Meyer’s law exponent. We have now added in section “3.3 Nanoindentation Response Analysis Using the Loading Segment P/h-curves Obtained at the Testing Peak Load of 8000 µN” the following clarifications:

 

“The physical interpretation of n is closely tied to the indentation size effect (ISE) and the work-hardening characteristics of the material. If n < 2, this typically corresponds to the normal ISE observed in most nanoindentation experiments on hard materials due to factors like geometrically necessary dislocations (GNDs) accumulating under small volumes of deformation. At smaller indentation volumes, the density of GNDs needed to accommodate the strain gradients, which are inherently promoted by the indenter geometry and amplified by the interfaces, would be higher, leading to an effectively greater resistance to plastic deformation (i.e., higher hardness). The complex nanostructure of the superlattice, with its high density of interfaces and confined layers, naturally creates conditions for significant strain gradients to develop. If n = 2, the relationship is equivalent to Kick's Law where ISE is absent, and hardness is independent of the indentation load (P) or size (d, h). If n > 2, the material exhibits reverse ISE (RISE), often pertaining to bulk, ductile materials where significant plastic deformation and work hardening occur within the indented volume, causing the material to resist further deformation more strongly as the indent grows larger and deeper.”

 

Reviewer: 5.⁠ ⁠The figures are detailed but more interpretive sentences should be added in the text.

 

We thank the reviewer for their comment on the figures and the suggestion to provide more interpretive captions. We have amended the captions throughout the manuscript. Please see below an example of an extended caption (example figure showing electron microscopy results)

 

Figure 1. Surface texture analysis of the NSC-1 sample (top panel): (a) SEM micrograph plan-view of the rectangle X*Y-selection; (b) surface 3D-roughness profile of the same selection in grayscale units averaged along Y-axis; (c) 3D-surface plot of the X*Y-selection in arbitrary units produced by ImageJ software. Fracture analysis of the NSC-1 sample (bottom panel): (a) SEM micrograph cross-sectional view; (b) coating’s bilayered superlattice structure with the period of about 17.6 nm; (c) fracture 3D-surface plot in arbitrary units produced by ImageJ software. The scale bars correspond to 200 nm for both SEM images. SEM analysis revealed an anisotropic one-directional undulating surface roughness pattern with spatial wavelengths distribution between 1.28 and 81.35 nm, and an average value of 49.85 nm. 

Reviewer: 6.⁠ ⁠Reference list needs updating, is inadequate. Does not adequately support new claims. Lacks recent citations and cross-field substantiation, needs to be significantly expanded to include both classical theory and current research.

 

We thank the reviewer for the opportunity to expand our references. We have now included additional citations, particularly pertaining to comparisons with other, related coating systems, with multiple studies published between 2020 and 2024. Our “References” section now include the following citations:

 

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1. Kanders, U.; Kanders, K.; Maniks, J.; Mitin, V.; Kovalenko, V.; Nazarovs, P.; Erts, D. Nanoindentation Response Analysis of Cu-Rich Carbon–Copper Composite Films Deposited by PVD Technique. Surf. Coatings Technol. 2015, 280, 308–316, doi:10.1016/J.SURFCOAT.2015.08.045. 

1. Das, J.; Linke, B. Evaluation and Systematic Selection of Significant Multi-Scale Surface Roughness Parameters (SRPs) as Process Monitoring Index. J. Mater. Process. Technol. 2017, 244, 157–165, doi:10.1016/J.JMATPROTEC.2017.01.017. 

1. Liu, Y.; Yu, S.; Shi, Q.; Ge, X.; Wang, W. Multilayer Coatings for Tribology: A Mini Review. Nanomater. 2022, Vol. 12, Page 1388 2022, 12, 1388, doi:10.3390/NANO12091388. 

1. Maniks, J.; Mitin, V.; Kanders, U.; Kovalenko, V.; Nazarovs, P.; Baitimirova, M.; Meija, R.; Zabels, R.; Kundzins, K.; Erts, D. Deformation Behavior and Interfacial Sliding in Carbon/Copper Nanocomposite Films Deposited by High Power DC Magnetron Sputtering. Surf. Coatings Technol. 2015, 276, 279–285, doi:10.1016/J.SURFCOAT.2015.07.004. 

1. Münz, W.D.; Donohue, L.A.; Hovsepian, P.E. Properties of Various Large-Scale Fabricated TiAlN- and CrN-Based Superlattice Coatings Grown by Combined Cathodic Arc–Unbalanced Magnetron Sputter Deposition. Surf. Coatings Technol. 2000, 125, 269–277, doi:10.1016/S0257-8972(99)00572-1. 

1. Kanders, U.; Lungevics, J.; Leitans, A.; Boiko, I.; Berzins, K.; Trubina, Z. Nanostructured TiAlSi-CN:Me/a-CN:Si3N4 Composite Coatings Deposited by Advanced PVD Technique. Solid State Phenom. 2021, 320, 37–42, doi:10.4028/WWW.SCIENTIFIC.NET/SSP.320.37. 

1. Fleck, N.; Hutchinson, J. Strain Gradient Plasticity. Adv. Appl. Mech. 1997, 33, 295–362. 

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1. Fischer-Cripps, A.C. Nanoindentation. 2004, doi:10.1007/978-1-4757-5943-3. 

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1. Mokios, G.; Aifantis, E.C. Gradient Effects in Micro-/Nanoindentation. Mater. Sci. Technol. 2012, 28, 1072–1078, doi:10.1179/1743284712Y.0000000053. 

1. Kanders, U.; Kanders, K. Nanoindentation Response Analysis of Thin Film Substrates-II: Strain Hardening-Softening Oscillations in Subsurface Layer. Latv. J. Phys. Tech. Sci. 2017, 54, 34–45, doi:10.1515/LPTS-2017-0011. 

