First-Principles Calculations on Electronic, Chemical Bonding and Optical Properties of Cubic Hf 3 N 4

Transcription

1 Commun. Theor. Phys. 59 (2013) Vol. 59, No. 1, January 15, 2013 First-Principles Calculations on Electronic, Chemical Bonding and Optical Properties of Cubic Hf 3 N 4 FENG Li-Ping (úû ), WANG Zhi-Qiang ( ãö), and LIU Zheng-Tang ( ) State Key Lab of Solidification Processing, College of Materials Science and Engineering, Northwestern Polytechnical University, Xi an , China (Received July 3, 2012; revised manuscript received October 30, 2012) Abstract Electronic, chemical bonding and optical properties of cubic Hf 3N 4(c-Hf 3N 4) are calculated using the firstprinciples based on the density functional theory (DFT). The optimized lattice parameter is in good agreement with the available experimental and calculational values. Band structure shows that c-hf 3N 4 has direct band gap. Densities of states (DOS) and charge densities indicate that the bonding between Hf and N is ionic. The optical properties including complex dielectric function, refractive index, extinction coefficient, absorption coefficient, and reflectivity are predicted. From the theory of crystal-field and molecular-orbital bonding, the optical transitions of c-hf 3N 4 affected by the electronic structure and molecular orbital are studied. It is found that the absorptive transitions of c-hf 3N 4 compound are predominantly composed of the transitions from N T 22p valence bands to Hf T 2 (d xy, d xz, d yz) conduction bands. PACS numbers: Mb, m, At, Ci Key words: first-principles, cubic Hf 3 N 4, electronic structure, optical properties 1 Introduction The research of hard materials is an active field by the need of industrial applications such as cutting tools, decorative coatings, wear protection, barrier films, turbine blades, and structural components, etc. [1 2] Especially, metal nitride compounds used as hard materials have attracted a lot of attention because of their relatively high hardness, brittleness, melting point, and interesting electronic, optical, and magnetic proprieties. [3 5] Novel c-hf 3 N 4 having Th 3 P 4 -type structure has been synthesized by Zerr et al. [6] at high pressure and temperature (18 GPa and 2800 K). It is shown that c-hf 3 N 4 has high bulk modulus more than 260 GPa, indicating that c-hf 3 N 4 has potential applications in hard materials. Hence, a large number of experiments were focused on the physical and mechanical properties of c-hf 3 N 4. [6 9] Additionally, a lot of theoretical works have been performed to study the mechanical, electronic, and optical properties of c-hf 3 N 4 using the first-principles calculations based on density functional theory. [10 15] Although the electronic and optical properties of c-hf 3 N 4 have been investigated, there are two problems need to be solved: (i) Detailed charge densities have not been shown and the bonding structure has not been expounded in detail; (ii) Physical origins of the optical properties have not been discussed. Therefore, this work is focused on solving the above two problems in detail by using the theory of crystal-field and molecular-orbital bonding. [16 19] 2 Computational Details All calculations are performed using the plane-wave ultra-soft pseudopotential (PWPP) technique [20] based on the density functional theory. The generalized gradient approximation (GGA) with the Perdew Burke Ernzerhof (PBE) functional [21] is applied to describe the exchange and correlation potential. Ultra-soft pseudopotential is adopted to represent the ionic cores of Hf and N atoms. The Hf (5d 2, 6s 2 ) and N (2s 2, 2p 3 ) electrons are treated as valence electrons. The plane wave cut-off energy is set to be 500 ev. For the Brillouin-zone sampling, the Monkorst-Pack scheme [22] with a grid of is adopted, where the self-consistent convergence of the total energy is ev/atom. All the calculations are implemented through the CASTEP code. [23] 3 Result and Discussion 3.1 Structure Optimization The c-hf 3 N 4 in I 43d space group has a local symmetry of T 6 d. The lattice parameter of c-hf 3N 4 has been optimized and listed in Table 1, along with experimental and other calculational values. It can be seen that the optimized lattice constant of c-hf 3 N 4 is about Å, which is in good agreement with the available experimental [6,9] and other calculational values. [12 13,15] 3.2 Electronic Structure Figure 1 shows the band structure of c-hf 3 N 4 along the Supported by the National Natural Science Foundation of China under Grant No , the Natural Science Foundation of Shaanxi Province under Grant No. 2012JM6012, the Research Fund of the State Key Laboratory of Solidification Processing under Grant No. 58- TZ-2011, the 111 Project under Grant No. B07040, and the Northwestern Polytechnical University Foundation for Fundamental Research under Grant No. JC Corresponding author, flpmerry@yahoo.com.cn c 2013 Chinese Physical Society and IOP Publishing Ltd

