High temperature phase decomposition in TixZryAlzN

Through a combination of theoretical and experimental observations we study the high temperature decomposition behavior of c-(TixZryAlzN) alloys. We show that for most concentrations the high forma ...


INTRODUCTION
The development of new hard coating materials for industrial machining tool inserts have high demands on performance properties, not only hardness but also lifetime and improved thermal stability.One way to improve such properties is to take advantage of the formation of nanoscale structures consisting of stable or metastable phases.2][3][4][5][6][7] However, additional heating, around 900 • C, will deteriorate the material properties when the AlN changes its structure from cubic to wurtzite. 80][21][22] However, due to a very strong tendency towards phase separation between ZrN and AlN a process similar to what was seen in (TiCrAl)N is unlikely to play a major role in this system, instead some other decomposition trends should be expected.Chen et al. 19 showed that alloying Zr into bulk (TiAl)N promoted the cubic phases and retarded formation of the detrimental wurtzite AlN phases.As a result it was seen that these kind of alloys were able to maintain high hardness, up to ∼40 GPa, at temperatures as high as 1100 • C. Holec et al. 21carried out calculations to determine the formation energy over the whole compositional range of (TiZrAl)N alloys and showed high tendency towards decomposition throughout the whole composition range.However, in both cases their conclusions on phase stability and spinodal decomposition are drawn solely on the values of the formation energy at a given composition at 0 K.Here we will show that in addressing the decomposition trends of thermodynamically unstable alloys it is also important to take into account the thermodynamic conditions for the spinodal decomposition.
We apply both theoretical first-principle calculations and experimental studies to determine high-temperature decomposition pathways in ternary (TiZrAl)N alloys as well as potentially stable and metastable phases in this system.We perform first principle calculations to determine the total energy for different compositions of (Ti x Zr y Al z )N.In addition to calculating the formation energy we determine spinodal decomposition trends by looking at the second derivative of the formation energy as the formal condition of such.We also consider the effect of temperature through configurational entropy on the formation energy, vibrational contributions are not considered due to the difficulty in calculating such for disordered alloys.Based on this we predict the formation of a stable high Zr-content (TiZr)N phase at elevated temperatures along with generally strong separation tendencies between Zr and Al due to a very high and positive formation energy.We also predict that a high Zr content (TiZrAl)N phase is expected to resist a process of spinodal decomposition.Experimental studies on arc evaporated (TiZrAl)N coatings confirm that the decomposition is delayed when the Zr-content is increased in the coating.

