Electronic, Optical, Mechanical and Lattice Dynamical Properties of MgBi2O6: A First-Principles Study
Electronic, Optical, Mechanical and Lattice Dynamical Properties of MgBi2O6: A First-Principles...
Liu, Lin;Wang, Dianhui;Zhong, Yan;Hu, Chaohao
2019-03-27 00:00:00
applied sciences Article Electronic, Optical, Mechanical and Lattice Dynamical Properties of MgBi O : A First-Principles Study 2 6 1 1 , 2 1 , 2 1 , 2 , Lin Liu , Dianhui Wang , Yan Zhong and Chaohao Hu * School of Materials Science and Engineering, Guilin University of Electronic Technology, Guilin 541004, China; liulinguet@163.com (L.L.); dhwang@guet.edu.cn (D.W.); yanzhong@guet.edu.cn (Y.Z.) Guangxi Key Laboratory of Information Materials, Guilin University of Electronic Technology, Guilin 541004, China * Correspondence: chaohao.hu@guet.edu.cn Received: 28 February 2019; Accepted: 18 March 2019; Published: 27 March 2019 Abstract: Electronic structure, optical, mechanical, and lattice dynamical properties of the tetragonal MgBi O are studied using a first-principles method. The band gap of MgBi O calculated from 2 6 2 6 the PBE0 hybrid functional method is about 1.62 eV and agrees well with the experimental value. The calculations on elastic constants show that MgBi O exhibits mechanical stability and strong 2 6 elastic anisotropy. The detailed analysis of calculated optical parameters and effective masses clearly indicate that MgBi O has strong optical response in the visible light region and high separation 2 6 efficiency of photoinduced electrons and holes. Keywords: MgBi O ; optical properties; mechanical anisotropy; lattice dynamics; first-principles 2 6 calculations 1. Introduction Currently, Bi-based oxides have received considerable attention due to their particular physical properties and wide applications in different fields like multiferroics [1,2], superconductivity [3,4], 3+ and photocatalysis [5,6]. Generally, Bi exists as the trivalent state (Bi ) in most of the Bi-based oxides like Bi O [7], BiVO [8], Bi WO [9], Bi Sn O [10], BiFeO [11], and BiMnO [12]. However, some 2 3 4 2 6 2 2 7 3 3 5+ Bi-containing oxides with the unusual pentavalent state (Bi ) have also attracted research interest. For example, NaBiO has been found to show the absorption of visible light and can be used as a prominent material for photooxidation of organics [13]. A recent work by Gong et al. [14] shows that AgBiO can self-produce significant amounts of reactive oxygen species without light illumination or any other additional oxidant and has an excellent oxidizing reactivity. BaBiO , as one kind of Bi-based 3+ 5+ oxides containing Bi and Bi mixed valent states, has been found to show the potential use for the absorber of all-oxide photovoltaics [15] and can be an active photocatalyst under visible-light irradiation [16]. 5+ MgBi O adopting the trirutile-type structure is also a Bi -containing compound. 2 6 Kumada et al. [17] first successfully prepared MgBi O by the low-temperature hydrothermal method 2 6 and characterized its crystal structure in detail. In 2003, Mizoguchi et al. [18] investigated the optical and electrical properties of MgBi O and found that MgBi O is a degenerate n-type semiconductor 2 6 2 6 with the band gap of about 1.8 eV, and it is possible to produce an optical band gap that extends into 5+ the visible region of the spectrum by tuning the Bi 6s–O 2p interaction in order to produce a disperse conduction band. The band structure makes MgBi O a good candidate of visible light-sensitive 2 6 photocatalysts for decomposition of organic species. Comparing with other pentavalent bismuthates such as LiBiO , NaBiO , KBiO , ZnBi O , SrBi O6, AgBiO , BaBi O , and PbBi O , MgBi O does not 3 3 3 2 6 2 3 2 6 2 6 2 6 possess the highest photocatalytic activity, but there is no adsorption observed in the decomposition Appl. Sci. 2019, 9, 1267; doi:10.3390/app9071267 www.mdpi.com/journal/applsci Appl. Sci. 2019, 9, 1267 2 of 13 of methylene blue [19]. It may be a good idea to adjust the wide band gap of some traditional photocatalysts such TiO by building complex compounds with MgBi2O . In our recent work, the 2 6 photocatalytic activity of MgBi O has been found to be significantly