# Dislocation structure and microstrain evolution during spinodal decomposition of reactive magnetron sputtered heteroepitaxial c-(Ti0.37,Al0.63)N/c-TiN films grown on MgO(001) and (111) substrates

K. M. Calamba¹,²,³), J. F. Pierson², S. Bruyère²,2 A. L. Febvrier³, P. Eklund³, J. Barrirero¹,⁴, F. Mücklich⁴, R. Boyd¹, M. P. Johansson Jõesaar¹,⁵, and M. Odén¹

¹Nanostructured Materials, Department of Physics, Chemistry and Biology (IFM), Linköping University, Linköping SE-58183, Sweden

²Université de Lorraine, CNRS, IJL, F-54000 Nancy, France

³Thin Film Physics Division, Department of Physics, Chemistry and Biology (IFM), Linköping University, Linköping SE-58183, Sweden

⁴Functional Materials, Department of Materials Science, Saarland University, Saarbrucken DE-66123, Germany

⁵SECO Tools AB, Fagersta SE-73782, Sweden

a) Electronic mail: katherine.calamba@liu.se

## ABSTRACT

Heteroepitaxial c-(Ti0.37,Al0.63)N thin films were grown on MgO(001) and MgO(111) substrates using reactive magnetron sputtering. High resolution high-angle annular dark-field scanning transmission electron micrographs show coherency between the film and the substrate.

In the as-deposited state, x-ray diffraction reciprocal space maps show a strained epitaxial film. Corresponding geometric phase analysis (GPA) deformation maps show a high stress in the film. At elevated temperature (900 °C), the films decompose to form iso-structural coherent c-AlN- and c-TiN-rich domains, elongated along the elastically soft <100> directions. GPA analysis reveals that the c-TiN domains accommodate more dislocations than the c-AlN domains. This is because of the stronger directionality of the covalent bonds in c-AlN compared with c-TiN, making it more favorable for the dislocations to accumulate in c-TiN. The defect structure and strain generation in c-(Ti,Al)N during spinodal decomposition is affected by the chemical bonding state and elastic properties of the segregated domains.

## I. INTRODUCTION

Improved understanding of the microstructural evolution of metastable NaCl B1 structured c-(Ti,Al)N solid solutions is essential for optimizing their properties for high temperature applications.¹⁻³ The spinodal decomposition of c-(Ti,Al)N into isostructurally coherent c-TiN and metastable c-AlN rich domains at elevated temperatures⁴⁻⁷ is particularly attractive because it results in hardening and improved wear resistance.⁸⁻¹¹ It has previously been reported that metal composition, vacancy concentration, and grain size affect the decomposition behavior, and improvement of thermal and mechanical properties can be achieved by microstructure optimization.¹²⁻¹⁷ However, these studies are performed on polycrystalline materials for which investigations of the local strain evolution and details of the defect structure during decomposition are difficult. Instead, single crystal c-(Ti,Al)N films with a low level of impurities are required to obtain such information from the decomposed but still coherent microstructure. Theoretical studies have shown that the compositional dependent anisotropic elastic properties cause strain and associated strain energy, which affect the spinodal decomposition in c-(Ti,Al)N.¹⁸⁻²¹

The approach of these studies is based on the Cahn–Hilliard equation,²² where the solute concentration is used to describe the thermodynamic energies involved in phase separation. Additional strain effects generated by dislocations or other lattice defects are normally ignored. Recent studies on phase-field modeling of spinodal decomposition in alloys have accounted for both the formation and the dynamics of dislocations, revealing that dislocation stress field energetically and kinetically facilitates phase separation even without initial compositional fluctuation.²³,²⁴ Dislocation structure and strain evolution in c-(Ti,Al)N alloys could play an important role during spinodal decomposition because strains in the film are generated in the process. Thus, more information on the strain fields present in this ternary alloy during phase separation is important. The use of aberration-corrected transmission electron microscope (TEM) and scanning TEM (STEM) offers significant improvement in terms of strain mapping combining electron diffraction and geometric phase analysis (GPA).¹⁷,²⁵,²⁶ GPA is an image analysis method using a Fast Fourier transform algorithm to quantify the lattice displacements and strain field in crystals relative to a reference region.²⁷ GPA performed on high-resolution STEM images results in the best spatial resolution among recently developed strain mapping techniques.²⁸ In this study, GPA was performed on high-angle annular dark-field scanning transmission electron micrographs (HAADF-STEMs) to determine the local strain tensor in (Ti,Al)N during spinodal decomposition while gaining compositional information.

Single crystal c-(Ti0.37,Al0.63)N films with a c-TiN buffer layer were grown by reactive magnetron sputtering on MgO substrates with a cube-on-cube epitaxial relationship on MgO(001) and (111) substrates with the orientational relationships (–100) [001]c-(Ti0.37,Al0.63)N/c-TiN||(–100)[001]MgO and (–11–1)[011] c-(Ti0.37,Al0.63)N/c-TiN||(–
11-1)[011]MgO. The films were subsequently annealed at 900 °C to investigate the strain distribution caused by coherent domains formed during spinodal decomposition of the c-(Ti,Al)N film. The crystal quality of the films was examined by high-resolution TEM/scanning TEM and XRD reciprocal space maps.