COMPUTATIONAL METHODS
In this work we make use of a multicomponent alloying concept first presented in Ref. 9  We apply first-principles calculations on a quasi-ternary c-Ti x Zr y Al z N alloy to determine thermodynamic properties and isostructural decomposition tendencies within the alloy.4][25] The choice of KKR-CPA is motivated by our need for a fine grid across the compositional space to evaluate the tendency of spinodal decomposition.Though CPA treats substitutional disorder at a mean-field level, it is proven to be effective and reliable for completely disordered alloy systems. 5,26xchange-correlation effects are treated within the Generalized Gradient Approximation according to Perdew, Burke and Ernzerhof. 27We restrict ourselves solely to the study of isostructural decomposition of the cubic B1, or rock-salt, structure of Ti x Zr y Al z N. Within this structure one of the fcc sublattices holds all the N atoms and has no compositional degrees of freedom, the other holds the metal atoms and is treated as a solid solution phase.Calculations were carried out over a compositional grid x,y,z spaced 0.05 from each other resulting in 21 compositions along each binary edge and 231 compositions in total.We determined the equilibrium volume for each of the compositions by calculating the energy of each composition at multiple volumes and fitting a Morse type Equation of State. 28ince the CPA assumes an ideal, undistorted crystal structure of an alloy, we treat a contribution to the alloy total energy from local ion relaxations, present in any real alloy separately by making use of the Independent Sublattice Model (ISM). 5Within the ISM the total energy of the system is calculated as where E chem is the energy of a substitutionally disordered alloy at the ideal underlying B1 crystal lattice and E relax is the relaxation energy.In this work we will treat the relaxation energy as if coming solely from the displacements of N atoms due to presence of chemically nonequivalent nearest neighbor metal atoms, an approximation that of materials. 5Accordingly, we obtain the expression for E relaxN for N atoms in c-Ti x Zr y Al z N: where v TiAl = -0.06394eV(f.u.) −1 , v ZrAl = -0.19159eV(f.u.) −1 and v TiZr = -0.04255eV(f.u.) −1 are the relaxation energies of a N atom between two unlike metal atoms in one direction and p TiAl = xz, p ZrAl = yz and p TiZr = xy are the probabilities of an N atom being surrounded by those two metal atoms in one direction.The relaxation energy parameters were determined by performing calculations on SQS structures 29 with and without relaxations, following the methodology described in Ref. 5.These calculations are performed using the projector augmented wave method within the Vienna Ab initio Simulation Package (VASP). 30,31hase stabilities of the random alloy in this work is determined based on the configurational Gibbs free energy defined as: where E(x,y,z) is the alloy total energy, S conf (x, y, z) is the configurational entropy, p is the pressure and V is the volume.However, since the calculations are done at equilibrium the pV term is 0 in all cases and will not be mentioned from now on.Vibrational free energy is not considered in this work and the configurational entropy is treated within the mean-field approximation where depends only on relative fractions of the alloy components.We emphasize that the reference to Gibbs free energy as configurational is because we have only considered configurational entropy for the temperature effects, vibrational entropy for instance is not considered, as such it is not a full Gibbs free energy.Another important property is the mixing free energy: also called the formation energy.If ∆G is positive then the solid solution with this composition is thermodynamically unstable with respect to isostructural decomposition into the end member compounds.Also, if the second directional derivative ∂ 2 G conf (x, y, z,T) /∂v 2 x, y, z within the constrained compositional plane is negative in at least one direction v x, y, z , then the system should decompose spinodally as any concentration fluctuation along that direction will reduce the total energy.If it is not negative in any direction then spinodal decomposition should not occur as any concentration fluctuations result in a net increase in energy, in this case the phase separation can only occur via nucleation and growth of the separation product phases.

EXPERIMENTAL DETAILS
In order to test the theoretical predictions, TiZrAlN coatings were prepared by cathodic arc evaporation and studied in their as-deposited state and after isothermal annealing.The coatings were deposited on polished tungsten carbide substrates in an industrial Oerlikon Balzers Innova cathodic arc evaporation system.Two cathodes were placed next to each other in the deposition chamber, one with a Ti:Al ratio of 33:67 and one consisting of pure Zr.The stationary substrates were placed such that different coating compositions were obtained and the deposition time was chosen to obtain coating thicknesses of approximately 10 µm.The depositions were conducted in a 3.5 Pa N 2 reactive gas environment using a substrate bias voltage of -30 V and a deposition temperature of ∼400 • C. The coating compositions were determined by energy dispersive x-ray spectroscopy (EDX) in a scanning electron microscope (Zeiss LEO 1550 FEG) operated at 20 kV.After deposition, the coated substrates were heat treated in a vacuum annealing chamber at a pressure below 6.7•10 −4 Pa, using heating and cooling rates of 20 K/min and an isothermal hold time of 2 h at 1100 • C. The structural decomposition was investigated by x-ray diffractometry (XRD) in Bragg-Brentano geometry (Panalytical X'Pert PRO) using Cu Kα -radiation, and analytical scanning electron transmission electron microscopy (STEM) using a FEI Technai G2 instrument operated at 200 kV.Cross-sectional TEM samples were prepared by mechanical polishing followed by ion beam milling.For one of the samples, the phase evolution with annealing time and temperature was studied by high-energy x-ray scattering in-situ during annealing.The experiment was performed at beamline P07 at Petra III using an x-ray energy of 57 keV and a beam size of 100x20 µm 2 .A 1 mm thick sample was placed in a vacuum chamber and heated with 20 K/min to T max =1100 • C and held at T max for 2 h.Experiments were performed in transmission geometry and diffracted x-rays were collected by a 2D detector (Perkin Elmer).The data was transformed to one-dimensional lineouts by integrating the data in a 20 • wide bin in the coating growth direction and the scattering angle was recalculated to corresponding plane spacing.

