# Investigation of the microstructure of a graded ZrN/Ti0.33Al0.67N multilayer coating using cross-sectional characterization methods

Florian Frank, Michael Tkadletz, Christian Saringer, Christoph Czettl,

Markus Pohler, Manfred Burghammer, Juraj Todt, Jakub Zalesak, Jozef

Keckes, Nina Schalk

► To cite this version:

Florian Frank, Michael Tkadletz, Christian Saringer, Christoph Czettl, Markus Pohler, et al. Investigation of the microstructure of a graded ZrN/Ti0.33Al0.67N multilayer coating using cross-sectional characterization methods. Surface and Coatings Technology, 2023, 453, pp.129126. 10.1016/j.surfcoat.2022.129126. hal-05080008

HAL Id: hal-05080008

https://hal.science/hal-05080008v1

Submitted on 22 May 2025

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# Investigation of the microstructure of a graded ZrN/Ti<sub>0.33</sub>Al<sub>0.67</sub>N multilayer coating using cross-sectional characterization methods

Florian Frank<sup>a, *</sup>, Michael Tkadletz<sup>b</sup>, Christian Saringer<sup>a</sup>, Christoph Czettl<sup>c</sup>, Markus Pohler<sup>c</sup>, Manfred Burghammer<sup>d</sup>, Juraj Todt<sup>b,e</sup>, Jakub Zalesak<sup>b,e</sup>, Jozef Keckes<sup>b,e</sup>, Nina Schalk<sup>a</sup>

<figure><img src="image_3.png" /></figure>

## ARTICLE INFO

### Keywords:

X-ray nanodiffraction

Residual stress

Multilayers

TiAlN

Hard coatings

Arc evaporation

## ABSTRACT

An approach to enhance the performance of protective hard coatings for cutting applications is to modify the coating architecture by combining two inherently different materials in a multilayer. Besides the choice of the materials, the thickness of the individual layers strongly influences the coating microstructure and consequently also its properties. Within this work, a graded ZrN/Ti<sub>0.33</sub>Al<sub>0.67</sub>N multilayer coating with constant Ti<sub>0.33</sub>Al<sub>0.67</sub>N and stepwise increasing ZrN layer thickness was investigated in detail by a combinatorial approach of cross-sectional X-ray nanodiffraction, electron backscatter diffraction and transmission electron microscopy. The primary aim was to obtain a profound understanding of the microstructure of the coating as well as of the residual stress state. (Semi-)coherent grain growth was observed independently of the ZrN layer thickness. Changes in the multilayer architecture were found to affect not only the grain size, but also the residual stress state of the coating. While the grain size increased with increasing ZrN layer thickness, the residual stress decreased. This work contributes to a deeper understanding of the influence of the multilayer architecture on the microstructure and stress state of heteroepitactic multilayer coatings.

## 1. Introduction

Multilayer coatings with two or more alternating layer materials have been reported to show superior machining performance compared to their single-layer counterparts [1,2]. There, not only the materials used for the multilayer coatings, but also the layer architecture significantly influences the properties [3–7]. ZrN and TiAlN already show good mechanical and thermal properties for cutting applications that can be further improved by depositing both materials in a multilayer approach [3,5,8–10]. The improved mechanical and thermal properties of cathodic arc evaporated (CAE) ZrN/TiAlN multilayer coatings, compared to their single-layer counterparts, can be attributed to the coherency and epitaxial stabilization between the ZrN and TiAlN layers, as well as alterations in grain size, texture and interface density, depending on the bilayer period [5,7,10,11]. Xu et al. observed a correlation between higher hardness and coherency as a result of

alternating stress fields of the two coherently grown materials with different lattice parameters, an effect that was also observed by other researchers for multilayer coatings with different layer materials [5,6,12–14]. However, not only the lattice parameters of the different materials, but also the thickness of the individual layers were reported to affect the coherency and thus the stress state of the coating [5]. In order to optimize the multilayer architecture, detailed knowledge about the residual stress state is of significant importance, as e.g. high stresses can lead to coating failure due to delamination and plastic deformation, especially at high thermal or mechanical loads [11,15]. Also, microstructural gradients can form within the individual layers of a multilayer coating, affecting the functional properties of the coating also on a macroscopic level [16]. Although the influence of the bilayer period of ZrN/TiAlN multilayer coatings on the coherency and the mechanical properties has already been investigated [5,7,10,11], a detailed study is still missing, of how the individual layer thickness affects the stress state