GPA strain maps showing symmetric strain tensor components, i.e., $\varepsilon_{xx}$, $\varepsilon_{yy}$, and $\varepsilon_{xy}$, were obtained. At elevated temperatures, the film segregated to form elongated c-TiN and c-AlN rich domains, wherein strain reduction is greater in c-AlN. The defect structure of (Ti,Al)N during spinodal decomposition is discussed in terms of elastic properties and chemical bonding characteristics of the domains.

## II. MATERIAL AND METHODS

Epitaxial c-(Ti0.37,Al0.63)N were grown onto magnesium oxide (MgO) substrates by UHV DC magnetron sputter deposition. Two orientations, (MgO)(001) and (111) wafers (>99.95% purity), with a size of 10 × 10mm2 were used as substrates. MgO has been used due to its small lattice mismatch of less than 1% to that of c-Ti1-xAlxN (0 ≤ x)₂₉,₃₀ Ti (>99.9% purity) and Ti0.35Al0.65 (>99.9% purity) targets with a diameter of 50mm were used for the deposition of TiN buffer layer and (Ti,Al)N film, respectively. Additionally, the coefficients of thermal expansion of these materials are similar (i.e., $\alpha_{MgO} \approx 14 \times 10^{-6}/^{\circ}\text{C}$, $\alpha_{TiN} \approx 9.4 \times 10^{-6}/^{\circ}\text{C}$, and $\alpha_{(Ti,Al)N} \approx 7.5 \times 10^{-6}/^{\circ}\text{C}$)₃₁,₃₂ making MgO a suitable substrate for epitaxial growth for many transition metal nitrides.³³⁻³⁷ The thermal strains due to cooling from the deposition temperature are 0.3% for TiN and 0.4% for (Ti,Al)N.

Prior to the deposition, the substrates were subjected to wet and dry cleaning processes comprising different sonifications in Hellmanex®II, acetone, and ethanol solvents and an in situ annealing at 900 °C for 1 h.³⁸ An Ar + N₂ gas mixture was used to synthesize the thin films, in which the argon flow rate was set to 30 sccm and the nitrogen flow rate was set to 10 sccm, resulting in a total gas pressure of 0.3 Pa. This reactive sputtering process was operated inside the hysteresis region (transition mode). The substrates were kept at 700 °C during the deposition. c-TiN buffer layers were first grown to a thickness of 15 nm before depositing the c-(Ti0.37,Al0.63)N films to a thickness of 150 nm. Thin TiN layers were deposited in order to prevent Al in (Ti,Al)N films from diffusing to the MgO substrate, i.e., Al and Mg are known to chemically react to form a spinel at high temperature.³⁹

All depositions were made at a constant current of 0.1 A. Heat treatments of the as-deposited films were conducted by post-deposition isothermal annealing using a tube furnace in 30 sccm of argon flow. The samples were heated at a rate of 20 °C/min up to a maximum temperature of either 850 °C and 900 °C and held for 120 min and then slowly cooled to room temperature. X-ray diffraction θ-2θ scans, azimuthal scans, rocking curves, and reciprocal space maps (RSMs) of (Ti,Al)N films were acquired using a PANalytical Empyrean diffractometer with Cu Kα radiation for the phase structure and growth orientation analysis. Symmetric and asymmetric RSMs were recorded around MgO 111 and MgO 113, respectively using a four-axis goniometer and a primary optics consisting of a parabolic graded multilayer mirror, collimator, and a channel-cut 2-bounce Ge(220) monochromator. The equations used for computation of the reciprocal lattice vectors are $Q_x = 2\pi r_E[\cos \omega - \cos(2\theta - \omega)]$ and $Q_z = 2\pi r_E[\sin \omega + \sin(2\theta - \omega)]$, where ω and θ are the instrumental coordinates and $r_E$ is Ewald's sphere radius ($1/λ = 1/0.1541$ nm).⁴⁰ Poisson's ratio used to measure the lattice constants is $v = 0.18$, the elastic modulus (E) used to determine the film stress is 490 GPa, and the elastic stiffness constants used to compute the Zener anisotropy (A) and shear modulus (G₀) are $C_{11} = 445$, $C_{12} = 161$, and $C_{44} = 223$.¹⁹

