A comparative study TiC/TiN and TiN/CN multilayers

Un estudio comparativo de las multicapas TIC/TiN y TiN/CN

We carried out a comparative study of TiC/TiN and TiN/CN multilayers using the linearized augmented plane wave (LAPW) scheme and density functional theory as implemented in the Wien2k code. Initially, we optimized the structural properties of the TiC/TiN and TiN/CN multilayers in the volume with NaCl structure, and the ground state energy, the bulk modulus, and the cohesive energy were determined. To determine the energy of formation, the total energy for TiN, TiC, and CN compounds was calculated. Finally, we determined the DOS (density of states) of the two multilayers. The analysis of the partial density of states reveals that multilayers has metallic behavior that can be explained by the strong p-d hybridization of N and Ti atoms.

En este trabajo se hace un estudio comparativo de las multicapas TiN/CN y TiC/TiN usando el esquema ondas plana aumentadas y linealizadas y la teoría del funcional de la densidad tal como se halla implementado en el código WIEN2k. Inicialmente, se optimizaron las propiedades estructurales de las multicapas TiN/CN y TiC/TiN en volumen en la estructura NaCl y se obtuvo la energía de estado base, el módulo de volumen y la energía de cohesión. Para obtener la energía de formación, se calcula la energía total para los compuestos TiN, TiC, CN. Finalmente, se obtiene la densidad de estados los dos multicapas. El análisis de la densidad de estados revela que las multicapas poseen un comportamiento metálico que puede ser explicado por la fuerte hibridación entre los orbitales p-d de los átomos de N y Ti.

https://doi.org/10.15446/dyna.v81n188.41637

Miguel J. Espitia-Rico ^a, Gladys Casiano-Jiménez ^b, César Ortega-López ^b, Nicolás De la Espriella-Vélez ^b & Luis Sánchez-Pacheco ^b

^a Grupo GEFEM Facultad de Ingeniería, Universidad Distrital Francisco José de Caldas, Bogotá, Colombia. mespitiar@udistrital.edu.co
^b Departamento de Física, Universidad de Córdoba, Montería, Colombia. gcasianoj@correo.unicordoba.edu.co, cortegal@correo.unicordoba.edu.co, naespriellav@correo.unicordoba.edu.co, lcpacheco@correo.unicordoba.edu.co.

Received: January 19^th, 2014. Received in revised form: September 10^th, 2013. Accepted: September 30^th, 2014.

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Abstract
We carried out a comparative study of TiC/TiN and TiN/CN multilayers using the linearized augmented plane wave (LAPW) scheme and density functional theory as implemented in the Wien2k code. Initially, we optimized the structural properties of the TiC/TiN and TiN/CN multilayers in the volume with NaCl structure, and the ground state energy, the bulk modulus, and the cohesive energy were determined. To determine the energy of formation, the total energy for TiN, TiC, and CN compounds was calculated. Finally, we determined the DOS (density of states) of the two multilayers. The analysis of the partial density of states reveals that multilayers has metallic behavior that can be explained by the strong p-d hybridization of N and Ti atoms.

Keywords: DFT, multilayers, electronic and structural properties.

Resumen
En este trabajo se hace un estudio comparativo de las multicapas TiN/CN y TiC/TiN usando el esquema ondas plana aumentadas y linealizadas y la teoría del funcional de la densidad tal como se halla implementado en el código WIEN2k. Inicialmente, se optimizaron las propiedades estructurales de las multicapas TiN/CN y TiC/TiN en volumen en la estructura NaCl y se obtuvo la energía de estado base, el módulo de volumen y la energía de cohesión. Para obtener la energía de formación, se calcula la energía total para los compuestos TiN, TiC, CN. Finalmente, se obtiene la densidad de estados los dos multicapas. El análisis de la densidad de estados revela que las multicapas poseen un comportamiento metálico que puede ser explicado por la fuerte hibridación entre los orbitales p-d de los átomos de N y Ti.

Palabras clave: DFT, multicapas, Propiedades electrónicas y estructurales.