<footnote><sup>a</sup> Christian Doppler Laboratory for Advanced Coated Cutting Tools at the Department of Materials Science, Montanuniversität Leoben, Franz-Josef-Strasse 18, 8700 Leoben, Austria</footnote>

<footnote><sup>b</sup> Department of Materials Science, Montanuniversität Leoben, Franz-Josef-Strasse 18, 8700 Leoben, Austria</footnote>

<footnote><sup>c</sup> Ceratizit Austria GmbH, Metallwerk-Plansee-Strasse 71, 6600 Reutte, Austria</footnote>

<footnote><sup>d</sup> European Synchrotron Radiation Facility, Cedex 9, 38043 Grenoble, France</footnote>

<footnote><sup>e</sup> Erich Schmid Institute for Materials Science, Austrian Academy of Sciences, Leoben, Austria</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: flofrank.frf@gmail.com (F. Frank).</footnote>
of both layers, as well as a detailed investigation of microstructural gradients that form during coating synthesis.

Thus, within this work a graded ZrN/Ti<sub>0.33</sub>Al<sub>0.67</sub>N multilayer coating was synthesized, with from the substrate towards to surface gradually increasing ZrN sublayer and constant Ti<sub>0.33</sub>Al<sub>0.67</sub>N sublayer thickness. Starting with a ZrN:Ti<sub>0.33</sub>Al<sub>0.67</sub>N thickness ratio < 1 at the interface to the substrate, the thickness ratio was gradually increased to >1 towards the surface and the effect on coherency, as well as the grain size and the stress state were investigated in detail. The complementary application of different investigation methods allowed to evaluate the microstructure and stress state on different length scales, starting on a macroscopic level, using laboratory X-ray diffraction (XRD), scanning electron microscopy (SEM) and electron backscatter diffraction (EBSD). Cross-sectional X-ray nanodiffraction (CSnanoXRD) was applied to study gradients in phase composition, residual stress, as well as crystallographic texture depth-resolved across the coating thickness with a local resolution of ~50 nm [16–21]. Furthermore, transmission electron microscopy (TEM) and energy dispersive X-ray spectroscopy (EDS) were applied.

## 2. Experimental details

### 2.1. Coating deposition

A graded ZrN/Ti<sub>0.33</sub>Al<sub>0.67</sub>N multilayer coating, with constant Ti<sub>0.33</sub>Al<sub>0.67</sub>N layer thickness and increasing ZrN layer thickness, was deposited using a commercially available CAE deposition chamber by Oerlikon Balzers, using two Zr and four Ti<sub>0.33</sub>Al<sub>0.67</sub> targets. Cemented carbide cutting inserts in SNUN 120412 geometry (ISO 1832 [22]) with a composition of 92 wt% WC, 6 wt% Co and 2 wt% mixed carbides served as substrate material. The substrates were mounted on a rotational substrate holder, enabling two-fold rotation of the substrates during deposition. The bias voltage and the temperature were kept constant at –40 V and 425 °C, respectively. A mixture of N<sub>2</sub> and Ar was used to synthesize the nitride multilayer coating. A schematic of the architecture of the graded ZrN/Ti<sub>0.33</sub>Al<sub>0.67</sub>N coating is displayed in Fig. 1a. A Ti<sub>0.33</sub>Al<sub>0.67</sub>N base layer was deposited on the substrate before the deposition of the multilayer blocks, followed by nine blocks of

different ZrN/Ti<sub>0.33</sub>Al<sub>0.67</sub>N bilayer thickness. Within each block, the layer thickness ratio was kept constant and the total block thickness was designed to lie between 400 and 600 nm. In blocks 1–4, the multilayers were formed due to the rotation of the substrates. As the ZrN layer thickness that can be achieved is limited by the maximum applied current to the Zr targets, blocks 5–9 with ZrN layer thickness >24 nm were deposited by opposed cyclic activation and deactivation of the Zr and TiAl targets, while maintaining the substrate rotation. The ZrN layer thickness was controlled by increasing the working time of the Zr target for each successive block. To guarantee an almost constant thickness of the individual Ti<sub>0.33</sub>Al<sub>0.67</sub>N layers of 13–17 nm, the TiAl target working time was kept constant throughout the deposition process. In addition to the graded ZrN/Ti<sub>0.33</sub>Al<sub>0.67</sub>N multilayer coating, ZrN and Ti<sub>0.33</sub>Al<sub>0.67</sub>N single-layer coatings were deposited from the same targets and at the same deposition conditions as the multilayer coating. The single-layer coatings were deposited on cemented carbide substrates and mild steel foils.