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1. Oliver, W.C.; Pharr, G.M. Measurement of Hardness and Elastic Modulus by Instrumented Indentation: Advances in Understanding and Refinements to Methodology. J. Mater. Res. 2004 191 2004, 19, 3–20, doi:10.1557/JMR.2004.19.1.3. 

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Reviewer: 7. There is an addition of numbers 40,41 in the references section. Literature 40 and 41 are not included in the text. It should be deleted.

 

We thank the reviewer for the careful reading of our manuscript and noting our errors. We have now corrected our reference section.

 

Reviewer: 8. References should be corrected according to the journal's rules.

 

We thank the reviewer for noting this. We have now corrected the formatting of our references.

 

Reviewer 9.⁠ ⁠There are grammatical errors and spelling mistakes. The sentence structure is too passive, more active structures should be used.

 

We thank the reviewer for the suggestion to improve the manuscript writing. We have now reviewed and improved the language throughout the manuscript. For example, in the Conclusions, we have now used active sentence structure:

 

“We demonstrated that Meyer's power law, historically developed for bulk materials, can be extended for thin films providing a semi-universal mathematical model across macro-, micro-, and nanoscale indentation tests. The evolution of the Meyer exponent n with indentation depth captures the transition from surface-dominated to bulk-like deformation and directly links to the SSF gradient beneath the indenter, offering a robust framework for comparing materials and capturing deformation behavior changes across scales. 

We  applied a simple empirical method to extract and analyze stress-strain field (SSF) gradient and divergence representations from nanoindentation load-displacement datasets measured regarding nanostructured tribological coatings (NSCs). The total strain gradient P’/h-profiles and divergence P”/h-profiles were calculated from load-displacement P/h-curves as normalized non-dimensional derivatives. By using this gradient-divergence approach, we revealed reproducible, depth-dependent oscillations across all samples, interpreted as alternating strain-hardening and strain-softening events related to local structural heterogeneities.”

Reviewer: 10. ⁠The phrasing is moderate. It can be improved by reducing redundancies.

 

We thank the reviewer for the suggestion to improve the phrasing of the manuscript. We have now reviewed and improved the language throughout the manuscript.

Reviewer: 11.⁠ ⁠The grammar is mostly correct, but there are gaps. Some articles have incorrect usage, which introduces agreement errors.

 

We thank the reviewer for the suggestion to improve the writing of the manuscript. We have now reviewed and improved the language, especially, the grammar throughout the manuscript.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The current paper reports on the “Nanoindentation response analysis of thin nanostructured nitride/carbonitride coatings based on transition metals using the strain gradient-divergence approach”. The major criticism of the present manuscript is the lack of adequate physical characterization of the coating; which make the presented mechanical properties of the coating in jeopardy. In addition to that, the presented nanoindentation technique, which is well established in literature, does not explore anything novel (both in terms of data analysis and critical scientific discussion), which can warrant the acceptance of this manuscript for publication. Thus, based on above mentioned grounds and my assessment, I reject this manuscript from publication.

The detail comments are as follows:

1. The title should be revised to make it concise.
2. The abstract should be re-written and include key numerical data. This is not the place to justify the present manuscript, as written in present case. The authors are encouraged to explore the relevant papers to understand how to write the abstract section properly.
3. The ‘keywords’ should be key-words, not the key sentences!
4. The novelty/knowledge gap of the current work did not stand out.
5. There are heaps of work available on the nanoindentation of coatings and related stress-strain field (SSF) gradient, divergence etc. In that respect, what new the present manuscript is contributing?
6. Section 2.2 and 2.3: What’s the purpose of these sections? Was this method originally developed by the authors? If not, then a very brief description with relevant citations will be enough, instead of such prolong description of the process.
7. Were the equations originally developed by the authors? If not it require adequate citations.
8. Adequate physical characterization of the coating was totally missing, which put the presented mechanical properties of the coating in jeopardy.
9. What was the micro-structure of the coatings?
10. What was the thickness of individual layers? And also their morphology.
11. Table 1: It was obvious that, all the coatings were about 5 μm think. On what basic the authors are claiming the coatings as ‘nanostructured’? What was the evidence against that?
12. It was never presented which coating was what (NSC-1- NSC-4).
13. Where the nanoindentation was conducted? On individual layers/bi-layers/ layer interfaces? Related proofs should ne included in the manuscript.
14. 1b,c and Fig. 2: what was the Y axis in those graphs?
15. There was no point of reviewing the paper beyond this point, as it raises significant concerns regarding the validity of the presented data.
16. The reviewer is totally in dark regarding the location of the nanoindentation sites, which make it impossible to review the manuscript further beyond this point (section 3.2).

 

Author Response

We thank the reviewer for assessing our manuscript and we express our regret about their decision. We have addressed the comments left by the reviewer, with the hope that the new revision of our manuscript has alleviated their concerns and it is now acceptable for publication.

 

Reviewer: 1. The title should be revised to make it concise.

 

We thank the reviewer and have adjusted the title as follows:

Simple strain gradient-divergence method for analysis of the nanoindentation load-displacement curves measured on nanostructured nitride/carbonitride coatings

Reviewer: 2. The abstract should be re-written and include key numerical data. This is not the place to justify the present manuscript, as written in the present case. The authors are encouraged to explore the relevant papers to understand how to write the abstract section properly.