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1. Introduction

Because of its hardness, high chemical and thermal stability, and high resistance to wear, oxidation, and corrosion, both titanium nitride (TiN) and titanium carbide (TiC) have been widely used as hard coatings in high-speed cutting tools and in devices operating at high degrees of power and high temperatures [1-4]. Unfortunately, hard coatings based only on traditional TiN or TiC offer limited benefit in terms of prevention of rupture or adherence to the workpiece, which is one of the main problems associated with tribological applications [5-7]. For this reason, many studies have sought to improve the mechanical properties of thin films of these nitrides and carbides through the growth of multilayers or nanocomposites based on TiN or TiC [5, 8-11].

A TiN/CN multilayer grown via magnetron sputtering [5] has been found to possess a higher resistance to wear, oxidation, and corrosion than TiN or TiC [5]; therefore hard coatings based on a TiN/CN multilayer will have better mechanical and tribological properties than those based on traditional carbides or nitrides. Furthermore, a titanium carbide/titanium nitride (TiC/TiN) multilayer is a very interesting material, because it combines the high degree of hardness and the low friction coefficient of TiC with the high degree of wear resistance of TiN [12-16]. This unusual combination of properties makes the TiC/TiN multilayer a material with great chemical stability and excellent mechanical properties, such as extreme hardness, a low friction coefficient, a high melting point, high electrical conductivity and a high degree of wear resistance [17-23]. Due to this combination of properties, hard coatings based on a TiC/TiN multilayer improve the performance of high-speed cutting tools, since the high thermal conductivity of the new compound reduces thermal gradients and reduces stress cracks as a result of thermal shock in the tools [14,25], whereby the high-speed cutting tools have a longer lifespan [23,26]. Finally, we haven't found any scientific publications that compare the properties of these multilayers. For this reason, the main objective of this paper is do a comparative study of the structural and electronic properties of TiN/CN and TiC/TiN multilayers using calculations based on density functional theory.

2. Computational method

Calculations were performed within the framework of density functional theory (DFT) and using the full potential augmented plane wave (FP-LAPW) method implemented in the Wien2k package [27]. The correlation and exchange effects of electrons were dealt with using the generalized gradient approximation (GGA) of Perdew, Burke, and Ernzerhof (PBE) [28]. In the LAPW method, the cell is divided into two types of regions, atomic spheres centered at nuclear sites and the interstitial region between the non-overlapping spheres. Within the atomic spheres, wave functions are linear combinations of products of radial and spherical harmonic functions, while in the interstitial region, the function expands as a linear combination of plane waves. The charge density and potentials are expanded in spherical harmonics up to l_max = 10 within the atomic spheres, and the wave function in the interstitial region is expanded in plane waves with a cutoff parameter of R_mtK_max = 8, where R_mt is the smallest radius of the atomic sphere in the unit cell and K_max limits the kinetic energy of the plane waves, where . To ensure convergence in the integration of the first Brillouin zone, 54 points were used at the irreducible first Brillouin zone. The integrals over the Brillouin zone were solved using special Monkhorst-Pack alignment points [29]. Self-consistency was achieved by requiring that the convergence of the total energy be less than 10^-4 Ry. For expanding the potential in the interstitial region, G_max =12 was considered. Muffin-tin radii were 1.60 for N, 1.95 for Ti, and 1.60 bohr for C. Calculations were performed taking into account the spin polarization, in order to check possible magnetic properties of the compounds.

For the lattice constant, the minimum volume, the bulk modulus, and the cohesive energy of each structure studied, the calculated data were fit to the Murnaghan equation of state, Eq. (1)

where B₀ is the bulk modulus, its first derivative is B^'₀, V₀ is equilibrium volume of the cell, and E₀ is the cohesive energy.

In order to verify the thermodynamic stability of the TiC/TiN and TiN/CN multilayers, with a concentration 50-50, we calculated the energy of formation of the multilayer in the rock salt structure. The energy of formation of a ternary (LMN) compound is defined as the difference between the total energy of the ternary L_1-xM_xN phase and the total energy of the binary compounds in the ground states of LN and MN, and respectively; therefore, the energy of formation is given by Eq. (2) [30],

3. Results

3.1. Structural properties

We first optimized the structural parameters of the binary compounds TiN, TiC, and CN, because these parameters were used to model the TiN/CN and TiC/TiN multilayers. CN has two stable crystalline structures, one hexagonal-type graphite and the other cubical [31]. The lattice constant a, the bulk modulus (B₀), and the minimum energy (E₀) of the binary compounds are shown in Table 1, together with experimental and theoretical values reported by other authors. Note that the lattice constant and the bulk modulus B₀ calculated in this study agree well with the experimental values, which shows the reliability of the DFT-based computations.