2 106 Communications in Theoretical Physics Vol. 59 high-symmetry points of the Brillouin zone. The top of the valence band is on the Fermi level. The band structure shows that c-hf 3 N 4 has direct band gap due to the top valence and the bottom conduction are found at the same G point. The calculated band gap is about 1.0 ev, which is comparable with previous calculational values [12 13,15] as shown in Table 1. Table 1 Optimized lattice constants of c-hf 3N 4 as well as experimental data [6,9] and other calculational values. [12 13,15] This work (GGA) Expt. [6] Expt. [9] Other calc. [12] Other calc. [13] Other calc. [15] a/å E g/ev The total and partial DOS of c-hf 3 N 4 are shown in Fig. 2. It is clear that lower valence bands are from 16 ev to 11.8 ev and that the peak of lower valence bands is located at 13.2 ev. The upper valence bands are from 7 to 0 ev and the main four peaks are located at 4.3 ev, 2.7 ev, 1.8 ev, and 0.6 ev, respectively. The conduction bands are from 1.0 ev to 5.5 ev and the main two peaks are located at 2.4 ev and 4.3 ev, respectively. Additionally, it can be seen that the lower valence bands are composed predominantly of N 2s and Hf 5d electrons. The upper valence bands consist of the N 2p and Hf 5d electrons. N 2s electrons that hybrid with Hf 6s electrons also contribute to the upper valence bands. The unoccupied conduction bands consist mainly of Hf 5d electrons, which have hybridization character with N 2p electrons. Moreover, N 2s and Hf 6s electrons also have a smaller contribution to the conduction bands. Hf T 2 (d xy, d xz, d yz ), and N T 2 2p electrons; The peak (f) is composed of the π* and σ* antibonding from the hybridization of Hf T 2 (d xy, d xz, d yz ) and N T 2 2p electrons; The peak (g) consists of the π nonbonding from Hf E(d x2 y 2, d z2), and the σ* antibonding from the hybridization of Hf A 1 6s and NA 1 2s. Furthermore, the total charge densities in (002) and (003) planes are shown in Fig. 5. It is clear from Fig. 5 that the bonding between Hf and N is ionic. Fig. 1 Band structure of c-hf 3N 4 along the highsymmetry points of the Brillouin zone. The charge densities of the total DOS at (a), (b), (c), (d), (e), (f), and (g) peak from (002) and (003) planes of c- Hf 3 N 4 are presented in Fig. 3. According to the theory of crystal-field and molecular-orbital bonding, a molecularorbital bonding structure for c-hf 3 N 4 is shown in Fig. 4. From Figs. 3 and 4, the detailed bonding structure of c- Hf 3 N 4 can be explained as follows: The peak (a) consists mainly of NA 1 2s and Hf T 2 (d xy, d xz, d yz ) electrons; The peak (b) is composed predominantly of the σ bonding from the hybridization of Hf T 2 (d xy, d xz, d yz ) and N T 2 2p electrons; The peak (c), (d), and (e) mainly involve the π and σ bonding contributed by the hybridization of Fig. 2 Total and partial density of states of c-hf 3N 4. Table 2 The calculated Mulliken atomic population of c-hf 3N 4. Species s p d Total Charge (e) N Hf The analysis of charge densities is more qualitative than quantitative. To further estimate the amount of electrons on and between the participating atoms, Mulliken

3 No. 1 Communications in Theoretical Physics atomic population approach has been adopted. The calculated Mulliken atomic population of c-hf3 N4 is listed in Table 2. It is obvious that each N expresses 0.84 charge state and each Hf shows charge state. From the molecule formula of c-hf3 N4, the total charge transfer 107 from Hf to N is 3.36 per molecule. Therefore, the chemical bonding between Hf and N has character of ionicity, which is consistent with our analysis of the bonding structure and charge densities. Fig. 3 Charge density of the DOS at (a), (b), (c), (d), (e), (f), and (g) peak from the (002) and (003) planes. Fig. 4 Molecular-orbital bonding structure of c-hf3 N4.