RESULTS
Starting with a conventional consideration of the stability of an alloy phase from the mixing free energy.From Fig. 1 it is immediately seen that (ZrAl)N is a highly unstable system.Even at 1300 K the formation energy is positive and very high, approximately 0.26 eV/atom for Zr 0.35 Al 0.65 N, compared to 0.08 eV/atom for Ti 0.35 Al 0.65 N at the same temperature.Generally, these results are in agreement with those of Refs.14, 18, 19, and 21.In ref 21 however, Holec et al. presented highly symmetric mixing enthalpies with respect to equiatomic composition for both (TiAl)N and (ZrAl)N.We attribute the differences between our results and those of Ref. 21 to their use of small supercells for complex disordered alloys and our use of a denser compositional grid.According to references 5, 14, and 18 the mixing enthalpies should be highly asymmetric relative to equiatomic composition, and in the case of (TiAl)N Alling et al. explained the effect by the peculiar dependence of the electronic structure of the alloy.As we will show below, the shape of the mixing enthalpy curve is essential for predicting a tendency towards the spinodal decomposition in the considered system.
As decomposition of (TiAl)N is well studied in literature [1][2][3][4][5] and considered to have a reasonably strong driving force for the phase separation, 32 we can expect an even stronger tendency for the separation of ZrN from AlN, if it can be grown as a solid solution at all.On the other hand, the formation energy of (TiZr)N is much smaller and as such it is conceivable that c-(TiZr)N might form as an intermediate phase, or even a final phase.Indeed, we see that (TiZr)N alloys with less than 30% TiN have negative formation energy at such high temperature, at the very least any decomposition process between TiN and ZrN could be expected to be slow.While c-AlN should be expected to separate out quickly, the subsequent transformation of cubic AlN into a wurtzite phase is beyond the subject matter of this study as we are focused on the spinodal decomposition which is isostructural.However, in Ref 19 it has been shown that the presence of ZrN phases tends to delay the formation of w-AlN phase up to higher temperatures, despite the fact that there should still be significant thermodynamic instability of c-AlN with respect to a w-AlN phase.
Let us now turn to the study of the spinodal decomposition, which is believed to be the most important mechanism for tuning mechanical properties of this class of alloys for hard coating applications.Fig 1(b) shows the most favorable paths of spinodal decomposition for each local composition of the original solid solution, determined by the direction for which the second derivative of the Gibbs free energy attains the highest in magnitude negative value.The length of the arrows thus indicates the relative strength of the driving force towards the decomposition.Again, our results confirm the strong tendency towards the decomposition between ZrN and AlN, but only for concentrations of at least 40-50% AlN, which are close to the peak of the formation energy.On the other hand, a lower concentration of Al leads to very weak tendency towards spinodal decomposition at this temperature despite very large positive formation energy of the alloys.Also, we note that any solid solution of (TiZrAl)N with more than 75-80% ZrN will resist the spinodal decomposition and can be expected to remain in a solid solution phase even at very high temperature.This is not unlike what has been presented previously for the sake of Zr-rich binary ZrAlN 18 and has also been observed in Ti-rich TiAlN 5 at elevated temperatures.As a matter of fact, this resistance only appears at sufficiently high temperature, and it is driven by the configurational contribution to the mixing entropy.Note that the observation above applies only with regard to spinodal decomposition, and that vibrational contributions to the free energy are not considered.Since the formation energy is still positive, if there are initial nuclei of the decomposition products present in the sample, the binodal decomposition may still occur to separate ZrN and AlN from each other.However, any decomposition process should be significantly slowed down due to the lack of spinodal decomposition, leading to a necessity to form nuclei of critical size with composition that should differ  significantly from the one of the solution phase, as well as due to the kinetic limitations, which are usually significant in ceramics.