Cross-sectional transmission electron microscopy (TEM) lamella with approximately 50 nm uniform thickness were prepared using an in situ lift-out technique in a focused ion beam (FIB)-scanning electron microscope (SEM) dual beam system (Helios Nanolab 600i). A FEI EasyLift EX system fitted with a W needle was used as the micromanipulator. Microstructural characterizations of the thin films were performed using a JEOL ACCEL ARM 200F-Cold FEG equipped with energy dispersive x-ray (EDX) spectrometer (JEOL Centurio EDS 1sr) for chemical analyses. The electron microscope was operated at an acceleration voltage of 200 kV. The specimen was kept in the equipment for few hours before the acquisition of the STEM images in order to sufficiently stabilize and minimize the sample drift. The electron microscopy data were processed using Gatan's Digital Micrograph with an added geometric phase analysis (GPA) script developed by Koch and co-workers.⁴¹ GPA of high-angle annular dark-field imaging (HAADF) STEM images was used to map the tensile and compressive strain at the atomic scale. Samples for atom probe tomography (APT) were prepared in a dual-beam FIB/SEM workstation (Helios NanoLab 600™, FEI Company, USA). Prior to FIB irradiation, the thin films were coated with an approximately 200 nm thick Ti sacrificial layer. Then, an electron beam induced Pt layer was added to protect from gallium implantation. After lift out and thinning of the samples, a low energy milling at 2 kV was performed to minimize Ga induced damage.⁴² APT was carried out in a laser mode with a LEAP™ 3000X HR (CAMECA) at a pulse frequency of 200 kHz, a specimen temperature of 60 K, pressure lower than $1 \times 10^{-10}$ Torr ($1.33 \times 10^{-8}$ Pa), and a laser pulse energy of 0.5 nJ. The evaporation rate of the specimen was set to 5 atoms per 1000 pulses. Datasets were reconstructed and analysed with the IVAS™ 3.6.14 software (CAMECA). To obtain the bulk composition of the specimens, a peak decomposition analysis routine available in IVAS was used to correct the nitrogen content due to a peak overlap in the mass-to-charge spectrum between N⁺ and N₂⁺.
### III. RESULTS

The chemical composition values of the as-deposited $c-(Ti_{1-x}Al_x)N_y$ film on MgO(111) obtained by the weighted average of 3 APT specimens are $Ti = 18.4 \pm 0.6$, $Al = 31.9 \pm 0.7$, and $N = 48.2 \pm 1$ at. %. APT specimens were taken from different positions along the film and the error reported depicts the intrinsic composition fluctuation in the as-deposited state which is not higher than 1 at. % for any of the elements. The film contains impurity elements such as O and C with a total content of 1.5 at. %. The film has $x = Al/(Al + Ti)$ and $y = N/(Al + Ti)$ values of $x = 0.63$ and $y = 0.96$, respectively, and can thus be considered stoichiometric.

Figure 1 shows transmission electron microscopy (TEM) micrographs including selected area electron diffraction (SAED) and Fast Fourier Transform (FFT) patterns of the as-deposited $c-(Ti_{0.37}Al_{0.63})N$ films on MgO(001) and (111). Results show that $c-(Ti_{0.37}Al_{0.63})N$ (001) first grows epitaxial on MgO(001) to a critical thickness ranging between 30 and 50 nm [Fig. 1(a)]. Beyond the critical thickness, growth of polycrystalline $c-(Ti_{0.37}Al_{0.63})N$ is initiated. The SAED of the sample in Fig. 1(b) shows a combination of well-defined spots and rings, which indicates the presence of large grains oriented with an epitaxial relationship to the substrate and smaller grains randomly oriented. Combining the above with high resolution TEM (HRTEM) data and the corresponding FFT pattern in Figs. 1(d) and 1(e), we conclude epitaxial growth of $c-(Ti_{0.37}Al_{0.63})N/c-TiN$ films on MgO(001) with a cube-on-cube epitaxial relationship, i.e., ($-100$)[001]$c-(Ti_{0.37}Al_{0.63})N/c-TiN$||($-100$)[001] MgO. In analogy, TEM, SAED, HRTEM, and FFT results of the $c-(Ti_{0.37}Al_{0.63})N/c-TiN$ grown on MgO(111) [Figs. 1(f)–1(j)] demonstrate a growth with an epitaxial relationship ($-11-1$)[011] $c-(Ti_{0.37}Al_{0.63})N/c-TiN$||($-11-1$)[011]MgO. The epitaxial growth of $c-(Ti,Al)N$(111) is sustained all through the film thickness.

<figure><img src="image_1.png" /><figcaption>FIG. 1. (a) TEM, (b) SAED, [(c) and (d)] HRTEM, (e) FFT images of as-deposited $c-(Ti_{0.37}Al_{0.63})N/c-TiN$ film on MgO(001), (f) TEM, (g) SAED, [(h) and (i)] HRTEM, and (j) FFT images of (Ti,Al)N on MgO(111). The size of the sample area used for SAED is 100 nm.</figcaption></figure>