Furthermore, it was found that both the TiN/CN multilayer modeled in the NaCl phase by inserting a layer of TiN and a layer of CN along the z axis as the TiC/TiN multilayer crystallize in a tetragonal structure with space group 123 (P4=mmm). Fig. 1 shows the total energy curves as a function of volume and fitted to the Murnaghan equation of state (Eq. 1) for the TiN/CN multilayer (black curve) and the TiC/TiN multilayer (gray curve).

We have taken as zero the sum of the energies of neutral atoms of isolated Ti, C, and N. Therefore, the absolute value of the minimum energy of each curve is the cohesive energy of the TiN/CN and TiC/TiN multilayers in the NaCl phase. Fig. 1 shows that each structure is considered metastable, since there is a minimum of energy in the corresponding curve. The lattice constant, the bulk modulus (B₀), and the minimum energy (E₀) of the TiN/CN and TiC/TiN multilayers calculated in the NaCl structure are shown in Table 2.

We note that the lattice constants calculated in this paper are in good agreement with the experimental and theoretical results reported by other authors. Additionally, we see that the values of the volume modules of the TiN/CN and TiC/TiN multilayers are quite high, confirming the hardness of these materials and making them ideal candidates for hard coatings on high-speed cutting tools and devices that must operate at a high degree of power and at high temperatures.

As a next step, we calculated the formation energy_E_f of the TiC/TiN and TiN/CN multilayers, with a 50-50concentration, that is, x = 50% TiC molecules, x = 50% TiN molecules, and x = 50% NC molecules. For this, we calculated the cohesive energy of the binary compounds TiC, TiN, and CN in their ground states, , , and . Table 3 shows the values of the energy of formation that we calculated using Eq. (2)

The energy of formation of the TiC/TiN and TiN/CN multilayers was calculated to be 3.69 and 5.22 eV, respectively. Because these values are positive as compared with the reference state for both multilayers, these TiC/TiN and TiN/CN multilayers are thermodynamically unstable, i.e. they cannot be formed under equilibrium conditions. Therefore, only when kinetic constrains prevent the system from reaching the equilibrium state, as found e.g. in plasma-induced physical and chemical vapor deposition (PVD and PCVD) at relatively low temperatures, can the metastable phase of TiC/TiN and TiN/CN multilayers in the rock salt structure be obtained, similar to the result predicted by Zhang and Veprek [30] for the ternary Ti_0,5Al_0,5N phase.

3.2. Electronic Properties

The total density of states (TDOS) and partial density of states (PDOS) for TiN/CN and TiC/TiN multilayers in the NaCl phase are shown in Figs. 2 and 3, respectively.

It can be observed that both TiC/TiN and TiN/CN multilayers exhibit a metallic behavior, determined by the Ti-d, C-p, and N-p hybrid states that cross the Fermi level. Moreover, according to the theory proposed by Jhi et al. [44], the highly directional coupling between metal d and non-metal p electrons results in covalent bonding, and this bonding makes a positive contribution to the hardness, which is responsible for the high degree of hardness of the TiC/CN and TiC/TiN multilayers. A similar result was found by Restrepo, Parra et al. [45] in their study of TIN and TiC. Additionally, it can be seen that the DOS of the TiC/CN multilayer at the Fermi level, mainly dominated by Ti-d states, is smaller than total density of states when compared with TiC/TiN. This may be caused by the metallic d-d interactions, which make a negative contribution to the bulk modulus [44]. This might be the cause of the low degree of hardness of TiN/CN [43]. Similar behavior was reported for the binary compounds TiC and TiN [46], and NbC and NbN [47].