### 2.2. Coating characterization

To determine the unstrained lattice parameter of the ZrN and Ti<sub>0.33</sub>Al<sub>0.67</sub>N single-layer coatings without the influence of the substrate material, the coated mild steel foils were dissolved in nitric acid and a coating powder was obtained. Furthermore, the elemental composition of the single-layer coatings was investigated by glow discharge optical emission spectroscopy (GDOES) using a Horiba GD-Profiler 2 spectrometer.

A Hitachi IM4000+ ion milling system was used to prepare a cross-section of the ZrN/Ti<sub>0.33</sub>Al<sub>0.67</sub>N multilayer coating, which was investigated using a Zeiss GeminiSEM 450. The EBSD analysis was conducted in the same SEM with an accelerating voltage of 10 kV and a step size of 20 nm, utilizing an Oxford Symmetry EBSD camera.

An FEI Helios NanoLab 660 workstation was used to prepare a thin lamella of the cross-section of the coating for the TEM investigations. The lamella was thinned down to an electron-transparent thickness using accelerating voltages from 30 to 2 kV and ion currents ranging from 20 nA to 40 pA. TEM investigations were performed on an FEI Titan Themis system, operated at 300 kV in scanning TEM (STEM) mode,

<figure><img src="image_4.png" /><figcaption>**Fig. 1.** (a) Schematic sketch of the graded coating architecture and (b) secondary electron SEM (SE-SEM) image of the FIB prepared cross-section of the graded ZrN/Ti<sub>0.33</sub>Al<sub>0.67</sub>N coating. (c) EBSD band contrast image displaying the grains and (d) EBSD inverse pole figure (IPF) map in growth direction showing the grain orientation.</figcaption></figure>
using a probe current of 1 nA. EDS was conducted applying an FEI SUPER-X spectrometer with 4x30mm² windowless silicon drift detectors (SDD).

The phase composition of the coating was investigated using a Bruker D8 Advance diffractometer with a Cu-Kα source (λ = 0.15406 nm) and an energy-dispersive Sol-X detector. A detailed investigation of the residual stress, texture and the unstrained lattice parameter was conducted on a Bruker D8 Advance DaVinci diffractometer using Cu-Kα radiation and a position sensitive LynxEye XE-T detector. The residual stress was determined using the ZrN 200 and Ti₀.₃₃Al₀.₆₇N 200 peaks employing the sin²ψ method in side-inclination mode with tilt angles ψ between 0 and 82° and X-ray elastic constants $\frac{1}{2}s_{22}^{hkl}$, as described at the end of this section. XRD pole figures (PFs) were recorded for the 111, 200 and 220 reflections of the fcc-ZrN and fcc-Ti₀.₃₃Al₀.₆₇N phase with tilt angles from 0 to 84°. To determine a reference unstrained lattice parameter, X-ray diffractograms of powdered single-layer ZrN and Ti₀.₃₃Al₀.₆₇N coatings were recorded in Bragg-Brentano geometry and evaluated applying a Pawley-refinement using the software Topas 6.

In order to enable the CSnanoXRD experiments, a 150 µm thick lamella of the substrate/coating compound was cut out using a diamond cutting wheel, mounted on a Struers Accutom-5R precision saw, and further thinned down to a thickness of ~45 µm using focused ion beam (FIB) milling. CSnanoXRD experiments were performed at the nanofocus extension of the ID13 beamline at the European Synchrotron Radiation Facility (ESRF) in Grenoble, France [16]. The raw data can be found under ref. [23]. The monochromatic X-ray beam with a photon energy of 13 keV and a point focus with a diameter of ~50 nm was directed at the lamella parallel to the sample surface. The cross-section of the sample was scanned along the substrate normal direction in transmission geometry by moving the sample through the beam with a step size of 25 nm. For each scan step, a two-dimensional diffraction pattern was recorded using a Dectris Eiger X 4M detector. The patterns were evaluated using the pyFAI software package [24,25]. The in-plane residual strain $\epsilon_{hkl}$ and in-plane stress $\sigma_{hkl}$ for the ZrN and Ti₀.₃₃Al₀.₆₇N 200 diffraction peaks were evaluated using the method described in refs. [17,26]. For this, each ring, resulting from the diffraction on {200} lattice planes of the ZrN or Ti₀.₃₃Al₀.₆₇N phase, was divided into 36 equal segments of 10° that were integrated and the resulting peaks were fitted using a pseudo-Voigt function to determine the d-spacing as a function of the azimuthal orientation [16,17,26]. According to Refs. [19,26,27], additionally, the stress-free d-spacing ($d_0^{hkl}$) was evaluated using the Poisson's ratio $\nu_{hkl}$. The stress-free lattice parameter ($a_0$) was then calculated from $d_0^{hkl}$. The X-ray elastic constants $\frac{1}{2}s_{22}^{hkl}$ and $\nu_{hkl}$ needed to calculate $\sigma_{hkl}$ were determined using the Hill grain interaction model [28], employing single-crystal elastic constants from literature as input [29,30]. For the 200 reflection, $\frac{1}{2}s_{22}^{200} = 2.74 \cdot 10^{-12} \text{ Pa}^{-1}$ and $\nu^{200} = 0.207$ were calculated for fcc-ZrN and $\frac{1}{2}s_{22}^{200} = 3.03 \cdot 10^{-12} \text{ Pa}^{-1}$ and $\nu^{200} = 0.234$ for fcc-Ti₀.₃₃Al₀.₆₇N.