4 108 Communications in Theoretical Physics Vol. 59 Fig. 5 Total charge density of c-hf 3N 4 from (002) plane (a) and (003) plane (b). 3.3 Optical Properties The optical properties of c-hf 3 N 4 can be extracted from the complex dielectric function: [24 25] ε(ω) = ε 1 (ω)+ iε 2 (ω), which consists of the imaginary part ε 2 (ω) and the real part ε 1 (ω). The imaginary part can be obtained from the band structure and the real part can be calculated using the Kramers Kroning relations. [26] Figure 6 shows the calculated complex dielectric function of c-hf 3 N 4 compound for the energy range up to 20 ev. The imaginary part exhibits three structures which are labeled A, B, and C. These structures are due to the absorptive transitions from the valence bands to the conduction bands. According to the theory of crystalfield and molecular-orbital bonding structure presented in Fig. 4, structures A and B originate mainly from the transitions of N T 2 2p into Hf T 2 (d xy, d xz, d yz ) conduction bands, structure C originates mainly from the transitions of N T 2 2p into Hf T 2 (d xy, d xz, d yz ), Hf E (d x 2 y 2, d z 2), and Hf A 1 6s conduction bands. It can be seen that the structures A and B have higher intensities than the structure C. Therefore, the absorptive transitions of c-hf 3 N 4 compound are predominantly composed of structures A and B. From Fig. 6, the static state dielectric constant of c-hf 3 N 4 is found to be 10.1, which is in good agreement with the reported values (8.0, [10] 10.1 [13] ). Fig. 7 The calculated refractive index and extinction coefficient (a), absorption coefficient (b) and reflectivity (c) of c-hf 3N 4. Fig. 6 c-hf 3N 4. The calculated complex dielectric function of Other optical properties including refractive index, extinction coefficient, absorption coefficient and reflectivity are presented in Fig. 7. It can be seen from Fig. 7(a) that the static refractive index of c-hf 3 N 4 is about 3.2, which is consistent with previous work (2.88 [10] ). Additionally, the refractive index reaches to maximum value of 4.4 at 2.8 ev and the extinction coefficient reaches to maximum value of 2.8 at 5.0 ev. The absorption spectrum is displayed in Fig. 7(b). The absorption edge for c-hf 3 N 4 starts from about 1.6 ev. Moreover, it is obvious that the maximal absorption of c-hf 3 N 4 appears at 9.0 ev. Figure 7(c) shows the reflectivity of c-hf 3 N 4. According to Fig. 7(c), the reflectivity of c-hf 3 N 4 has maximum value

5 No. 1 Communications in Theoretical Physics 109 of about 100% within the energy range from 11.4 ev to 13.8 ev, which is in the ultraviolet region. Thus, c-hf 3 N 4 may be served as shields for ultraviolet radiation. 