Structural, phonon and thermodynamic properties of fcc-based metal nitrides from first-principles calculations
Highlights
► The phonon properties of cubic TiN, AlN, ZrN and HfN have been investigated. ► The finite temperature thermodynamic properties of cubic nitrides are studied. ► The thermodynamic properties of fcc-AlN are investigated for the first time.
Introduction
Metal nitrides with the rock salt structure, such as TiN, AlN, ZrN and HfN, have been extensively studied both experimentally and theoretically due to their high hardness, strong wear resistance, and promising oxidation resistance [1], [2], [3], [4]. Recently, it was reported that the cubic binary nitrides formed through thermal decomposition, e.g., cubic TiN and cubic-AlN [5] due to spinodal decomposition of Ti–Al–N coating, can improve the cutting performance of ternary nitrides coated inserts during annealing within the temperature range of age-hardening. In addition, the miscibility gap was observed in TiN–AlN [6], TiN–ZrN and TiN–HfN systems [7], [8], [9]. The microstructure resulting from the miscibility gap plays an important role in the improvement of coating performance due to the likely formed cubic TiN, AlN, ZrN and HfN.
Experimental measurements pertaining to the thermodynamic properties of TiN [10], [11], ZrN [12] and HfN [11], [13] were reported previously, but a complete thermodynamic description for these metal nitrides is still lacking. For instance, the thermodynamic properties of the Ti–N system were assessed by Ohtani et al. [14], Zeng et al. [15] and Jonsson [16]. However, considerable uncertainties about thermodynamics are still remained in the Ti–N system: (i) the assessed heat capacity [14] does not agree satisfactorily with the experimental data, (ii) Jonsson’s assessment of heat capacities cannot be used below 200 K [16], and (iii) the heat capacities assessed by Zeng et al. [15] do not agree with the experiments below about 500 K. Recently, the thermal expansions and heat capacities of MN (M = Ti, Zr, Hf, V, Nb, Ta) were reported by Lu et al. [17] using the first-principles Debye–Grüneisen model with Slater approximation and Dugdale–MacDonald (DM) approximation. It was concluded that the Debye–Grüneisen model using DM approximation can describe the experimental heat capacities reasonably, but less satisfactory results were obtained for thermal expansions [17]. Additionally, Saha et al. [18] studied the phonon, lattice heat capacity, and thermal conductivity of ScN, ZrN, and HfN by using the density functional perturbation theory. According to their work, HfN has the largest heat capacity followed by ZrN and ScN below 300 K due to its softer acoustic branches with respect to those of ZrN and ScN. Recently, the heat capacity of cubic carbides and nitrides have been investigated by Iikubo et al. [19] via a quasiharmonic approximation approach using LDA approximation. They calculated the heat capacities of TiN and ZrN. Besides the incomplete thermodynamic descriptions of the Ti–N, Zr–N and Hf–N systems, the thermodynamic properties for rock salt AlN are still lacking. In contrast to the experimental difficulty in determining the thermodynamic data of solid phases, first-principles quasiharmonic approximation has been proved to be an effective approach in predicting thermodynamics at finite temperatures [20].
The present work aims to investigate the structural, vibrational and thermodynamic properties of fcc-based metal nitrides MN (M = Ti, Al, Zr, Hf) from first-principles calculations within both GGA [21] and LDA [22]. To these ends, in Section 2, the methodologies to predict structural and thermodynamic properties are presented and the details of first-principles and phonon calculations are introduced. In Section 3, the structural, phonon, and thermodynamic properties of these nitrides are presented and discussed, followed by the summary in Section 4.
Section snippets
Equation of state
In order to estimate the structural properties of metal nitrides, volume vs. energy data points obtained from first-principles calculations are fitted by a four-parameter Birch–Murnaghan equation of state (EOS) [23] where is volume, , and are the fitting parameters. The EOS can be used to calculate the equilibrium volume , energy , bulk modulus and its pressure derivative .
Finite-temperature thermodynamic properties
The quasiharmonic approach is adopted to evaluate the
Structural and phonon properties
The calculated energy vs. volume data points for each nitride are fitted by the four-parameters Birch–Murnaghan EOS of Eq. (1). The obtained properties at 0 K (without the zero-point vibrational energy) are summarized in Table 1, including lattice parameter , bulk modulus and its pressure derivative , and Debye temperature, which are compared with the available experimental data [33], [34], [35], [42], [43], [44], [49], [50], [51] and previous first-principles calculations [3], [18],
Conclusion
Based on first-principles calculations with the GGA and the LDA as the exchange–correction functions, the structural, phonon, finite-temperature thermodynamic properties of TiN, AlN, ZrN and HfN with cubic rock salt structure have been investigated. The calculated structural properties, phonon DOS’s, and Debye temperatures are in good agreement with the available experiments and other calculations. GGA yields 1%–2% larger lattice parameters and 6%–15% smaller bulk modulus compared to those from
Acknowledgments
The authors thank the National Natural Science Foundation of China (NSFC) with the Grant Nos. 51028101 and 51001120, the postdoctoral foundation of China with Grant No. 20100470060 and 201104485, and National Basic Research Program of China No. 2010CB735807B. ZKL and SLS acknowledge the supports from the NSFC with the Grant No. 51028101 and United States National Science Foundation under the Grant No. DMR-1006557.
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