# 3. Results

## 3.1. Architecture, microstructure and elemental composition

In Fig. 1a, the architecture of the ZrN/Ti₀.₃₃Al₀.₆₇N multilayer coating is schematically shown. The 9 blocks are numbered in ascending order, starting from the Ti₀.₃₃Al₀.₆₇N base layer. The ZrN layer thickness is constant within the respective blocks, but increases with increasing block number, while the Ti₀.₃₃Al₀.₆₇N layer thickness is constant over the whole coating thickness. For each block the individual layer thicknesses are given in Fig. 1a. In the SEM image in Fig. 1b, the ZrN and Ti₀.₃₃Al₀.₆₇N layers are clearly distinguishable due to their differences in the elemental contrast, where brighter layers correspond to ZrN and darker ones to Ti₀.₃₃Al₀.₆₇N. The EBSD band contrast image in Fig. 1c shows that grain growth is not interrupted by the ZrN/Ti₀.₃₃Al₀.₆₇N interfaces, leading to the assumption that the individual layers grow

coherently or semi-coherently. Even at smaller bilayer thicknesses in blocks 1–3 the grains are larger than the single layers. The influence of the bilayer thickness on the grain size is also visible; it can be seen that the grain size increases with the bilayer thickness. Especially in blocks 5–9 a gradual increase of the grain size with the bilayer thickness can be observed. In the EBSD inverse pole figure (IPF) map in growth direction (Y-direction), shown in Fig. 1d, the grain orientation is displayed. In blocks 1–4 only a small number of grains with a sufficiently large grain size can be indexed, making an estimation of the grain orientation with this method impossible. However, larger grains from block 5 towards the surface display a tendency towards a (100) out-of-plane preferred orientation, although the texture is not that pronounced. All indexed grains exhibited a face-centered cubic (fcc) crystal structure.

The TEM micrographs in Fig. 2a and b show an overview of the cross-section of the coating. At the interface between blocks 4 and 5, the Ti₀.₃₃Al₀.₆₇N layer appears thicker than the other Ti₀.₃₃Al₀.₆₇N layers. This can be related to the change in deposition mode from substrate rotation to target on/off. In the annular dark-field (ADF) image it can be seen that the grain size increases in blocks 1–9 and complex variations of the contrast in the image might indicate dislocations along the cross-section. Due to the high elemental contrast (Z-contrast) in the high-angle ADF (HAADF) image, the brighter ZrN and darker Ti₀.₃₃Al₀.₆₇N are clearly visible and seem to be well separated. EDS maps show a clear distinction between the Zr in the ZrN layers and the Ti and Al in the Ti₀.₃₃Al₀.₆₇N layers. Although the N content appears homogeneous for blocks 1–5, it seems to increase in the Ti₀.₃₃Al₀.₆₇N layers and decrease in the ZrN layers in blocks 6–9, where the ZrN layer thickness is significantly larger than the Ti₀.₃₃Al₀.₆₇N layer thickness. This effect can be attributed to an overestimation of the N content in Ti₀.₃₃Al₀.₆₇N layers, due to the vicinity of the Ti-Lα and N-Kα lines in the EDS spectrum [3]. In order to quantify the chemical composition, GDOES investigations of the single-layer ZrN and Ti₀.₃₃Al₀.₆₇N coatings, which were deposited under the same conditions as the ZrN/Ti₀.₃₃Al₀.₆₇N multilayer coating, were conducted and revealed a N content of ~50 at. % for both, the ZrN and the Ti₀.₃₃Al₀.₆₇N coating. The Ti and Al content of the Ti₀.₃₃Al₀.₆₇N coating were ~16 at.% and ~33 at.%, respectively. These findings show that the coatings were stoichiometric regarding their metal/non-metal ratio and that the Ti:Al ratio in the coating matches well with the Ti:Al ratio of the target, which can also be assumed for the multilayer coatings.