Figure 2 shows high resolution XRD reciprocal space maps (RSMs) of the as-deposited and annealed $c-Ti_{0.37}Al_{0.63})N/c-TiN$ films on MgO(111) as the function of the reciprocal lattice vector in the film growth direction ($q_x$) and parallel to its surface ($q_y$). The shape and distribution of the peaks in these maps may reveal information of crystal tilt as well as in-plane and out-of-plane strain, mismatch, and relaxation. In addition, a two-dimensional RSM covers a relatively larger area compared to TEM due to its larger probe size and it statistically represents the nitride film. However, its large probe size also leads to difficulty in resolving the reciprocal lattice point of epitaxial $c-(Ti_{0.37}Al_{0.63})N$(001) film on the MgO(001) substrate because of the low epitaxial film thickness. The RSM of $c-(Ti_{0.37}Al_{0.63})N/c-TiN$ films on MgO(001) has only one distinct reciprocal lattice point with slight broadening to the top, which is
caused by the relaxation of the epitaxial c-(Ti0.37,Al0.63)N/TiN layers (figure not shown). Thus, the RSM analysis here is limited to the thicker epitaxial films deposited on MgO(111). Figures 2(a) and 2(d) show symmetric RSMs for the 111 plane of the c-(Ti0.37, Al0.63)N/TiN films and the MgO substrate in as-deposited and annealed state, respectively. Larger qz for the films indicates a smaller interplanar d-spacing for the films than the substrate in the out-of-plane direction. The 360° azimuthal scans over 002 reflection [Figs. 2(b) and 2(e)] show the characteristic feature of a cubic system oriented along the [111] direction.43 The films have distinct diffraction spots from which lattice constants can be measured. The c (out-of-plane, a⊥) and a (in-plane, a‖) unit-cell parameters are obtained using the equations c = d⊥ and a = [1(h2 + k2)/(1/d2 hkl·l2/c2)]1/2, where d⊥ is measured from the perpendicular component of the Qhkl reciprocal lattice vector, l is the length of the direction vector, and dhkl is the d-spacing of the (111) plane.29,44 The c and a lattice parameters of as-deposited c-(Ti0.37,Al0.63)N are 4.12 Å and 4.30 Å, respectively. The c and a lattice parameters of the annealed film are 4.13 Å and 4.31 Å, respectively. The relaxed lattice constant is obtained using the equation a0 = c(1 - [2v(c - a)/a(1 + v)]),40 where v is obtained from ab initio calculation.19 The a0 of both as-deposited and annealed (Ti,Al)N films is 4.15 Å. The a0 of the MgO substrate and TiN buffer layer are 4.21 Å45 and TiN = 4.24 Å,30 resulting in a lattice misfit with respect to the film of 1.43% and 2.12%, respectively. A small variation of the d-spacing along the growth direction is observed in both films, as denoted by the broadening along the 2θ-ω direction in comparison to the ω direction (see Fig. 2). The c-(Ti,Al)N material is elastically anisotropic; however, a (111)-oriented film has an in-plane isotropy. Thus, Eqs. (1) and (2) can be used to calculate the in-plane strain (εa) and stress (σf), respectively,44

$$ \epsilon_a = - \frac{1 - \nu}{2\nu} \left( \frac{c - a_0}{a_0} \right), \qquad (1) $$

$$ \sigma_f = - \frac{E}{2\nu} \left( \frac{c - a_0}{a_0} \right), \qquad (2) $$

where v is Poisson's ratio and E is the elastic modulus along the [111] direction.19 Table I shows the strain, stress, and coherence lengths of the epitaxial films along a and c directions. The coherence lengths along the a (ξa) and c (ξc) directions are calculated using Eqs. (3) and (4), respectively,40

$$ \xi_a = \frac{\frac{\lambda}{2\Gamma_\omega \sin \theta'}}{\Gamma_\omega}, \qquad (3) $$

$$ \xi_c = \frac{\lambda}{\Gamma_{2\theta} \cos \theta'}, \qquad (4) $$

where λ is the x-ray wavelength and Γ is the full width at half maximum (FWHM) intensity. The FWHM values of the c-(Ti0.37, Al0.63)N 111 peak of the as-deposited film are Γ2θ = 0.0055 rad and Γω = 0.0027 rad, obtained from the XRD 2θ-ω scans and ω-rocking curves, respectively. The FWHM of the c-(Ti0.37, Al0.63)N 111 peak of the annealed film are Γ2θ = 0.0057 rad and Γω = 0.0029 rad. Asymmetric RSMs [Figs. 2(c) and 2(f)] show a horizontal shifting of the layer peak to the left of the substrate peak, which indicates that the film is partially relaxed during the deposition process.46 The FWHM of the 113 peak in the asymmetric Q scans is directly related to the lateral uniformity of the epitaxial layer and the amount of mosaic spread present.47 The average value of the separation of the lateral irregularities is referred to as the lateral correlation length. The range of the microscopic tilt in the layer due to its fine mosaic structure is called the mosaic spread. Table II shows the measurement of FWHM, correlation length, and mosaic spread. The annealed film has lower lateral correlation, broader FWHM, and higher mosaism as compared to the as-deposited. This is attributed to the chemical fluctuations occurring during spinodal decomposition leading to a less perfect crystal.
<figure><img src="image_2.png" /><figcaption>FIG. 2. (a) Symmetric RSM, (b) azimuthal XRD on (002) reflection, (c) asymmetric RSM of as-deposited, (d) symmetric RSM, (e) azimuthal XRD on (002) reflection, and (f) asymmetric RSM of annealed c-(Ti<sub>0.37</sub>Al<sub>0.63</sub>)N/c-TiN films on MgO(111).</figcaption></figure>