 

We thank the reviewer for the suggestion to improve the abstract of our manuscript. We have adjusted it according to reviewer’s recommendations:

 

“Abstract: This study investigates the fabrication, nanomechanical behavior, and tribological performance of nanostructured superlattice coatings (NSCs) composed of alternating TiAlSiNb-N/TiCr-CN bilayers. Deposited via High-Power Ion-Plasma Magnetron Sputtering (HiPIPMS) onto 100Cr6 steel substrates, the coatings achieved nanohardness values of ~25 GPa and elastic moduli up to ~415 GPa. A novel empirical method was applied to extract stress–strain field (SSF) gradient and divergence profiles from nanoindentation load–displacement data. These profiles revealed complex, depth-dependent oscillations attributed to alternating strain-hardening and strain-softening mechanisms. Fourier analysis identified dominant spatial wavelengths, DWL, ranging from 4.3 to 42.7 nm. Characteristic wavelengths WL1 and WL2, representing fine and coarse oscillatory modes, were 8.2–9.2 nm and 16.8–22.1 nm, respectively, aligning with the superlattice period and grain-scale features. The hyperfine structure exhibited non-stationary behavior, with dominant wavelengths decreasing from ~5 nm to ~1.5 nm as indentation depth increased. We attribute the SSF gradient and divergence spatial oscillations to alternating strain-hardening and strain-softening deformation mechanisms within the near-surface layer during progressive loading. This cyclic hardening-softening behavior was consistently observed across all NSC samples, suggesting it represents a general phenomenon in thin film/substrate systems under incremental nanoindentation loading. The proposed SSF gradient-divergence framework enhances nanoindentation analytical capability, offering a tool for characterizing thin-film coatings and guiding advanced tribological material design.”

Reviewer: 3. The ‘keywords’ should be key-words, not the key sentences!

 

We thank the reviewer for the suggestion to improve the keywords of our manuscript. We have now indicated the following keywords:

 

“Keywords: nitride/carbonitride coating; superlattice; nanoindentation; nanohardness; wear; coefficient of friction; stress-strain field; strain gradient;”

Reviewer: 4. The novelty/knowledge gap of the current work did not stand out.

 

We thank the reviewer for the opportunity to clarify the novelty of our current work. We have now adjusted our Introduction to expand on this. Firstly, we provide justification for studying the nanomechanical behaviour of our chosen TiAlSiNb-N/TiCr-CN bilayer system:

 

“Nitride/carbonitride superlattice coatings outperform both amorphous carbon films and conventional monolayers in tribological applications. Their alternating nanolayers enhance hardness by strengthening interfacial bonding and hindering dislocation movement, resulting in superior mechanical properties compared to amorphous carbon, which lacks long-range order [1,2]. While amorphous coatings can achieve high hardness, they are brittle. In contrast, superlattice architectures combine low friction with excellent wear resistance, as their layered structure distributes stress and enables controlled deformation under harsh conditions [3–9]. 

This study focuses on the nanomechanical behavior of a TiAlSiNb-N/TiCr-CN bilayer system developed via High-Power Ion-Plasma Magnetron Sputtering (HiPIPMS) [10]. The selected elements and multilayer design aim to enhance hardness, toughness, thermal stability, and wear resistance. A modified, non-stoichiometric multilayer structure, TiAlSiMe₁-N/TiMe₂-CN, has emerged as a promising candidate for next-generation self-healing nanostructured coatings, combining low friction with ultra-high wear resistance [4,11-13]. Here, Me₁ and Me₂ denote refractory metals. This strategy addresses the limitations of pure hard carbon coatings, such as high residual stress, poor adhesion to steel substrates, and low thermal stability [1,2].”

 

Secondly, we provide justification for going beyond typically used analysis approaches and investigating SSF gradients.

 

“Nanoindentation measurements at shallow depths (tens to hundreds of nanometers) often exhibit significant variability, requiring an averaging of at least ten indentation tests. Mechanical properties are typically evaluated at 200–300 nm depth or greater, where values stabilize and approximate bulk material properties conventionally assessed by micro- or macroindentation. However, steady-state responses may not be achieved even at depths of several hundred nanometers. This behavior stems from factors such as reverse indentation size effects (RISE) [1,2], structural defects, or substantial substrate influence on thin coatings [21,22]. Near-surface regions are often structurally heterogeneous, complicating steady-state value attainment [5]. Analyzing gradients and divergences of the local stress–strain field (SSF) induced by structural inhomogeneities can provide valuable insights into nanomechanical behavior of a material investigated.  

Therefore, to complement characterization of the TiAlSiNb-N/TiCr-CN bilayer system and overcome limitations of conventional analytical approaches, we present a novel, straightforward method for extracting local SSF gradient and divergence information from nanoindentation datasets. These strain-gradient-based representations are sufficiently sensitive to reveal even subtle structural heterogeneities, such as interfaces between mechanically distinct microzones (e.g., sublayer boundaries in superlattice architectures) or grain boundaries within sublayers in near-surface regions. Applying this SSF gradient-divergence analysis to nanostructured tribological coatings (NSCs) enabled us to identify both work-hardening and work-softening processes occurring beneath the indenter during nanoindentation.”

 

Overall, a central claim to novelty in the current work is the application of this SSF gradient-divergence analysis to identify and interpret quasi-periodic spatial oscillations in the first derivatives P′(h) of the load–displacement curves for the TiAlSiNb-N/TiCr-CN NSCs. These oscillations, which are most clearly discernible in individual indentation test data at shallow penetration depths, are attributed to alternating cycles of strain-hardening and strain-softening events occurring within the coating during progressive loading. We suggest that this cyclic hardening-softening behavior may represent a general phenomenon in thin film/substrate systems subjected to incremental stress loading. 