enhanced via constructing 2 6 AgBr/MgBi O heterostructured composites [20]. Theoretically, the band gap of MgBi O was 2 6 2 6 calculated to be about 1.10 eV using the Heyd-Scuseria-Ernzerhof (HSE) functional method within the framework of the density functional theory (DFT), and was found to be widely tuned by applying external strain [21]. On the basis of theoretical calculations, however, the deeper understanding of the physical properties of MgBi O is still in lacking. In this work, we investigated the electronic structure, 2 6 optical, mechanical, and lattice dynamical properties MgBi O using first-principles calculations. 2 6 2. Computational Details All calculations were carried out using the Vienna ab-initio simulation package (VASP) [22,23], which is an implement of DFT. The projector augmented wave (PAW) method [24,25] was used to describe the ion-electron interactions. The generalized gradient approximation (GGA) parameterized by Perdew, Burke and Ernzerhof (PBE) [26] was applied for the exchange-correlation function. The cutoff energy for the plane wave basis set was fixed at 500 eV. The Brillouin zone is sampled by a Monkhorst-Pack type k-point mesh with density of 2 0.03 Å . Full relaxation of MgBi O unit 2 6 cell was performed until the changes in total energy and force on each atom are less than 10 eV and 10 eV/Å, respectively. In this work, Mg-3s, Mg-2p, Bi-6s, Bi-6p, O-2s, and O-2p states are taken as valence electrons. Based on the DFT calculation, a more accurate screened coulomb hybrid functional (HF) developed by Heyd, Scuseria, and Ernzerhof (PBE0) [27,28] (containing 30% of the exact exchange, and 70% of the PBE exchange, and 100% of the PBE correlation energy in this work) was used to calculate the electronic structure. In the calculations of optical properties, a dense k-point density of 2 0.015 Å including the G point was used to ensure the accurate precision. Moreover, 88 extra empty bands are included in the calculations to hold the excited electronic states. Phonon calculations were performed within the framework of density functional perturbation theory to investigate the lattice dynamical properties of MgBi O . The phonon dispersion curve and phonon density of states 2 6 (PDOS) were calculated by the PHONOPY code [29] on the basis of force constants obtained from VASP code. In the phonon calculations, a 2 2 1 supercell was used. 3. Results and Discussion 3.1. Optimized Crystal Structure of MgBi O 2 6 At ground state, MgBi O crystallizes in a tetragonal trirutile-type structure with P4 /mnm 2 6 2 space group. It can be seen from the crystal structure depicted in Figure 1 that BiO and MgO 6 6 octahedrons connect with the sharing edges and stack along the [001] direction by 2:1 ratio. In the [110] and 110 directions, BiO and MgO octahedrons are connected with each other by sharing O 6 6 vertices. The optimized lattice constants listed in Table 1 are in good agreement with the experimental values [17]. The BiO octahedrons are slightly distorted and the bond lengths of Bi-O(8j) are not completely identical. Appl. Sci. 2019, 9, x FOR PEER REVIEW 3 of 13 Appl. Sci. 2019, 9, 1267 3 of 13 Figure 1. Crystal structure of the trirutile-type MgBi O represented as two different views. Figure 1. Crystal structure of the trirutile-type MgBi 2 2O 6 6 represented as two different views. Table 1. Optimized structural parameters of MgBi O , Bi-O and Mg-O interatomic distances. 2 6 Table 1. Optimized structural parameters of MgBi2O6, Bi-O and Mg-O interatomic distances. The The experimental values [17] are listed in brackets for comparison. experimental values [17] are listed in brackets for comparison. Atomic Coordinates (Fractional) Lattice Constants Atomic Coordinates (Fractional) Lattice Constants (Å) Atom Site x y z (Å) Atom Site x y z a = 4.920 (4.826) Bi 4e 0 0 0.333 (0.332) a = 4.920 (4.826) Bi 4e 0 0 0.333 (0.332) c = 9.924 (9.719) Mg 2a 0 0 0 c = 9.924 (9.719) Mg 2a 0 0 0 O1 4f 0.302 (0.305) 0.302 (0.305) 0 O2 8j 0.309 (0.307) 0.309 (0.307) 0.336 (0.335) O1 4f 0.302 (0.305) 0.302 (0.305) 0 BiO octahedron MgO octahedron 6 O2 8j 0.309 (6 0.307) 0.309 (0.307) 0.336 (0.335) Bi-O(1) 2.156 (2.114) 2 Mg-O(1) 2.107 (2.084) 