<table><caption>TABLE I. Calculated strain, stress, and coherence length of the as-deposited and annealed (Ti,Al)N(111) films.</caption><thead><tr><th>Quantity</th><th>As-deposited</th><th>Annealed (900 °C)</th></tr></thead><tbody><tr><td>In-plane strain, ε<sub>a</sub></td><td>0.0109</td><td>0.0119</td></tr><tr><td>In-plane film stress, σ<sub>f</sub></td><td>6.51 GPa</td><td>7.08 GPa</td></tr><tr><td>In-plane coherence length, ξ<sub>||</sub></td><td>87.2 nm</td><td>82.2 nm</td></tr><tr><td>Out-of-plane coherence length, ξ<sub>⊥</sub></td><td>29.8 nm</td><td>28.6 nm</td></tr></tbody></table>

<table><caption>TABLE II. Measured correlation length, FWHM, and mosaic spread of the as-deposited and annealed (Ti,Al)N(111) films. Reciprocal lattice units (rlu) = Å⁻¹.</caption><thead><tr><th>Quantity</th><th>As-deposited</th><th>Annealed (900 °C)</th></tr></thead><tbody><tr><td>FWHM</td><td>0.018 rlu</td><td>0.036 rlu</td></tr><tr><td>Lateral correlation length</td><td>68 nm</td><td>35 nm</td></tr><tr><td>Mosaic spread</td><td>2.5°</td><td>5.0°</td></tr></tbody></table>

The c-(Ti<sub>0.37</sub>Al<sub>0.63</sub>)N/c-TiN(001) and c-(Ti<sub>0.37</sub>Al<sub>0.63</sub>)N/c-TiN (111) films exhibit a homogeneous composition with no indication of elemental segregation in their as-deposited states. This is shown in the STEM/STEM-EDX images in Figs. 3 and 4 for c-(Ti,Al)N (001) and c-(Ti,Al)N(111), respectively. FFT insets are obtained from the STEM images [Figs. 3(a), 3(e), 4(a), and 4(e)] on either the [001] or [011] zone axis (marked). The reciprocal −200 lattice point, which is separated to two distinct spots in Fig. 3(e) is attributed to Moiré fringes observed in the STEM image of the annealed c-(Ti<sub>0.37</sub>Al<sub>0.63</sub>)N (001) film. The long streaks normal to the edges of the mask in the FFTs of the HRSTEM images are
artifacts in the Fourier-filtering process.48 The c-(Ti0.37,Al0.63)N films annealed at 850 °C have a homogeneous composition similar to the as-deposited state (figures not shown). At 900 °C, the formation of coherent c-TiN and c-AlN rich domains is observed in the STEM-EDX micrographs shown in Figs. 3(f)–3(h) and 4(f)–4(h), respectively. This is consistent with the expected spinodal decomposed state at an elevated temperature.4,5 The shape of the domains are elongated along <001> directions in both the annealed c-(Ti,Al)N(001) and c-(Ti,Al)N(111) films as shown in Figs. 3(f)–3(h) and 4(f)–4(h), similar to what have been seen after annealing of arc deposited polycrystalline c-(Ti,Al)N films.6

<figure><img src="image_3.png" /><figcaption>FIG. 3. (a) STEM with FFT inset, [(b)–(d)] STEM-EDX: Ti (red), Al (green) of as-deposited c-(Ti0.37,Al0.63)N(001) film, (e) STEM with the FFT inset, and [(f)–(h)] STEM-EDX: Ti (red), Al (green) of the film annealed at 900 °C.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>FIG. 4. (a) STEM with the FFT inset, [(b)–(d)] STEM-EDX: Ti (red), Al (green) of as-deposited c-(Ti0.37,Al0.63)N(111) film, (e) STEM with the FFT inset, and [(f)–(h)] STEM-EDX: Ti (red), Al (green) of the film annealed at 900 °C.</figcaption></figure>