The X-ray diffractogram in Fig. 3a indicates an fcc structure for both, ZrN and Ti₀.₃₃Al₀.₆₇N phases. While several distinct ZrN peaks are visible, only the Ti₀.₃₃Al₀.₆₇N 200 peak can be observed clearly. This can be related to the smaller diffacting volume of the thinner Ti₀.₃₃Al₀.₆₇N layers compared to thicker ZrN layers and to the higher atomic form factor of Zr compared to Ti and Al, which leads to a more intense signal from ZrN than from Ti₀.₃₃Al₀.₆₇N [31]. The Ti₀.₃₃Al₀.₆₇N 200 peak is situated between the reference positions for fcc-TiN and fcc-AlN, indicating the formation of a Ti₀.₃₃Al₀.₆₇N solid solution. Also for ZrN the most pronounced peak is the 200 peak, suggesting a (100) preferred orientation. The additionally recorded XRD pole figures of the ZrN (Fig. 3b) and Ti₀.₃₃Al₀.₆₇N (Fig. 3c) 111, 200 and 220 peaks corroborate a strong (100) fiber texture for both phases. The texture seems aligned for both phases, confirming the coherent or semi-coherent layer growth. However, no conclusions can be drawn as to whether the variation of the individual layer thickness as a function of the coating thickness leads to a change in preferred orientation of the crystallites.

## 3.2. CSnanoXRD analysis

To investigate the effect of the layer architecture on the microstructure of the ZrN/Ti₀.₃₃Al₀.₆₇N multilayer coating, position-resolved CSnanoXRD investigations as a function of the film thickness were conducted. In Fig. 4a, the phase evolution along the cross-section is displayed. For this, the two-dimensional Debye-Scherrer rings were integrated azimuthally in the range of 0–360° and the resulting radial XRD
<figure><img src="image_5.png" /><figcaption>**Fig. 2.** (a) ADF and (b) HAADF images of the ZrN/Ti<sub>0.33</sub>Al<sub>0.67</sub>N cross-section. (c) The EDS maps display Zr, Ti, Al and N and were recorded from the region highlighted in the HAADF image.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>**Fig. 3.** (a) X-ray diffractogram of the ZrN/Ti<sub>0.33</sub>Al<sub>0.67</sub>N multilayer coating. The reference positions for fcc-ZrN (PDF 00-035-0753), fcc-TiN (PDF 00-038-1420), fcc-AlN (PDF 00-025-1495) and WC from the substrate (PDF 00-003-1096) are indicated with dashed lines [32]. XRD pole figures of the (b) ZrN and (c) TiAlN 111, 200 and 220 peaks.</figcaption></figure>

patterns are plotted for each measured position along the cross-section. It can be seen that the phase composition does not change with increasing ZrN layer thickness and blocks 1–9 show an fcc structure for both, ZrN and Ti<sub>0.33</sub>Al<sub>0.67</sub>N phases. Besides the phase composition, CSnanoXRD allows to investigate the crystallographic texture of the coating. In Fig. 4b, the out-of-plane component of the Debye-Scherrer rings is shown. The intensity of the ZrN 200 peak is the highest and the intensities of the different peaks do not change with respect to each

other over the whole coating thickness, indicating that 〈100〉 is the preferred crystal orientation, independent of the bilayer thickness. Analogously, Ti<sub>0.33</sub>Al<sub>0.67</sub>N also displays a 〈100〉 preferred orientation over the whole coating thickness.

In addition to the phase composition and the texture, the in-plane biaxial X-ray elastic strain and residual stress state of the ZrN and Ti<sub>0.33</sub>Al<sub>0.67</sub>N phases were determined from the distortion of Debye-Scherrer rings and are presented in Fig. 5a and b. The in-plane elastic
<figure><img src="image_7.png" /><figcaption>**Fig. 4.** (a) Phase plot of the ZrN/Ti<sub>0.33</sub>Al<sub>0.67</sub>N multilayer coating for a full circle (0–360°) integration of Debye-Scherrer rings, next to a STEM HAADF image to the right and indicated blocks as reference for the coating architecture. (b) Phase plot in out-of-plane direction of the Debye-Scherrer ring (integration range out-of-plane direction ±5°).</figcaption></figure>

<figure><img src="image_8.png" /></figure>

strain in Fig. 5a is directly determined from the distorted Debye-Scherrer rings and only $v$ is required for the calculation, while for the in-plane residual stress the X-ray elastic constants are needed [16,17]. For simplicity it was assumed that both, $v$ and the X-ray elastic constants do not change along the cross-section [16,17,19]. It can be seen that the trends in elastic strain and residual stress are comparable. Thus, the discussion focuses on the evolution of the residual stress.