 

The observation of SSF gradient and divergence oscillations, and their interpretation as alternating strain hardening-softening plastic deformation cycles, was indeed established by Kanders et al. for bulk solids, including various steels, silicon, glasses, and fused silica, particularly at shallow penetration depths (h<100 nm), cf. Refs 21,32,33 in the manuscript. However, the current study extends this analytical framework and observational finding to a significantly more complex and heterogeneous material system of nanostructured multicomponent superlattice coatings. Superlattices, by their very nature, possess a high density of interfaces and nanometer-scale layers with potentially distinct mechanical properties; these intrinsic structural features are expected to mediate deformation in a manner fundamentally different from that in bulk, monolithic materials. Therefore, the novelty of the present work lies not in the application of the SSF method itself, but in its specific application to (i) observe such complex oscillatory deformation phenomena within these TiAlSiNb-N/TiCr-CN superlattice coatings, and (ii) interpret these oscillations in the context of the unique nanolayered architecture and the critical role of its inherent interfaces. This advances the understanding of localized deformation in such advanced engineered surfaces.

 

The observed oscillatory behavior is likely a direct mechanical signature of the indenter tip interacting sequentially with these distinct nanolayers and their interfaces. Each such interaction can trigger a local hardening or softening response, providing a level of detail that conventional, averaged nanoindentation analysis might smooth out or entirely miss. The novelty is thus further supported by the method's capability to probe and reveal mechanical responses modulated by these nanoscale interfaces in superlattices, offering a more detailed understanding of local deformation events than is typically achievable with standard techniques. 

We hope that the justification above and findings in current research will alleviate any doubts concerning the novelty of our results presented in the manuscript.

 

Reviewer: 5. There is heaps of work available on the nanoindentation of coatings and related stress-strain field (SSF) gradient, divergence etc. In that respect, what is new in the present manuscript is contributing?

 

Similarly to the question above, we thank the reviewer for the opportunity to clarify the novelty of our current work. We have now adjusted our Introduction to expand on this. Firstly, we provide justification for studying the nanomechanical behaviour of our chosen TiAlSiNb-N/TiCr-CN bilayer system:

 

“Nitride/carbonitride superlattice coatings outperform both amorphous carbon films and conventional monolayers in tribological applications. Their alternating nanolayers enhance hardness by strengthening interfacial bonding and hindering dislocation movement, resulting in superior mechanical properties compared to amorphous carbon, which lacks long-range order [1,2]. While amorphous coatings can achieve high hardness, they are brittle. In contrast, superlattice architectures combine low friction with excellent wear resistance, as their layered structure distributes stress and enables controlled deformation under harsh conditions [3–9]. 

This study focuses on the nanomechanical behavior of a TiAlSiNb-N/TiCr-CN bilayer system developed via High-Power Ion-Plasma Magnetron Sputtering (HiPIPMS) [10]. The selected elements and multilayer design aim to enhance hardness, toughness, thermal stability, and wear resistance. A modified, non-stoichiometric multilayer structure, TiAlSiMe₁-N/TiMe₂-CN, has emerged as a promising candidate for next-generation self-healing nanostructured coatings, combining low friction with ultra-high wear resistance [4,11-13]. Here, Me₁ and Me₂ denote refractory metals. This strategy addresses the limitations of pure hard carbon coatings, such as high residual stress, poor adhesion to steel substrates, and low thermal stability [1,2].”

 

Secondly, we provide justification for going beyond typically used analysis approaches and investigating SSF gradients.

 

“Nanoindentation measurements at shallow depths (tens to hundreds of nanometers) often exhibit significant variability, requiring an averaging of at least ten indentation tests. Mechanical properties are typically evaluated at 200–300 nm depth or greater, where values stabilize and approximate bulk material properties conventionally assessed by micro- or macroindentation. However, steady-state responses may not be achieved even at depths of several hundred nanometers. This behavior stems from factors such as reverse indentation size effects (RISE) [1,2], structural defects, or substantial substrate influence on thin coatings [21,22]. Near-surface regions are often structurally heterogeneous, complicating steady-state value attainment [5]. Analyzing gradients and divergences of the local stress–strain field (SSF) induced by structural inhomogeneities can provide valuable insights into nanomechanical behavior of a material investigated.  

Therefore, to complement characterization of the TiAlSiNb-N/TiCr-CN bilayer system and overcome limitations of conventional analytical approaches, we present a novel, straightforward method for extracting local SSF gradient and divergence information from nanoindentation datasets. These strain-gradient-based representations are sufficiently sensitive to reveal even subtle structural heterogeneities, such as interfaces between mechanically distinct microzones (e.g., sublayer boundaries in superlattice architectures) or grain boundaries within sublayers in near-surface regions. Applying this SSF gradient-divergence analysis to nanostructured tribological coatings (NSCs) enabled us to identify both work-hardening and work-softening processes occurring beneath the indenter during nanoindentation.”

 

Overall, a central claim to novelty in the current work is the application of this SSF gradient-divergence analysis to identify and interpret quasi-periodic spatial oscillations in the first derivatives P′(h) of the load–displacement curves for the TiAlSiNb-N/TiCr-CN NSCs. These oscillations, which are most clearly discernible in individual indentation test data at shallow penetration depths, are attributed to alternating cycles of strain-hardening and strain-softening events occurring within the coating during progressive loading. We suggest that this cyclic hardening-softening behavior may represent a general phenomenon in thin film/substrate systems subjected to incremental stress loading. 

 

The observation of SSF gradient and divergence oscillations, and their interpretation as alternating strain hardening-softening plastic deformation cycles, was indeed established by Kanders et al. for bulk solids, including various steels, silicon, glasses, and fused silica, particularly at shallow penetration depths (h<100 nm), cf. Refs 21,32,33 in the manuscript. However, the current study extends this analytical framework and observational finding to a significantly more complex and heterogeneous material system of nanostructured multicomponent superlattice coatings. Superlattices, by their very nature, possess a high density of interfaces and nanometer-scale layers with potentially distinct mechanical properties; these intrinsic structural features are expected to mediate deformation in a manner fundamentally different from that in bulk, monolithic materials. Therefore, the novelty of the present work lies not in the application of the SSF method itself, but in its specific application to (i) observe such complex oscillatory deformation phenomena within these TiAlSiNb-N/TiCr-CN superlattice coatings, and (ii) interpret these oscillations in the context of the unique nanolayered architecture and the critical role of its inherent interfaces. This advances the understanding of localized deformation in such advanced engineered surfaces.