For the total density of states of the TiN/CN multilayer, it can be observed that the valence band is divided into two regions. The first one, between ~ - 16.0 eV and ~ -13.0 eV, is mainly governed by the N-s states, with a small contribution from C-s states. The region between ~ -11.6 eV and the Fermi level is in great part composed of the N-p states, with a small contribution of Ti-d and C-p electrons. Between ~ -13.0 eV and ~ -11.6 eV, an intraband gap of ~ -1.4 eV is present. The multilayer does not exhibit magnetic properties, because the total density of spin up is fully offset by the total density of spin down.

In the total density of states of the multilayer it can be observed that valence band is divided into three regions. The first, between ~ -15.0 eV and -13.0 eV, is mainly governed by the N-s states, with a small contribution from C-s states. The region between ~ -10.8 eV and ~ -7.7 eV is mainly dominated by C-s states, with a small contribution of N-p electrons. The region between ~ -6.3 eV and the Fermi level is governed by the Ti-d, C-p, and N-p states. The TiCN compound has two intraband gaps, one in the region between ~-13.0 eV and ~ -10.8 eV and the other in the region between ~ -7.7 eV and ~ -6.3 eV, with widths of ~ -2.2 eV and ~ -1.4 eV, respectively. As before, the multilayer does not exhibit magnetic properties, because the total density of spin up is fully offset by the total density of spin down.

Conclusions

We reported first-principles calculations to determine the structural and electronic properties of TiN/CN and TiC/TiN multilayers and carried out a comparative study of them. The calculated lattice constants are in good agreement with experimental data. The calculated values of bulk modulus are quite high, which means that these materials are very rigid. This property is due to the strong covalent bonds that exist between the metallic Ti-d and the nonmetallic C-p and N-p states. This confirms that these materials exhibit a high degree of hardness, which makes them attractive for potential applications at high temperature and for hard coatings. However, we found that the bulk modulus of the TiC/TiN multilayer was larger than that of the TiN/CN multilayer.

From the density of states it was found that the compounds exhibit metallic behavior, because of the Ti-d, C-p, and N-p hybrid orbitals traversing the Fermi level.

Acknowledgements

The authors thank the Research Center of the University of Cordoba CUIC for its financial support.

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M.J. Espitia-Rico, received the BSc in Physicist degree in 1999 from the Universidad de Córdoba, Colombia; the MSc degree in Physical Science and is Dr. candidate in Physical Sciences, from the Universidad Nacional de Colombia. Bogotá, Colombia. From 1999 to 2004, he worked as a professor in the Physical Department, Universidad de Córdoba. Montería, Colombia. Since 2005 to day, he is a Full Professor in the Universidad Distrital Francisco José de Caldas, Colombia. His research interests include: simulation, computational calculation of new materials.

G.R. Casiano-Jiménez, received the BSc in Physicist degree in 1990 from the Universidad de Córdoba, Colombia, the MSc degree in Physical Science and is Dr. candidate in Physical Sciences, from the Universidad de Córdoba. Montería, Colombia. Since 2005 to day, she is a Full Professor in the Universidad de Córdoba, Colombia. His research interests include: simulation, modeling and computational calculation of new materials.

C. Ortega-López, received the BSc in Physicist degree in 1989 from the Universidad de Córdoba, Colombia, the MSc degree in Physical Science in 2002, and the PhD degree in Physical Science in 2009, from the Universidad Nacional de Colombia, Bogotá, Colombia. Since 1997 to day, he is a Full Professor in the Universidad Córdoba, Colombia. His research interests include: simulation, modeling and computational calculation of new materials.

N.A. De la Espriella-Vélez, received the BSc in Physicist degree in 1987 from the Universidad de Córdoba, Colombia, the MSc degree in Physical Science in 2002 from the Universidad Nacional de Colombia, Colombia, and the PhD degree in Physical Science in 2010, from the Universidad Central de Venezuela, Caracas, Venezuela. Since 1997 to day, he is a Full Professor in the Universidad Córdoba, Colombia. His research interests include: simulation, modeling and computational calculation of new materials.

L.C. Sánchez-Pacheco, received the BSc in Physicist degree in 2003, the MSc degree in Physical Science in 2006, and the PhD degree in Physical Science in 2012, all of them from Universidad de Antioquia, Medellín, Colombia. Since 2010 to day, he is a Full Professor in the Universidad Córdoba, Colombia. His research interests include: simulation, modeling and computational calculation of new materials.