<caption>**Fig. 5.** Evolution of the (a) in-plane strain $\epsilon^{200}$, (b) in-plane residual stress $\sigma^{200}$, (c) unstrained lattice parameter $a_0$ and (d) full width at half maximum (fwhm$^{200}$) as a function of the coating thickness for the ZrN and Ti<sub>0.33</sub>Al<sub>0.67</sub>N layers of the ZrN/Ti<sub>0.33</sub>Al<sub>0.67</sub>N multilayer coating, determined by CSnanoXRD. The average residual strain and stress, determined on a laboratory XRD including the standard deviation is also displayed in (a) and (b), respectively. Reference positions for $a_0$, determined from powdered single-layer ZrN and Ti<sub>0.33</sub>Al<sub>0.67</sub>N coatings, are added in (c).</caption>

The average residual strain and stress of the multilayer coating including the standard deviation, obtained by laboratory XRD and the $\sin^2\omega$ method, is also added to Fig. 5a and b, respectively. The considerably higher standard deviation of Ti<sub>0.33</sub>Al<sub>0.67</sub>N compared to ZrN can be related to the weaker diffraction intensity of Ti<sub>0.33</sub>Al<sub>0.67</sub>N peaks. It can be seen that the average stress correlates well with the apparent mean stress over the whole coating thickness determined from the
CSnanoXRD analysis for both, ZrN and Ti<sub>0.33</sub>Al<sub>0.67</sub>N. Independent of the layer thickness, a compressive residual stress state is observed over the whole coating thickness for ZrN and Ti<sub>0.33</sub>Al<sub>0.67</sub>N. A trend can be observed, where the residual stress decreases in blocks 1–9 for both phases. The highest stress is observed in the vicinity of the base layer in blocks 1 and 2 and is approximately –5 and –3.5 GPa for ZrN and Ti<sub>0.33</sub>Al<sub>0.67</sub>N, respectively. The difference between ZrN and Ti<sub>0.33</sub>Al<sub>0.67</sub>N diminishes gradually with increasing coating thickness, as the residual stress drops faster in the ZrN than in Ti<sub>0.33</sub>Al<sub>0.67</sub>N layers. In blocks 6–9 the stresses are roughly equal for both layers and further decrease towards the surface. In block 5, the residual stress in the ZrN layer rises by ~1 GPa, which is most probably related to the change in the deposition mode from substrate rotation to target on/off.

In Fig. 5c the stress-free lattice parameter $a_0$ evaluated from the ZrN and Ti<sub>0.33</sub>Al<sub>0.67</sub>N 200 peaks, is displayed with respect to the coating thickness. In addition, the reference positions of the unstrained lattice parameter are shown, determined from the powders of the ZrN and Ti<sub>0.33</sub>Al<sub>0.67</sub>N single-layer coatings, which are 4.58 Å and 4.16 Å, respectively. The Ti<sub>0.33</sub>Al<sub>0.67</sub>N $a_0$ does not change significantly over the coating thickness and is in good agreement with the $a_0$ of the single-layer coating. The ZrN $a_0$ displays minor deviations from the reference $a_0$ over the whole coating thickness, which are more pronounced in the surface and base layer near regions.

The evaluation of the full-width at half maximum of the 200 diffraction peaks ($fwhm^{200}$), determined from the 360°-integrated Debye-Scherrer rings, allows to draw conclusions on the size of the coherently diffracting domains, which correlates with the grain size [33–36], and the density of structural defects such as dislocations that induce stresses of second and third order. In Fig. 5d, the $fwhm^{200}$ for ZrN and Ti<sub>0.33</sub>Al<sub>0.67</sub>N are shown with respect to the coating thickness. Both phases show a decreasing $fwhm^{200}$ with increasing coating thickness up to the surface-near region in block 9. For Ti<sub>0.33</sub>Al<sub>0.67</sub>N, only a minor $fwhm^{200}$ decrease with increasing coating thickness is observed. For blocks 7–9, the $fwhm^{200}$ error increases in the Ti<sub>0.33</sub>Al<sub>0.67</sub>N layers, which can be attributed to a decreasing relative volume of the Ti<sub>0.33</sub>Al<sub>0.67</sub>N layers compared to the increasing volume of the ZrN layers.