 

The observed oscillatory behavior is likely a direct mechanical signature of the indenter tip interacting sequentially with these distinct nanolayers and their interfaces. Each such interaction can trigger a local hardening or softening response, providing a level of detail that conventional, averaged nanoindentation analysis might smooth out or entirely miss. The novelty is thus further supported by the method's capability to probe and reveal mechanical responses modulated by these nanoscale interfaces in superlattices, offering a more detailed understanding of local deformation events than is typically achievable with standard techniques. 

We hope that the justification above and findings in current research will alleviate any doubts concerning the novelty of our results presented in the manuscript.

Reviewer: 6. Section 2.2 and 2.3: What’s the purpose of these sections? Was this method originally developed by the authors? If not, then a very brief description with relevant citations will be enough, instead of such prolong description of the process.

 

We thank the reviewer for this question. Indeed, the approach to SSF gradient-divergence approach used in this manuscript has been gradually developed and explored by the authors of this manuscript over the recent years, cf. Refs 21, 32, 33 in the manuscript: Kanders et al. Nanoindentation Response Analysis of Cu-Rich Carbon–Copper Composite Films Deposited by PVD Technique. Surf. Coatings Technol. 2015, 280, 308–316; Kanders et al. Nanoindentation Response Analysis of Thin Film Substrates-I: Strain Gradient-Divergence Approach. Latv. J. Phys. Tech. Sci. 2017, 54, 66–76; Kanders et al. Nanoindentation Response Analysis of Thin Film Substrates-II: Strain Hardening-Softening Oscillations in Subsurface Layer. Latv. J. Phys. Tech. Sci. 2017, 54, 34–45.

 

Given the relative novelty of this approach, we found it valuable to include a detailed derivation of this method in the Materials and Methods section.

Reviewer: 7. Were the equations originally developed by the authors? If not it require adequate citations.

 

We thank the reviewer for this question. Indeed, the approach to SSF gradient-divergence approach used in this manuscript has been gradually developed and explored by the authors of this manuscript over the recent years, cf. Refs 21, 32, 33 in the manuscript: Kanders et al. Nanoindentation Response Analysis of Cu-Rich Carbon–Copper Composite Films Deposited by PVD Technique. Surf. Coatings Technol. 2015, 280, 308–316; Kanders et al. Nanoindentation Response Analysis of Thin Film Substrates-I: Strain Gradient-Divergence Approach. Latv. J. Phys. Tech. Sci. 2017, 54, 66–76; Kanders et al. Nanoindentation Response Analysis of Thin Film Substrates-II: Strain Hardening-Softening Oscillations in Subsurface Layer. Latv. J. Phys. Tech. Sci. 2017, 54, 34–45.

 

Given the relative novelty of this approach, we found it valuable to include a detailed derivation of this method in the Materials and Methods section.

 

Reviewer: 8. Adequate physical characterization of the coating was totally missing, which put the presented mechanical properties of the coating in jeopardy.

 

We thank the reviewer for the opportunity to provide a more complete physical characterization of the coating. We have now added a table characterising the superlattice structure of the coatings (Table 1) as well as electron microscopy measurements (Figures 1-2).

 

We have now written:

 

“The cross-field configuration of the corresponding mosaic-type MSTs, combined with the rotating carousel of the substrate holder, enabled identification of the superlattice structure based on the PVD process technological parameters. Specifically, since the total coating thickness, t, is always measured after completion of the PVD process, an approximate superlattice structure can be calculated using process parameters such as deposition duration and the number of substrate holder carousel revolutions (Table 1). Additionally, by considering the sputtering yields of individual chemical elements (e.g., Ti ~0.5-0.8; C ~0.1-0.3; Cr ~0.6-1.0; Nb ~1.0-1.4), one can estimate the thickness of each sublayer, t₁ and t₂, from the total bilayer thickness, tb = t₁ + t₂, based on the average sputtering yields of the respective MSTs.”

 

Table 1. Characterization of the superlattice periodic structure of the NSC samples.

 

To characterise the structural properties in further detail, we have now added a section “3.2. Scanning Electron Microscopy Examinations of the NSC Film Samples” and write:

 

“The SEM plan view micrograph study of the bilayered nitride/carbonitride superlattice NSC film samples revealed a one-directional undulating anisotropic morphology pattern as surface roughness waving. The wavelengths of the undulations span between 1.28 and 81.35 nm, while the average wavelength was 49.85 nm for the NSC-1 sample. The narrow bands run through the entire SEM image height of about 1360 nm (VFW parameter). Thus, the fine-grained nodule-like morphology pattern contains very pronounced narrow bands, which could be characterized as having a very high aspect ratio of more than 27:1. The one-directional undulating surface pattern suggests that the coating morphology is governed by a combination of atomic-scale self-organization mechanisms, strain effects, and directional growth influences (Figures 1-2). The observed one-directional undulating morphology pattern was not sensitive to substrate temperatures within 350-400 °C range.”