As the phase separation of ZrN and AlN is strongest at low ZrN fractions we predict that even at only 5% ZrN, the phase separation of ZrN from AlN will dominate over separation of TiN from AlN, this applies at all relative fractions of TiN and AlN.Moreover, we observe that the arrows indicating the strongest driving force for spinodal phase separation are not fully parallel to the (TiZr)N edge, here also the separation of ZrN and AlN contribute strongly relative to the separation of TiN and ZrN.Instead they point towards the stable (TiZr)N phase thus aiding in the formation of such a phase.Two coatings were selected to experimentally study the decomposition trends at high temperatures, (Ti 0.13 Zr 0.69 Al 0.18 )N, with a low tendency for spinodal decomposition, and (Ti 0.30 Zr 0.24 Al 0.46 )N, a composition predicted to be highly unstable.The selected compositions are marked as stars in the compositional diagrams in Fig. 1.Both as-deposited films display a single phase with a face center cubic crystal structure in the x-ray diffractograms in Fig. 2 (a).The c-200 diffraction peaks are shifted between the samples due to different lattice parameters, suggesting that the as-deposited coatings are solid solution c-(TiZrAl)N.The (Ti 0.30 Zr 0.24 Al 0.46 )N film decomposes into two cubic phases during annealing for 2 h at 1100 • C, one with smaller lattice parameter (higher diffraction angle) and one with larger lattice parameter (lower diffraction angle).In addition, diffraction peaks from w-AlN are present.The diffractograms from in-situ annealing experiments in figure 2 (b) reveal that the decomposition is initiated by formation of cubic domains enriched in either ZrN-or TiAlN, observed as two broad shoulders, one of each side of the original c-200 peak.This behavior is thus in agreement with the predictions, where the first step of decomposition is predicted to be separation between ZrN and AlN.In addition, the shift of the original c-200 diffraction peak with annealing temperature is too large to be explained by only thermal expansion and is thus assigned to enrichment of ZrN, or corresponding depletion of AlN, in this phase.After 2 h hold at 1100 • C, the TiAlN-rich shoulder (at d≈2.10 Å) has decreased in size and a small diffraction peak from w-AlN is observed at d≈2.49 Å.There is, however, only very small changes in the peak position of the ZrN-rich phases with annealing time at 1100 • C, suggesting that both these Al-depleted (Zr,Ti)N phases are relatively stable.The high angle annular dark field STEM image and EDX elemental maps of this coating annealed for 2 h at 1100 • C shown in Fig. 3  In the (Ti 0.13 Zr 0.69 Al 0.18 )N film, for which the predicted tendency for spinodal decomposition is low, there is only a small shift of the cubic 200 diffraction peak in the XRD pattern (c.f.Fig. 2) upon annealing which is assigned to stress relaxation. 12Also for this film, there might be an enrichment in ZrN of the cubic phase upon annealing while the peak shift is much smaller compared to that of the (Ti 0.30 Zr 0.24 Al 0.46 )N film and thus the possible change in composition is small.The elemental contrast STEM micrograph in Fig. 3 (b), however, reveals that decomposition is initiated also in this film.In this case, the microstructure is much finer and dark contrast domains rich in AlN have formed, while there is no contrast variation observed within the brighter regions.Most of the AlN-rich domains formed are in the order of 2-10 nm in size, approximately 5 times smaller compared to the (Ti 0.30 Zr 0.24 Al 0.46 )N film, while a few larger (∼20-40 nm) domains can also be observed.The smaller domains and thus, much slower decomposition of this film are in agreement with the theoretical results, as the predicted lower driving force for spinodal decomposition would result in a slower decomposition rate.In addition, the wider size distribution of domains in this film compared to that of spinodally decomposed (TiAl)N films [32][33][34] suggests that the decomposition may be binodal in this case where the first step is nucleation and growth of an AlN-rich phase.The structure of the AlN-rich domains is not clear due to the small domain size while only a cubic structure is found by the XRD and selected area electron diffraction.While the STEM micrograph indicates phase separation the x-ray diffractogram only shows one broad diffraction peak that matches the TiZrAlN solid solution.Hence, this alloy has a microstructure containing small domains with slightly different compositions, perhaps with some still in the as-deposited overall alloy composition even after the annealing process.
Thus, in agreement with the calculations, the first step of phase separation in the (TiZrAl)N coatings is separation into ZrN-and AlN-rich domains, followed by enrichment of AlN and transformation into w-AlN, where the second step is completed only in the low Zr-containing sample.The AlN-depleted cubic phase separates into Zr-and Ti-rich (TiZr)N, a process that has not reached its final phases after annealing at 1100 • C for 2 h in either of the two coatings.Further, the difference in decomposition rate between the two samples agrees well with the calculated difference in driving force for decomposition.

