Electronic, elastic, optical properties of rutile TiO 2 under pressure: A DFT study Tariq Mahmood a,b , Chuanbao Cao a,n , Waheed S. Khan a , Zahid Usman a , Faheem K. Butt a , Sajad Hussain a a Research Centre of Materials Science, School of Material Science and Engineering, Beijing Institute of Technology, Beijing 100081, People’s Republic of China b Centre for High Energy Physics, University of the Punjab, Lahore 54590, Pakistan article info Article history: Received 28 October 2011 Accepted 19 December 2011 Available online 5 January 2012 Keywords: Ultrasoft pseudopotential Density of states Acoustic-waves-speed Refractive index Hydrostatic-pressure Debye temperature abstract The electronic, elastic constants and optical properties of rutile TiO 2 have been investigated using first principle pseudopotential method within generalized gradient approximation (GGA) proposed by Perdew–Burke–Ernzerhof (PBE). The calculated volume, bulk modulus and pressure derivative of bulk modulus are in good agreement with previous experimental and computational results. An under- estimated band gap (1.970 eV) along with the higher density of states and expanded energy bands around the fermi level is obtained. Calculated elastic constants satisfying the Born stability criteria suggest that rutile TiO 2 is mechanically stable under higher hydrostatic pressure. The acoustic wave speeds in [1 0 0], [0 1 0], [0 0 1], [1 1 0] and [451 to [1 0 0] and [0 0 1]] directions are predicted using the investigated elastic constants. The dielectric constant is identified with respect to electronic band structure and is utilized to derive the other optical properties like refractive index, energy loss function, reflectivity and absorption. The effect of hydrostatic pressure (0–70 GPa) is described for listed properties. Our investigated results are in good accord with the existing theoretical and experimental results. & 2011 Elsevier B.V. All rights reserved. 1. Introduction There are number of complex transition metal oxides (Na x CoO 2 , ZnO, GeO 2 , TeO 2 , ZrO 2 , etc.) among which TiO 2 is found naturally in abundance. Due to its broad range of applications [1], it has undergone immense experimental and theoretical research. In order to get better understanding, TiO 2 is classified in four separate polymorphs: rutile, anatase, brokite and an n-TiO 2 . All these polymorphs are normally found in inorganic from, but only anatase and rutile are important in technological applica- tions. Both rutile and anatase TiO 2 have tetragonal structures with P42/mnm (1 3 6) and I41/amd (1 4 1) space groups, respectively. They have versatile range of industrial applications such as optics [2], electronics [3], gas-sensing, painting [4] and dye-sensitized solar cells [5]. Because of long term chemical steadiness, marve- lous photocatalytic activity and photoelectrochemical hydrogen production through water splitting, researchers put their atten- tion on TiO 2 [6–13]. Thermodynamically rutile TiO 2 is stable at ordinary pressure and temperatures up to its melting point 1830 K [14]. Rutile TiO 2 is a poor absorber of visible light due to its wide band gap [15] (3.0 eV), which limits its use as an ideal photo electrode. To get better efficiency much efforts have been done like doping by metal and nonmetal such as Fe, Mo, Cr, Co, C and N [16–20] or introducing oxygen vacancies [21] to activate the visible region of TiO 2 . First principle studies are optimistic approaches, which provide better experimental parameters leading to rapid material improve- ments economically. Extensive theoretical research on the electro- nic, elastic, optical and phonon studies of rutile titanium dioxide have been reported in the previous research articles [22–28], employing different methods (Pseudopotential Hartree-Fock (PHF), orthogonalized linear combination of atomic orbitals (OLCAO), full- potential linearized augmented plane-wave (FP-LAPW), etc.). Elastic properties are important for solid materials because they relate various basic solid-state physical properties such as equations of state, phonon spectra, thermal expansion, specific heat and Debye temperature. Among many theoretical investigations [29–34] few studies have discussed its elastic and optical properties with hydrostatic pressure. Moreover the sound velocities, load deflection, internal strain, thermo-elastic stress and fracture toughness [35,36] are calculated through the knowledge of elastic constants. Al-Khatatbeh et al. [37] has studied the different phase transitions of rutile TiO 2 structure at high pressures with and without temperature application both Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/physb Physica B 0921-4526/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2011.12.114 n Corresponding author. Tel.: þ86 10 6891 3792; fax: þ86 10 6891 2001. E-mail address: cbcao@bit.edu.cn (C. Cao). Physica B 407 (2012) 958–965