Figures 5(a) and 5(d) show high resolution HAADF-STEM micrographs over the interface region of the as-deposited and annealed c-(Ti0.37,Al0.63)N/TiN(001) films. For such images, contrast is directly proportional to the atomic number or composition, where bright regions are attributed to Ti- and dark regions to Al-rich domains. In agreement with the HRTEM results, coherent c-(Ti0.37,Al0.63)N/c-TiN interfaces are observed also by STEM, both in as-deposited and annealed states [Figs. 5(a) and 5(d)]. In addition, Figs. 5(b) and 5(c) show the $\varepsilon_{xx}$ and $\varepsilon_{yy}$ (x along the [100]
direction and y along the [001] direction) components of the strain tensor, respectively. The generated histograms are from the entire area in the strain map, which includes the c-TiN buffer layer. The strain maps are deduced by GPA from the STEM image [Fig. 5(a)] and using the c-TiN buffer layer as the reference region because it contains almost no strain. A strain field is present across the entire film in the as-deposited state. After annealing, the c-(Ti0.37,Al0.63)N film decomposes into coherent c-TiN and c-AlN rich domains [Fig. 5(d)]. The corresponding deformation maps [Figs. 5(e) and 5(f)] show that c-TiN domains contain more dislocations as compared to c-AlN, i.e., the locations with sharp contrast in the GPA strain maps correspond to the dislocations present in the sample. This was established by direct comparison of the location of dislocations and the strain concentrations. The locations of the dislocations were determined by FFT-filtering of the HR-HAADF-STEM images.⁴⁹

<figure><img src="image_5.png" /><figcaption>FIG. 5. (a) HAADF-STEM of as-deposited c-(Ti0.37,Al0.63)N/c-TiN(001) with the FFT inset and the corresponding deformation maps for (b) $\varepsilon_{xx}$ and (c) $\varepsilon_{yy}$ directions, and (d) HAADF-STEM of annealed c-(Ti0.37,Al0.63)N/c-TiN (001) with the FFT inset and the corresponding deformation maps for (e) $\varepsilon_{xx}$ and (f) $\varepsilon_{yy}$ directions. The inset histograms represent the distribution of strain values in each map.</figcaption></figure>

Figure 6 shows HAADF-STEM micrographs and deformation maps over the interface region of the as-deposited and annealed c-(Ti0.37,Al0.63)N/c-TiN(111) films. Overall, this orientation shows a similar trend with coherent interfaces [Figs. 5(a) and 5(d)] and strain maps [Figs. 6(b), 6(c), 6(e), and 6(f)] as the c-(Ti0.37,Al0.63)N/c-TiN(001) films. The strains are mostly concentrated in c-TiN rich domains, indicating that strain reduction is dependent on the chemical environment. Due to the difference in the unit cell volume, the c-TiN-rich domain is mostly under compressive strain while a tensile strain is present in the c-AlN domain. The streaks in the FFTs of the STEM images are more dominant in the [001] direction because the acquisition of STEM images is through rastering of the beam across the sample in the perpendicular direction. GPA is based on the FFTs of the acquired images and it is observed that there is more contrast in the map of the strain tensor $\varepsilon_{yy}$ than $\varepsilon_{xx}$ because of this artifact during rastering. This is a systematic error, wherein a contrast variation appearing as thick horizontal lines is observed [Figs. 5(c), 5(f), 6(c), and 6(f)]. Nevertheless, both $\varepsilon_{xx}$ and $\varepsilon_{yy}$ show a similar trend that the buffer layer has the minimum strain and that the dislocations is mainly inside the c-TiN rich domains.

Higher magnification HAADF-STEM micrographs and the corresponding shear component ($\varepsilon_{xy}$) of the strain tensor (in the xy-plane) of the spinodal decomposed c-(Ti0.37,Al0.63)N(001) and c-(Ti0.37,Al0.63)N(111) films are shown in Fig. 7. The GPA strain maps in Figs. 7(b) and 7(h) demonstrate some shear strain near the interface of the segregated domains (indicated by white arrows). Starting from the FFT of the STEM images, masks were applied on 0-20 and 0-20 spots of c-(Ti,Al)N(001) [Fig. 7(d)] and on 1-11 and 11-1 spots of c-(Ti,Al)N(111) [Fig. 7(g)]. Then, an inverse FFT algorithm was performed to reconstruct a filtered real space images as shown in Figs. 7(c) and 7(i). Insets 1 and 2 are different regions showing the presence of defects such as lattice distortions and dislocations in the masked planes. The comparison reveals that the local microstrain concentrations in the GPA maps are directly correlated to the presence of dislocations and the strain fields around the dislocations. The shear strain maps also show that strain field around the dislocations in the c-(Ti0.37,Al0.63)N(111) film is larger and wider than in the c-(Ti0.37,Al0.63)N(100) film.
<figure><img src="image_6.png" /><figcaption>FIG. 6. (a) HAADF-STEM of as-deposited c-(Ti0.37,Al0.63)N/c-TiN(111) with the FFT inset and the corresponding deformation maps for (b) Exx and (c) Eyy directions, and (d) HAADF-STEM of annealed c-(Ti0.37,Al0.63)N/c-TiN(111) with FFT inset the corresponding deformation maps for (e) Exx and (f) Eyy directions. The inset histograms represent the distribution of strain values in each map.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>FIG. 7. High resolution HAADF-STEM of spinodally decomposed (a) c-(Ti0.37,Al0.63)N(001) and (g) c-(Ti0.37,Al0.63)N(111) films, their corresponding [(b) and (h)] experimental shear component Exy, and [(c) and (i)] reconstructed FFT -1 images of the masked planes in the [(d) and (j)] FFT patterns. [(e), (f), (k), and (l)] Insets 1 and 2 are magnifications of crystal defects in c-(Ti0.37,Al0.63)N.</figcaption></figure>