Figure 1. Surface texture analysis of the NSC-1 sample (top panel): (a) SEM micrograph plan-view of the rectangle X*Y-selection; (b) surface 3D-roughness profile of the same selection in grayscale units averaged along Y-axis; (c) 3D-surface plot of the X*Y-selection in arbitrary units produced by ImageJ software. Fracture analysis of the NSC-1 sample (bottom panel): (d) SEM micrograph cross-sectional view; (e) coating’s bilayered superlattice structure with the period of about 17-18 nm; (f) fracture 3D-surface plot in arbitrary units produced by ImageJ software. Scale bars correspond to 200 nm. SEM analysis revealed an anisotropic one-directional undulating surface roughness pattern with spatial wavelength distribution between 1.28 and 81.35 nm, and an average value of 49.85 nm. 

Figure 2. SEM micrographs of plan-view (top panel) and cross-sectional view (bottom panel) of the NSC film samples NSC-2, NSC-3, and NSC-4. Scale bar correspond to 200 nm for all the NSC samples. All the NSC samples under investigation revealed anisotropic coating morphology that represents itself as a one-directional undulating surface roughness pattern. The coating’s bilayered superlattice period was estimated at around 17.9, 18.3, and 17.1 nm for the NSC-2, NSC-3, and NSC-4 samples, respectively. The fracture-view micrographs, in addition to the multilayered superlattice structure, contain remains of the crystalline Ti-adhesion layer at the bottom of the images. All NSC film samples exhibited very similar undulating roughness and superlattice structure profiles. 

 

“Several interconnected mechanisms could explain the observed morphological pattern. The atomic shadowing effect during PVD deposition, where sputtered material flux arrives at the substrate at oblique angles rather than normal incidence, can result in preferential growth directions. Some regions receive greater flux and grow faster, leading to an undulating or rippled structure that becomes further amplified by self-shadowing, which reinforces surface roughness. 

Additionally, strain-driven surface instabilities may contribute to the undulating pattern. The bilayered {TiAlSiNb-N/TiCr-CN}n superlattice structure introduces internal stress variations due to alternating composition, creating strain gradients across sublayers. Surface undulations can develop to relieve compressive stresses, potentially representing an example of the Asaro-Tiller-Grinfeld instability [29,30,34], where surface perturbations grow due to anisotropic stress relaxation. 

The undulating pattern with nanometer-scale wavelengths indicates that limited surface diffusion plays a significant role. Because adatom mobility is restricted, roughness increases over time through kinetic roughening. Low-temperature deposition or high deposition rates can enhance this effect, reinforcing the undulating pattern. Finally, the bilayered superlattice nature of the NSC films may contribute to periodic growth modulation. 

In summary, we propose a NSC growth model based on competitive columnar growth mechanisms balanced against strain-driven instability factors. Initially, PVD growth begins with fine nucleation, forming separate grain-island structures. Atomic shadowing contributes to local thickness variations, with columnar growth dominating the initial stages. As alternating TiAlSiNb-N/TiCr-CN sublayers are deposited, strain accumulates at their interfaces. This accumulated strain induces periodic wavelength-modulated structures. Since adatom mobility remains limited, kinetic roughening reinforces the undulation. The self-organized morphology suggests anisotropic diffusion-driven instability. 

The morphological anisotropy described above likely produces direction-dependent tribological behavior [42-44]. When tribological contact occurs parallel to undulation ridges, the surface offers reduced resistance, functioning similarly to rails and potentially decreasing friction and wear in that direction. Conversely, sliding perpendicular to these undulations requires greater energy to overcome topographical barriers, resulting in higher friction coefficients and increased abrasive wear. Furthermore, the periodic surface roughness (with average wavelengths of 49-52 nm in our samples) may promote stick-slip motion at nano- and microscale contacts. These undulations can interact with asperity dimensions or lubricant molecular sizes, significantly affecting friction dynamics. In dry or boundary lubrication regimes, such unidirectional undulations may provide additional benefits by channeling lubricants along specific directions, enhancing hydrodynamic lubrication along preferred paths while restricting flow in others.”

 

Accordingly, we have also added a section titled “2.6. Electron Microscopy Examinations of the NSC Samples” in the Materials and Methods section:

 

“The morphology of the NSC sample structures was investigated with a scanning electron microscope (SEM) Lyra3 (Tescan, Czech Republic, Brno), equipped with an energy-dispersive X-ray spectrometer (EDS), AZtecCrystal (Oxford Instruments, United Kingdom). SEM and EDS measurements were performed using a beam-accelerating voltage of up to 30 kV and a beam current of 500 pA.”

 

Reviewer: 9. What was the micro-structure of the coatings?

 

We thank the reviewer for this question. We hope the newly added characterization of the superlattice structure and electron microscopy measurements (please see our response to Comment 8 above) have sufficiently addressed this point.

 

Reviewer: 10. What was the thickness of individual layers? And also their morphology.

 

We thank the reviewer for this question. We hope the newly added characterization of the superlattice structure and electron microscopy measurements (please see our response to Comment 8 above) have sufficiently addressed this point.

 

For reviewer’s convenience, we repeat the newly added characterization below:

 

“The cross-field configuration of the corresponding mosaic-type MSTs, combined with the rotating carousel of the substrate holder, enabled identification of the superlattice structure based on the PVD process technological parameters. Specifically, since the total coating thickness, t, is always measured after completion of the PVD process, an approximate superlattice structure can be calculated using process parameters such as deposition duration and the number of substrate holder carousel revolutions (Table 1). Additionally, by considering the sputtering yields of individual chemical elements (e.g., Ti ~0.5-0.8; C ~0.1-0.3; Cr ~0.6-1.0; Nb ~1.0-1.4), one can estimate the thickness of each sublayer, t₁ and t₂, from the total bilayer thickness, tb = t₁ + t₂, based on the average sputtering yields of the respective MSTs.”

 

Table 1. Characterization of the superlattice periodic structure of the NSC samples.