## 4. Discussion

In the SEM and EBSD images in Fig. 1b and c, as well as in the TEM ADF image in Fig. 2a it can be seen that grains grow through the interfaces between the ZrN and Ti<sub>0.33</sub>Al<sub>0.67</sub>N layers, showing the formation of heteroepitactic multilayers with (semi-)coherent interfaces. Furthermore, the texture alignment of ZrN and Ti<sub>0.33</sub>Al<sub>0.67</sub>N in Figs. 3b and 4b also corroborates coherency of the multilayers. The (100) fiber texture observed in the XRD pole figures (Fig. 3b) is prevalent throughout the whole coating thickness, as can be seen in the CSnanoXRD texture evaluation (Fig. 4b). This texture develops due to the combination of a low bias voltage and moderate deposition temperature, which favors (100) out-of-plane oriented grains [37,38]. The EBSD band contrast image (Fig. 1c) clearly shows that the grain size increases from the substrate towards the surface with increasing ZrN layer thickness, which is also reflected by a decreasing $fwhm^{200}$ (Fig. 5d). It has to be noted that also the strains of second and third order influence the $fwhm^{200}$, wherefore a correlation of the $fwhm^{200}$ with the grain size has to be taken with care [17]. An increasing grain size with increasing bilayer thickness in multilayer coatings was observed by other authors as well [3,4,39,40]. The lattice mismatch of ~9.2% between ZrN and Ti<sub>0.33</sub>Al<sub>0.67</sub>N can be overcome either by a strained interface or by misfit dislocations (interfacial defects) or a combination thereof. It is suggested that most grains grow (semi-)coherent, due to the isostructurality of the fcc-ZrN and the fcc-TiAlN [10]. The interfacial defects are assumed to lead to grain re-nucleation [37]. Thus, with the decreasing number of interfaces with increasing bilayer thickness also the number of interfacial defects decreases, leading to larger grains [3,37].

Xu et al. have shown, supported by density functional theory

calculations, that the level of coherency increases with the ZrN:TiAlN layer thickness ratio [5]. The driving force behind the formation of coherent interfaces is the minimization of interfacial energy. Usually, the coherency strain energy is high for a lattice mismatch of 9.2% and the formation of coherent ZrN/Ti<sub>0.33</sub>Al<sub>0.67</sub>N multilayers is thermodynamically not stable under equilibrium conditions [5]. However, due to the formation of dislocations at the interface and due to the nonequilibrium deposition process, this strain energy barrier can be overcome and locally coherent interfaces can be stabilized [5]. As the development of semi-coherent interfaces can be assumed in this coating, coherency strain/stress fields develop at the interface that reach several nm into the individual layers, which also influence the in-plane residual strain/stress state in the coating [15]. The main components contributing to the total residual stress are intrinsic ($\sigma_{intrinsic}$) and extrinsic ($\sigma_{extrinsic}$) stress [41]. The main contributions to $\sigma_{intrinsic}$ are ion irradiation-induced growth stress and the grain size [41]. The irradiation-induced stress develops due to the ion bombardment of the coating that generates defects during coating growth, leading to a volume increase of the lattice and thus to compressive residual stress [42–44]. The grain size contributes to $\sigma_{intrinsic}$ in a way that a decreasing grain size leads to an increase in the volume fraction of grain boundaries. Since the atoms in the grain boundary are weaker bonded and disordered compared to the atoms inside the grains, adatoms can more easily penetrate into the grain boundary, leading to an increase in the specific grain boundary volume that also increases the compressive residual stress in the grains [41,45]. One component of $\sigma_{extrinsic}$ is the thermal stress ($\sigma_{thermal}$) that develops during cooling down from the deposition temperature of 425 °C, due to differences in the coefficient of thermal expansion (CTE) between the individual coating layers and between the coating and the substrate material. This contribution is tensile, since the CTEs of ZrN and TiAlN are ~7.2 × 10<sup>-6</sup> K<sup>-1</sup> [46] and ~8.1 × 10<sup>-6</sup> K<sup>-1</sup> [9], respectively and thus higher than the one of the cemented carbide substrate (~5.7 × 10<sup>-6</sup> K<sup>-1</sup> [47]). The second relevant contribution of the $\sigma_{extrinsic}$ can be related to structural misfits at the interface, leading to coherency strain/stress ($\sigma_{coherency}$) [41,45]. Incoherent interfaces with a large number of misfit dislocations lead to low $\sigma_{coherency}$, whereas coherent interfaces lead to a high contribution of $\sigma_{coherency}$ to the total residual stress. The changes in the residual stress state along the cross-section (Fig. 5b) can be attributed to the coating architecture and accompanying changes in the microstructure. The changing bilayer thickness affects the absolute values of the respective stress contributions [48–50]. The divergence of the residual strain/stress between ZrN and Ti<sub>0.33</sub>Al<sub>0.67</sub>N in blocks 1–5 is assumed to be related to $\sigma_{coherency}$. As a result of the larger d-spacing of ZrN compared to Ti<sub>0.33</sub>Al<sub>0.67</sub>N, the ZrN layers are additionally stressed compressively and due to the low individual ZrN layer thickness of <24 nm the coherency stress cannot relax into the ZrN layer and the layers are dominated by this coherency stress. This leads to an increase in the compressive residual stress in the ZrN layers compared to the Ti<sub>0.33</sub>Al<sub>0.67</sub>N layers. As the Ti<sub>0.33</sub>Al<sub>0.67</sub>N individual layer thickness is constant, the $\sigma_{coherency}$ has the same influence on the measured residual strain and stress over the whole thickness. The in-plane residual stress is, in contrast to blocks 1–5, similar for the ZrN and Ti<sub>0.33</sub>Al<sub>0.67</sub>N layers for an individual ZrN layer thickness >24 nm (blocks 6–9), which is an indication that the residual stress state in this region mainly depends on the deposition conditions, e.g. $\sigma_{thermal}$ and irradiation-induced residual stress, and $\sigma_{coherency}$ only plays a minor role.