4 Conclusion The electronic, chemical bonding, and optical properties of c-hf 3 N 4 have been investigated using the firstprinciples based on the DFT. The lattice parameter optimized by GGA is in good agreement with the available experimental data and other calculational values. The band structure, DOS, charge densities and molecularorbital bonding structure of c-hf 3 N 4 are presented. Results show that c-hf 3 N 4 has a direct band gap. The lower valence bands are composed of N A 1 2s and Hf T 2 (d xy, d xz, d yz ) electrons. The upper valence bands consist of the π and σ bonding from the hybridization of Hf T 2 (d xy, d xz, d yz ) and N T 2 2p electrons. The lower conduction bands involve the π and σ antibonding from the hybridization of Hf T 2 (d xy, d xz, d yz ) and N 2p electrons. The higher conduction bands consist of the π nonbonding from Hf E (d x 2 y 2, d z 2) and the σ antibonding from the hybridization of Hf A 1 6s and N A 1 2s. The bonding between Hf and N is ionic. Moreover, the optical properties of c-hf 3 N 4 have been predicted, which are in accord with previous calculational values. References [1] S. Veprek, R.F. Zhang, M.G.J. Veprek-Heijman, S.H. Sheng, and A.S. Argon, Surf. Coat. Technol. 204 (2010) [2] S.K. Tien, C.H. Lin, Y.Z. Tsai, and J.G. Duh, J. Alloy. Compd. 489 (2010) 237. [3] G. Soto, Comput. Mater. Sci. 61 (2012) 1. [4] W. Chen and J.Z. Jiang, J. Alloy. Compd. 499 (2010) 243. [5] E. Ateser, H. Ozisik, K. Colakoglu, and E. Deligoz, Comput. Mater. Sci. 50 (2011) [6] A. Zerr, G. Miehe, and R. Riedel, Nat. Mater. 2 (2003) 185. [7] D.A. Dzivenko, A. Zerr, R. Boehler, and R. Riedel, Solid. State. Commun. 139 (2006) 255. [8] E. Horvath-Bordon, R. Riedel, A. Zerr, P. F. McMillan, G. Auffermann, Y. Prots, W. Bronger, R.D. Kniep, and P. Kroll, Chem. Soc. Rev. 35 (2006) 987. [9] D.A. Dzivenko, A. Zerr, G. Miehe, and R. Riedel, J. Alloy. Compd. 480 (2009) 46. [10] T. Chihi, M. Fatmi, B. Ghebouli, and M. Guemmaz, Solid. State. Sci. 13 (2011) [11] W.Y. Ching, Y.N. Xu, and L.Z. Ouyang, Phys. Rev. B 66 (2002) [12] P. Kroll, Phys. Rev. Lett. 90 (2003) [13] M. Xu, S. Wang, G. Yin, J. Li, Y. Zheng, L. Chen, and Y. Jia, Appl. Phys. Lett. 89 (2006) [14] P. Kroll, J. Phys. Condens. Matter 16 (2004) S1235. [15] M. Mattesini, R. Ahuja, and B. Johansson, Phys. Rev. B 68 (2003) [16] Q.J. Liu, Z.T. Liu, L.P. Feng, and H. Tian, Commun. Theor. Phys. 54 (2010) 908. [17] C. Edmiston and K. Ruedenberg, Rev. Mod. Phys. 35 (1963) 457. [18] H.L. Chen, Advanced Inorganic Chemistry, Advanced Education Press, Beijing (2005). [19] D.K. Pan, C.D. Zhao, and Z.X. Zheng, Structure of Matter, Advanced Education Press, Beijing (1989). [20] G. Kresse and D. Joubert, Phys. Rev. B 59 (1999) [21] J.P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 78 (1997) [22] H.J. Monkhorst and J.D. Pack, Phys. Rev. B 13 (1976) [23] M.D. Segall, P.J.D. Lindan, M.J. Probert, C.J. Pickard, P.J. Hasnip, S.J. Clark, and M.C. Payne, J. Phys. Condens. Matter 14 (2002) [24] R.C. Fang, Solid Spectroscopy, Chinese Science Technology University Press, Hefei (2003). [25] Y. Zhang and W.M. Shen, Basic of Solid Electronics, Zhe- Jiang University Press, Hangzhou (2005). [26] M.F. Li, Physics of Semiconductor, Science Press, Beijing (1991).