2 BiO6 octahedron MgO6 octahedron Bi-O(2) 2.153 (2.102) 2 Mg-O(2) 2.103 (2.073) 4 Bi-O(1) 2.156 (2.114) × 2 Mg-O(1) 2.107 (2.084) × 2 Bi-O(3) 2.141 (2.084) 2 Bi-O(2) 2.153 (2.102) × 2 Mg-O(2) 2.103 (2.073) × 4 3.2. Bi-O Electr (3onic ) Properties 2.14of 1 (MgBi 2.084)O × 2 2 6 To study the electronic property of tetragonal MgBi O , the electronic band structure along high 2 6 3.2. Electronic Properties of MgBi2O6 symmetry directions in the Brillouin zone (BZ) and density of states are calculated. The band structure calculated by conventional DFT (dotted line in Figure 2) shows that there is a bit of overlap between To study the electronic property of tetragonal MgBi2O6, the electronic band structure along high the conduction band and valence band, indicating the metallic feature of MgBi O . This contradicts symmetry directions in the Brillouin zone (BZ) and density of states are calculated. The band 2 6 the experimental findings. It is well known that DFT calculations do not take into account the effects of structure calculated by conventional DFT (dotted line in Figure 2) shows that there is a bit of overlap electron excitation and thus tend to underestimate the electronic band gap. To acquire the more accurate between the conduction band and valence band, indicating the metallic feature of MgBi2O6. This results, the calculations based on the HF PBE0 method are further performed. The HF corrected band contradicts the experimental findings. It is well known that DFT calculations do not take into structure (solid line in Figure 2) shows that MgBi O is a direct semiconductor with a band gap of account the effects of electron excitation and thus tend to underestimate the electronic band gap. To 2 6 about 1.62 eV, which is well consistent with the experimental measured data (1.6~1.8 eV) [18–20] acquire the more accurate results, the calculations based on the HF PBE0 method are further and larger than the previously calculated value (1.10 eV) based on the HF method [21]. The valence performed. The HF corrected band structure (solid line in Figure 2) shows that MgBi2O6 is a direct band near the Fermi level (E ) is flat, while the dispersion of the conduction band close to the E is semiconductor with a band ga F p of about 1.62 eV, which is well consistent with the experimental F relative strong. measured data (1.6~1.8 eV) [18–20] and larger than the previously calculated value (1.10 eV) based on the HF method [21]. The valence band near the Fermi level (EF) is flat, while the dispersion of the conduction band close to the EF is relative strong. Appl. Sci. 2019, 9, x FOR PEER REVIEW 4 of 13 Appl. Sci. 2019, 9, 1267 4 of 13 Figure 2. Calculated electronic band structure of MgBi O using hybrid functional PBE0 method. 2 6 Figure 2. Calculated electronic band structure of MgBi2O6 using hybrid functional PBE0 method. Band structure from conventional DFT calculation (dotted line) is also presented for comparison. Band structure from conventional DFT calculation (dotted line) is also presented for comparison. The effective mass (m ) of carriers is an important parameter, because it determines the transfer and separation The effective efficiency mass (m of) of c electr aons rriers is and an holes, important par and directly ameter, bec influences ause the photophysical it determines the tr properties ansfer of and sep semiconductors. aration efficienc m can y o be f electron calculated s anas d holes, an follows: d directly influences the photophysical properties of semiconductors. m can be calculated as follows: 1 1 ¶ E(k) = , i, j = x, y, z, (1) m } ¶k k i j = ,𝑖, 𝑗 = 𝑥,𝑦,𝑧 , ij (1) where E (k) represents the band energy, k is the wave vector, and } is the reduced Planck constant. where En(k) represents the band energy, k is the wave vector, and ℏ is the reduced Planck constant. * * For MgBi O , the effective electron mass (m ) at the conduction band and hole mass (m ) at the 2 6 e * * For MgBi2O6, the effective electron mass (me ) at the conduction band and hole mass (mh ) at the valence band at the G point are calculated and listed in Table 2. The calculated tensors of m clearly valence band at the Γ point are calculated and listed in Table 2. The