 

To characterise the structural properties in further detail, we have now added a section “3.2. Scanning Electron Microscopy Examinations of the NSC Film Samples” and write:

 

“The SEM plan view micrograph study of the bilayered nitride/carbonitride superlattice NSC film samples revealed a one-directional undulating anisotropic morphology pattern as surface roughness waving. The wavelengths of the undulations span between 1.28 and 81.35 nm, while the average wavelength was 49.85 nm for the NSC-1 sample. The narrow bands run through the entire SEM image height of about 1360 nm (VFW parameter). Thus, the fine-grained nodule-like morphology pattern contains very pronounced narrow bands, which could be characterized as having a very high aspect ratio of more than 27:1. The one-directional undulating surface pattern suggests that the coating morphology is governed by a combination of atomic-scale self-organization mechanisms, strain effects, and directional growth influences (Figures 1-2). The observed one-directional undulating morphology pattern was not sensitive to substrate temperatures within 350-400 °C range.”

Figure 1. Surface texture analysis of the NSC-1 sample (top panel): (a) SEM micrograph plan-view of the rectangle X*Y-selection; (b) surface 3D-roughness profile of the same selection in grayscale units averaged along Y-axis; (c) 3D-surface plot of the X*Y-selection in arbitrary units produced by ImageJ software. Fracture analysis of the NSC-1 sample (bottom panel): (d) SEM micrograph cross-sectional view; (e) coating’s bilayered superlattice structure with the period of about 17-18 nm; (f) fracture 3D-surface plot in arbitrary units produced by ImageJ software. Scale bars correspond to 200 nm. SEM analysis revealed an anisotropic one-directional undulating surface roughness pattern with spatial wavelength distribution between 1.28 and 81.35 nm, and an average value of 49.85 nm. 

Figure 2. SEM micrographs of plan-view (top panel) and cross-sectional view (bottom panel) of the NSC film samples NSC-2, NSC-3, and NSC-4. Scale bar correspond to 200 nm for all the NSC samples. All the NSC samples under investigation revealed anisotropic coating morphology that represents itself as a one-directional undulating surface roughness pattern. The coating’s bilayered superlattice period was estimated at around 17.9, 18.3, and 17.1 nm for the NSC-2, NSC-3, and NSC-4 samples, respectively. The fracture-view micrographs, in addition to the multilayered superlattice structure, contain remains of the crystalline Ti-adhesion layer at the bottom of the images. All NSC film samples exhibited very similar undulating roughness and superlattice structure profiles. 

 

In addition, we provide further confirmation of the measured thickness values using the figure below (not shown in the final manuscript).

 

Figure 3. Fracture analysis of the NTC-4 sample: (left) SEM micrograph fracture view under oblique viewing angle given of about 30° instead of normal viewing angle; (right) fracture surface plot in arbitrary units produced by ImageJ software. Using the measurement under oblique viewing angle, the apparent bilayer thickness can be estimated at around 50 nm, which is 3 times larger than observed at normal viewing angle, i.e., 17.1 nm. Apparent thickness in the image will allways be greater than the true thickness if viewed obliquely; we can estimate the viewing angle as TETA = ACOS(treal/tapparent) and compare with the given angle. ACOS(17.1/50) value corresponds well to the 30 degree viewing angle value.

Reviewer: 11. Table 1: It was obvious that, all the coatings were about 5 μm think. On what basic the authors are claiming the coatings as ‘nanostructured’? What was the evidence against that?

 

We thank the reviewer for this question. We hope the newly added characterization of the superlattice structure and electron microscopy measurements (please see our response to comments above) have sufficiently addressed this point.

Reviewer: 12. It was never presented which coating was what (NSC-1- NSC-4).

 

We thank the reviewer for this question. We hope the newly added characterization of the superlattice structure and electron microscopy measurements (please see our response to comments above) have sufficiently addressed this point.

Reviewer: 13. Where the nanoindentation was conducted? On individual layers/bi-layers/ layer interfaces? Related proofs should ne included in the manuscript.

 

We thank the reviewer for the opportunity to clarify the location of the nanoindentation sites. We have now written in the section “3.1. Preparation and Characterization of the NSC Film Samples”:

 

“Nanoindentation experiments were conducted using a TriboIndenter apparatus (model TI980) to generate load-displacement loops (LDLs). A total of 40 nanoindentation tests were performed on four NSC samples (Table 2) at a peak load of 8000 µN. For each NSC sample, an indentation matrix of 10 positions with controllable coordinates (Xi, Yi) was established on the sample surface through careful microscopic examination. Indentation sites were selected using optical microscopy to identify the smoothest possible surface areas and were spaced at least 4000 nm apart to prevent mutual interference between neighboring indentations. Each NSC sample underwent 10 indentation tests, yielding load-displacement data from the corresponding 10 LDLs, with each dataset containing 2600 measurement points acquired during successive loading, drift, and unloading segments. All experiments were conducted in a single session to ensure identical measurement conditions and enable reliable comparison between NSC samples.”

Reviewer: 14. 1b,c and Fig. 2: what was the Y axis in those graphs?

 

We thank the reviewer for this question. The figure design optimizes space utilization, allowing for larger figures with enhanced optical clarity. To reduce ambiguity, we have now added clarifications to the captions of the corresponding figures:

 

Figure 1 (now Figure 3):

 

“Figure 3. The collection of the LDL and P/h-curves obtained at the testing peak load of 8000 µN measured at ten different positions within the indentation matrix of the NSC-1 film sample: (a) LDLs; (b) P/h-curves of the loading segment presented in a conventional linear plot; (c) the same P/h-curves in a log-log plot. Y-axes show Load On Sample, P (µN) for all panels (a-c).”