CONCLUSIONS
Decomposition behavior of (TiZrAl)N alloys has been investigated using a combination of first-principles theory and experiment.According to our calculations we predict that phase separation between ZrN and AlN occurs first.Even though the phase separation tendency of TiN from AlN is less pronounced, once the separation of ZrN and AlN has begun, precipitations of TiN should be expected as well.However, since at high enough temperature a high Zr-content (TiZr)N phase is predicted to be stabilized thermodynamically due to configurational contribution to the entropy of mixing, preventing a complete separation betweenTiN and ZrN.Consequently theory predicts that the final result of the isostructural decomposition should be TiN, AlN and (TiZr)N.
The exception is a solution with a high Zr content (>∼75%) which, despite high thermodynamic instability, is expected to resist the spinodal decomposition.In this case phase separation will not occur without an initial nucleation, resulting in very slow decomposition processes.
Experiments carried out on samples with two different compositions confirm predictions regarding the phase separation into ZrN and AlN rich domains.In both cases AlN segregates, but in the case of an alloy with the high Zr-content this process is greatly delayed and after 2 h of annealing has barely begun.In addition any decomposition in this solution is mainly attributable to binodal decomposition, rather than to the spinodal.

FIG. 1 .
FIG. 1. Isostructural formation energy a) and spinodal decomposition trends b) of c-(TiZrAl)N solid solution at 1300K.The high value for (ZrAl)N (compare to values for (TiAl)N and results in other literature) suggests considerable difficulty in the formation of such solutions.Also note a small miscibility region for (TiZr)N with high Zr content.b) Spinodal phase decomposition diagram for (TiZrAl)N at 1300K, the arrows indicate the direction with strongest decompositional trends, the length of the arrows show relative strength of the decompositional trend.The absence of arrows in solutions of high Zr content means there is no spinodal decomposition, this can also be seen in the formation energy diagram in a).The compositions of the experimental samples are marked in the diagrams with stars, a red star marks the high Zr content Ti 0.13 Zr 0.69 Al 0.18 N and the blue star marks the lower Zr content Ti 0.30 Zr 0.24 Al 0.46 N.

FIG. 2 .
FIG. 2. (a) x-ray diffractograms from (Ti 0.13 Zr 0.69 Al 0.18 )N (red) and (Ti 0.30 Zr 0.24 Al 0.46 )N (blue) films in their as-deposited and annealed at 1100 • C for 2h states and.(b) lineouts from in-situ x-ray diffraction experiments on the (Ti 0.30 Zr 0.24 Al 0.46 )N film during annealing at different annealing temperatures and times.Reference peak positions are marked for the room temperature value for TiN, ZrN and ZrN.Peaks labeled 's' arise from the substrate.

FIG. 3 .
FIG. 3. Elemental contrast STEM micrographs of (a) (Ti 0.30 Zr 0.24 Al 0.46 )N and (b) (Ti 0.13 Zr 0.69 Al 0.18 )N coatings annealed for 2 hours at 1100 • C. Inserted in (a) is an EDX map from the area marked with red box.