#### IV. DISCUSSION

Epitaxial growth requires sufficient adatom surface mobility for rearrangements on the growth surface such that renucleation is avoided.50 Using high substrate temperature during sputter deposition is a route to attain good epitaxy of the nitride film (i.e., film density close to the bulk value with high crystal coherence length) because it promotes surface diffusion and agglomeration of the impinging adatoms.51,52 The use of MgO with a close match in lattice parameter to the film is needed to obtain epitaxial growth because the crystal structure of a substrate affects the nucleation kinetics.53,54 In this study, c-(Ti0.37,Al0.63)N/c-TiN(001) and c-(Ti0.37,Al0.63)N/c-TiN(111) films were
simultaneously grown at 700 °C using MgO(001) and MgO(111) substrates, respectively (i.e., all the deposition conditions are the same except the substrate orientation). Single crystal c-(Ti0.37,Al0.63)N(001) is only achieved in the first 30-50 nm while c-(Ti0.37,Al0.63)N(111) is sustained at large thickness. The growth orientation of transition metal nitrides is governed by growth kinetics and conditions leading to the lowest overall Gibbs free energy of the film.53,55 Strain and surface energies contribute to the overall free energy, wherein strain energy is directly proportional to the film thickness (H<sub>strain</sub>/VEε<sub>2</sub>, where E is the elastic modulus, ε is the strain, and V is the volume) while surface energy is independent of thickness.56 Sangiovanni et al.57 have shown in a molecular dynamic study on transition metal nitrides that incoming adatoms have higher diffusivity on fcc(100) planes than on fcc(111) of the same material at all temperatures. High-diffusivity denotes that the average residence time of surface atoms is low and the mean-free path is large, which would promote epitaxial growth. Instead, it is likely the contribution of the elastic energy to the overall Gibbs free energy of the film that causes a growth transition of the c-(Ti0.37,Al0.63)N(001) film when reaching a certain thickness. The measured in-plane strain of the c-(Ti0.37, Al0.63)N(111) by XRD is low (0.11%), which is consistent with the in-plane strain (ε<sub>xx</sub>) recorded by GPA (Fig. 5) for the as-deposited c-(Ti0.37,Al0.63)N(111) film, and distinctly lower than ε<sub>xx</sub> of the c-(Ti0.37,Al0.63)N(001) film. All involved materials (MgO, TiN, and TiAlN) have cubic symmetry and their coefficients of thermal expansion are isotropic, i.e., the induced thermal strain during cooling down from the deposition temperature does not affect the strain difference between the two samples. Hence, a higher strain energy is accumulating in the c-(Ti0.37,Al0.63)N(001) film during growth compared to the c-(Ti0.37,Al0.63)N(111) film that causes the break-down of the epitaxial growth mode. The result is the formation of a polycrystalline film after a certain thickness when growing on MgO(100).

The presence of a biaxial strain state causes in-plane expansion and out-of-plane compression of the c-(Ti0.37,Al0.63)N lattice parameter in the as-deposited state (Table I). This strain occurs because of the differences in the lattice parameters and thermal expansion coefficients between the nitride films and MgO substrate. RSM reveals that the film has a minimal variation of d-spacing along the growth direction (out-of-plane). The broadening that occurs along the ω-direction (in-plane) of the symmetric and asymmetric scans signifies the occurrence of induced mosaic tilts and twists caused by dislocations.46 The presence of dislocations in the as-deposited films is confirmed using GPA as indicated by the sharp contrast of the image in the deformation maps. These are likely threading dislocations that are formed during growth.50,58

Upon annealing, the c-(Ti0.37,Al0.63)N films decompose into iso-structural and coherent c-TiN and c-AlN domains. These domains have elongated shape because the material is elastically anisotropic.19 The Zener anisotropy, A = 2C44/(C11-C12) of this cubic material is 1.57, which is greater than 1. Thus, domains elongate along the elastically soft <100> directions.59 The observed strain changes during decomposition are caused by the lattice mismatch between c-TiN and c-AlN domains and some of the strain is relieved by the formation of misfit dislocations. For cubic materials, the elastic stiffness coefficients and shear moduli are directionally dependent.60 Ab initio calculations show that c-TiN is stiffer than c-AlN along <100> implying stronger chemical bonds in c-TiN than c-AlN.21 However, the covalent chemical bonds in c-AlN have a higher degree of directionality compared to c-TiN.19 Our GPA analysis reveals that the c-TiN domains are more frequently populated with dislocations than c-AlN domains, i.e., misfit dislocations aggregate in c-TiN or in the chemical gradients next to c-TiN domains. This suggests that the directionality of the chemical bonding has greater effect than the bond strength on the dislocation structure. The primary slip system of TiN is [110] <1-10> for mechanically induced dislocations,61 while it is yet to be determined for (Ti,Al)N. The generation of dislocations during spinodal decomposition is, as mentioned above, associated with misfit strain that occurs between Al and Ti-rich domains. Such misfit dislocations are not necessarily the same as the ones caused by mechanical deformation. Hence, different types of dislocations may be present.