 

Figure 2 (now Figure 4):

 

“Figure 4. Meyer’s power law exponent n (y-axis) for individual P/h-curves obtained at the testing peak load of 8000 µN of the NSC-1 sample: (a) n-values for each P/h-curve within four consecutive h-intervals covering nearly the full penetration depth; (b) boxplots of n-values grouped by the consecutive h-intervals, showing an overall increase along the indenter penetration depth. ”

Reviewer: 15. There was no point of reviewing the paper beyond this point, as it raises significant concerns regarding the validity of the presented data.

 

We hope the new revision of our manuscript has alleviated the reviewer's concerns.

Reviewer: 16. The reviewer is totally in dark regarding the location of the nanoindentation sites, which make it impossible to review the manuscript further beyond this point (section 3.2).

 

We thank the reviewer for the opportunity to clarify the location of the nanoindentation sites. We have now written in the section “3.1. Preparation and Characterization of the NSC Film Samples”:

 

“Nanoindentation experiments were conducted using a TriboIndenter apparatus (model TI980) to generate load-displacement loops (LDLs). A total of 40 nanoindentation tests were performed on four NSC samples (Table 2) at a peak load of 8000 µN. For each NSC sample, an indentation matrix of 10 positions with controllable coordinates (Xi, Yi) was established on the sample surface through careful microscopic examination. Indentation sites were selected using optical microscopy to identify the smoothest possible surface areas and were spaced at least 4000 nm apart to prevent mutual interference between neighboring indentations. Each NSC sample underwent 10 indentation tests, yielding load-displacement data from the corresponding 10 LDLs, with each dataset containing 2600 measurement points acquired during successive loading, drift, and unloading segments. All experiments were conducted in a single session to ensure identical measurement conditions and enable reliable comparison between NSC samples.”

Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

Though substantial improvements were made by the authors, following points should also be addressed:

1. Details of the surface profilometer should be included.
2. SEM images on the residual nanoindentation imprints should be included.

Author Response

Reviewer 3

Reviewer: Though substantial improvements were made by the authors, following points should also be addressed:

 

We thank the reviewer for noting the substantial improvements of the manuscript.

 

Reviewer: Details of the surface profilometer should be included.

 

We have now added a section in the Materials and Methods part, titled “2.6. Surface roughness evaluation using roughness tester Mitutoyo AVANT”, to provide additional information about the surface profilometer:

“Surface roughness measurements were performed using a Mitutoyo AVANT roughness tester (model AVANT 3D, Mitutoyo, Japan), with details provided in Appendix A for all NSC samples investigated in this study (cf. Table A1). Measurement conditions were established according to ISO 21920-3:2021 (Geometrical product specifications (GPS) Surface texture: Profile — Part 2: Terms, definitions, and surface texture parameters). For each NSC sample, three symmetric roughness profiles were measured at 120-degree intervals from the sample center toward the outer perimeter. Average values were calculated for Ra (arithmetic mean deviation of the profile), Rq (root mean square deviation of the profile), and Rz (maximum height of the profile). The Mitutoyo AVANT is a high-precision contact profilometer that employs a stylus-based method to evaluate surface roughness parameters, including amplitude parameters Ra, Rq, and Rz. The instrument achieves a vertical resolution of 0.1 nm under optimal operating conditions. The measurement results were post-processed using MCube Map Ultimate 8.0 software.”

 

Further details and measurement results are added in a new section “Appendix A. Surface Roughness Evaluation Using Roughness Tester Mitutoyo AVANT”:

 

“The surface roughness tester Mitutoyo AVANT 3D was equipped with an S-3000 roughness detector module, a high-accuracy Y-axis table, and an auto-leveling table. The S-3000 roughness detector module featured a 0.75 mN detector and a standard stylus 12AAC731 with a cone angle of 60 degrees and a tip radius of 2 µm. Prior to the roughness measurements, the NCS samples were cleaned using compressed air flow and leveled using the auto-leveling function to ensure optimal alignment with the stylus. Three radial roughness profiles separated by an angle of 120 degrees were measured for each NSC sample. The average 3-profile Raqz values for each sample were calculated from 3 x 10,000 measurement points and presented in Table A1.”

 

Table A1. Surface roughness parameters Raqz-values (nm) of the NSC film samples

 

Reviewer: SEM images on the residual nanoindentation imprints should be included.

 

We thank the reviewer for this excellent suggestion to provide SEM images of residual nanoindentation imprints, which would indeed provide complementary information to our load-displacement analysis. We appreciate this insightful recommendation, as SEM imaging of residual imprints is recognized as an important characterization technique in nanoindentation studies. However, obtaining reliable SEM images of nanoindentation imprints at the low peak loads employed in this study (8000 µN) presents significant technical challenges for hard nitride/carbonitride coatings. At these low loads, the residual imprints are extremely shallow (typically <150 nm depth) and small in lateral dimensions, making them difficult to resolve with adequate contrast in SEM imaging, even with optimized parameters such as low accelerating voltages (1-5 kV) and tilted sample positioning. The high hardness of our NSC coatings, combined with their surface roughness (Ra values ranging from 9.56-13.17 nm as detailed in Table A1), further compounds this imaging challenge, as the shallow indentations can be obscured by the existing surface topography, making reliable identification and characterization of the residual imprints difficult.

 

Importantly, the major focus of this work is the application of the strain gradient-divergence method for analyzing load-displacement curves, rather than detailed post-indentation surface characterization. The mechanical properties and deformation behavior are comprehensively captured through the high-resolution load-displacement data and our novel analytical approach. The load-displacement curves themselves provide the complete mechanical response information needed for the strain gradient analysis, making direct imaging of residual imprints not essential for the conclusions drawn in this study. 

 

Therefore, we hope the comprehensive load-displacement analysis presented in the present version of the manuscript, combined with the additional surface roughness characterization, provides sufficient evidence for the validity of our nanoindentation results and the effectiveness of the proposed analytical method.