## 5. Conclusions

Within this work, a graded ZrN/Ti<sub>0.33</sub>Al<sub>0.67</sub>N multilayer coating with constant Ti<sub>0.33</sub>Al<sub>0.67</sub>N and stepwise increasing ZrN layer thickness was synthesized by cathodic arc evaporation, in order to study the influence of the individual layer thickness on the microstructure and strain as well as residual stress state. Microstructural investigations by electron backscatter diffraction and transmission electron microscopy revealed an increasing grain size with higher individual ZrN layer thickness and
(semi-)coherent growth of the layers. A (100) fiber texture over the whole coating thickness was observed for both, ZrN and Ti₀.₃₃Al₀.₆₇N phases which further corroborated the (semi-)coherent layer growth. Investigations of the residual stress state by cross-sectional X-ray nanodiffraction showed compressive stress in the range of -5 to -1 GPa for ZrN and -3.5 to -2 GPa for Ti₀.₃₃Al₀.₆₇N. Both phases show declining stresses with increasing ZrN layer thickness, which can mainly be explained by an increasing grain size and thus, a lower density of grain boundaries. Furthermore, ZrN exhibits higher stress than Ti₀.₃₃Al₀.₆₇N for ZrN layers <24 nm, but nearly identical stress for ZrN layers >24 nm. This effect can be attributed to dominating coherency stress for thinner ZrN layers. The present work contributes to the establishment of a fundamental understanding of the microstructure of a ZrN/Ti₀.₃₃Al₀.₆₇N multilayer coating and the effect of the bilayer thickness on the residual stress state of the coating.

CRediT authorship contribution statement

**Florian Frank:** Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Data curation, Writing – original draft, Visualization. **Michael Tkadletz:** Validation, Writing – review & editing, Supervision. **Christian Saringer:** Software, Validation, Writing – review & editing. **Christoph Czettl:** Resources, Writing – review & editing, Funding acquisition. **Markus Pohler:** Resources, Writing – review & editing. **Manfred Burghammer:** Investigation, Resources. **Juraj Todt:** Investigation, Writing – review & editing. **Jakub Zalesak:** Investigation, Writing – review & editing. **Jozef Keckes:** Resources, Writing – review & editing. **Nina Schalk:** Writing – review & editing, Supervision, Project administration, Funding acquisition.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability

Data will be made available on request.

Acknowledgement

The authors want to thank Bernhard Sartory and Dr. Jaroslav Wosik (Materials Center Leoben) for the SEM and EBSD investigations. The financial support by the Austrian Federal Ministry for Digital and Economic Affairs and the National Foundation for Research, Technology and Development is gratefully acknowledged. We acknowledge Czech-NanoLab Research Infrastructure supported by MEYS CR (LM2018110).

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