calculated tensors of m clearly * * * show that m is fairly isotropic and m shows a relatively strong anisotropy. m along the [001] e * * * h h show that me is fairly isotropic and mh shows a relatively strong anisotropy. mh along the [001] direction is larger than those along the [100] and [010] directions. The values of m in Table 2 are also direction is larger than those along the [100] and [010] directions. The values of me in Table 2 are also comparable to the previously calculated value (0.277) for MgBi O [21]. Moreover, the values of m 2 6 * comparable to the previously calculated value (0.277) for MgBi2O6 [21]. Moreover, the values of mh are distinctly larger than those of m , which indicates that the mobility of holes at the valence band is are distinctly larger than those of me , which indicates that the mobility of holes at the valence band is obviously slower than that of electrons at the conduction band. The big difference in mobility between obviously slower than that of electrons at the conduction band. The big difference in mobility electrons and holes is undoubtedly beneficial to the separation of charge carriers and the reduction between electrons and holes is undoubtedly beneficial to the separation of charge carriers and the * * of the recombination rate of electron-hole pairs. In addition, the values of m /m of MgBi O e * 2* 6 reduction of the recombination rate of electron-hole pairs. In addition, the values of mh /me of are in the range of 6.2~10.9, being larger than the corresponding value (2.1) of anatase TiO [30] MgBi2O6 are in the range of 6.2~10.9, being larger than the corresponding value (2.1) of anatase TiO2 widely investigated as an important photocatalytic material. Thus, semiconducting MgBi O can be 2 6 [30] widely investigated as an important photocatalytic material. Thus, semiconducting MgBi2O6 can considered as a photocatalyst with highly efficient separation of photoinduced electrons and holes. be considered as a photocatalyst with highly efficient separation of photoinduced electrons and holes. * * Table 2. Calculated effective electron mass (m ) and hole mass (m ) along the three principal directions at the G point. All values are in units of free electron mass (m ). * * Table 2. Calculated effective electron mass (me ) and hole mass (mh ) along the three principal directions at the Γ point. All values are in units of free electron mass (m0). Conduction Band Valence Band 0 1 0 1 0.221 0 0 1.572 0 0 Conduction Band Valence Band @ A @ A G 0 0.206 0 0 1.370 0 0.221 0 0 1.572 0 0 0 0 0.171 0 0 1.871 Γ 0 0.206 0 0 1.370 0 0 0 0.171 0 0 1.871 Appl. Sci. 2019, 9, x FOR PEER REVIEW 5 of 13 Appl. Sci. 2019, 9, 1267 5 of 13 The calculated electronic total and partial density of states (DOS) of MgBi2O6 is shown in Figure 3. It can be clearly seen that the DOS near the top of the valence band is derived from the Bi-5d, The calculated electronic total and partial density of states (DOS) of MgBi O is shown in Figure 3. 2 6 Mg-2p and O-2p states. The bottom of the conduction band is mainly composed of O-2p, Bi-6s, and It can be clearly seen that the DOS near the top of the valence band is derived from the Bi-5d, Mg-2p and Mg-3s states. The strong hybridizations between Bi-5d and O-2p states in BiO6 octahedrons and O-2p states. The bottom of the conduction band is mainly composed of O-2p, Bi-6s, and Mg-3s states. bonding interactions between Mg-2p or Mg-3s and O-2p states in MgO6 octahedrons should be The strong hybridizations between Bi-5d and O-2p states in BiO octahedrons and bonding interactions directly responsible for the structural stability of MgBi2O6. between Mg-2p or Mg-3s and O-2p states in MgO octahedrons should be directly responsible for the structural stability of MgBi O . 2 6 Figure 3. Calculated electronic density of states of MgBi O using PBE0 method. 