The misfit dislocations are expected to appear where they effectively relieve elastic strain energy, and since the domains are coherent, separated with a chemical gradient, and elongated along <100> directions, such location would be the chemical gradient and their Burger's vectors should collectively cause lattice displacements along <100> directions. The data presented in this paper support aggregation of dislocations in the chemical gradients, while their Burger's vectors could not be conclusively determined.

The elastic shear moduli on c-(Ti0.37,Al0.63)N(001) and c-(Ti0.37,Al0.63)N(111) are G'001 = c44 = 223 GPa and G'111 = (3/(1+2α))c44 = 162 GPa, respectively.60 The higher shear strain observed in the deformation maps on (111) planes than on (100) planes is attributed to its lower shear modulus which also causes a wider shear strain field around the dislocations when viewing the strain by (111) compared to (100) planes.

Theoretical and experimental studies on the (Ti1-x,Alx)N_y system show that the kinetics of decomposition is highly dependent on chemical composition,21,62 presence of surfaces or interfaces,63,64 and point defects (e.g., N vacancies, metal vacancies, interstitials).13,14,65,66 In this study, it is expected that the (Ti0.37,Al0.63)N film has an earlier onset of spinodal decomposition than (Ti1-x,Alx)N_y films with other x compositions because this material system has an asymmetric free energy curve, which peaks at approximately x = 0.65.3 The polycrystalline Ti0.34Al0.66N film deposited by cathodic arc deposition shows an onset of decomposition at 817 °C,63 while the single crystal (Ti0.37,Al0.63)N film has not yet decomposed when annealed at 850 °C and the segregation of the domains is only observed at 900 °C. The lower thermal stability of the polycrystalline film than the single crystal film with a similar Al-content is attributed to its large number of internal interfaces such as grain and column boundaries that affect initiation of decomposition by surface-directed spinodal decomposition (SDSD). The tendency for decomposition is enhanced by SDSD because
the internal surfaces result in a chemical potential gradient that provides a preferential direction for uphill
diffusion.⁶⁷,⁶⁸ The film has a nitrogen to metal ratio of y ≈ 1; thus, the effects of N and metal vacancies on its thermal
stability are expected to be small.¹²⁻¹⁴,¹⁷

The spinodal decomposition of alloys quenched in the metastable region of the phase diagram is accelerated in the presence of dislocation stress field.²³ Thus, an interplay between dislocations and phase separation is expected. Although a direct link between the performed local strain analysis and the observed macroscopic age hardening behavior of (Ti,Al)N is still an open question, this study points out the role of the chemical nature and anisotropic elastic properties of the segregated domains in the understanding of the local strain state of the material.

V. CONCLUSIONS

Heteroepitaxial c-(Ti0.37,Al0.63)N/c-TiN thin films were grown on MgO(001) and (111) substrates. In the as-deposited state, high resolution HAADF-STEM micrographs show coherency between the films and the substrate. By RSM, a strain field is observed across the entire film and the corresponding GPA maps reveal a high stress field, attributed to plastic deformation and condensation of selfinterstitials and vacancies during growth. At elevated temperature, a clear segregation of c-AlN- and c-TiN rich domains is observed, with strain mostly accommodated near the domain interfaces as well as inside c-TiN rich domains. Further, the c-AlN rich domains contain less crystal defects, e.g., lattice distortions and edge dislocations, because the dominant component of its chemical bonding is strongly covalent. This suggests that the type of chemical bonding of the domains is a controlling factor for the dislocation structure and strain generation in c-(Ti,Al)N during spinodal decomposition.

ACKNOWLEDGMENTS

The work was supported by the European Union's Erasmus Mundus doctoral program in Materials Science and Engineering (DocMASE), the Swedish Research Council (Grant No. 621-2012-4401), the Swedish government strategic research area grant AFM-SFO MatLiU (No. 2009-00971), and VINNOVA (FunMat-II project Grant No. 2016-05156 and M-ERA.net project MC2 Grant No. 2013-02355). The Atom Probe was financed by the German Research Foundation (DFG) and the Federal State Government of Saarland, Germany (INST 256/298-1 FUGG). Per Eklund also acknowledges the Knut and Alice Wallenberg foundation through the Wallenberg Academy Fellow program. The authors thank Michelle Marie S. Villamayor for her assistance with reciprocal space map measurements, Sylvie Migot for the TEM sample preparation, and Jaafar Ghanbaja for the acquisition of TEM images.

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