2 6 Figure 3. Calculated electronic density of states of MgBi2O6 using PBE0 method. To get a deeper understanding of the bonding nature of Bi, Mg, and O atoms, the electron localization To get a deeper understandi function (ELF) was further ng of calculated. the bondi Accor ng na ding ture of Bi, Mg, a to the original n definition, d O atom the s, the el ELF values ectron ar loca e scaled lization f in the unct range ion ( frELF om) wa 0 to s f 1. The urther high calc ELF ulat means ed. Accordin strong covalent g to the orig bonding inal def interaction inition, t between he ELF atoms values and are sc theale very d in the range from 0 to low ELF close to 0 corr 1. The esponds high to the ELF mean ionic bonding. s strong covalent bonding interaction Figure 4 shows the calculated ELF between atoms and the v for (110) plane of MgBi ery low E O passing LF close to 0 co through Bi, rre Mg, sponds to the ionic bond and O atoms. The ELF ing. Figur values e between 4 shows the Mg 2 6 and calcO ulat atoms ed EL ar F fo e extr r (1 emely 10) pllow ane o , indicating f MgBi2Othe 6 passin ionicg th bonding rough Bi, in MgO Mg, and O octahedr atoms. The ons. This EL canF v be a well lues understood between Mg on and O the basis atoms ar of the e extreme previouslyly low obtained , indic recognition ating the on ionic MgO, bonding which in is MgO usually 6 oct consi ahedrons. dered as This c one a kind n be of well classical underionically stood on t bonded he basis o compounds. f the previous Thely obt maximal ained reco value gnit of ELF ion on M between gO, Bi which i and Os atoms usually reaches considered aboutas one 0.61, which kind of clearly classical ion identifies ically b the partially onded comp Bi-O ou covalent nds. The m bonding aximal v interaction alue of EL inF BiO betwoctahedr een Bi aons. nd O atoms reaches about 0.61, which clearly identifies the partially Bi-O covalent bonding interaction in BiO6 octahedrons. Appl. Sci. 2019, 9, x FOR PEER REVIEW 6 of 13 Appl. Sci. 2019, 9, 1267 6 of 13 Figure 4. Calculated electron localization function for (110) plane across Bi, Mg, and O atoms. Figure 4. Calculated electron localization function for (110) plane across Bi, Mg, and O atoms. 3.3. Optical Properties of MgBi O 2 6 3.3. Op In ti or cal der Prto operti understand es of MgBi the 2O6optical performance of semiconducting MgBi O , we calculated its 2 6 dielectric functions using the hybrid functional PBE0 method, and further computed its optical In order to understand the optical performance of semiconducting MgBi2O6, we calculated its properties such as complex refractive index n, extinction coefficient k, reflectivity R, absorption dielectric functions using the hybrid functional PBE0 method, and further computed its optical coefficients a, and electron energy-loss function L. The calculated dielectric functions are depicted in properties such as complex refractive index n, extinction coefficient k, reflectivity R, absorption Figure 5. It can be clearly seen that the static dielectric function is found to be 4.1 at 0 eV. With the coefficients α, and electron energy-loss function L. The calculated dielectric functions are depicted in increase of the polarization intensity and energy, the dielectric function, the real part # is also gradually Figure 5. It can be clearly seen that the static dielectric function is found to be 4.1 at 0 eV. With the increased and reaches a maximum value of 5.4 when the energy value is about 2.8 eV. When the photon increase of the polarization intensity and energy, the dielectric function, the real part ε1 is also energy reaches 1.6 eV, which is the width of electronic band gap, the electrons in the valence bands gradually increased and reaches a maximum value of 5.4 when the energy value is about 2.8 eV. begin to excite and transit to conduction bands. As the carrier concentration increases, the degree of When the photon energy reaches 1.6 eV, which is the width of electronic band gap, the electrons in polarization decreases and the dielectric function decreases slightly. With the further increment of the valence bands begin to excite and transit to conduction bands. As the carrier concentration photon energy, the dielectric function values begins to fluctuate, which corresponds to the change of increases, the degree of polarization decreases and the dielectric function decreases slightly. With carrier concentration in the crystal. The imaginary part # reflects the transition between occupied and the further increment of photon energy, the dielectric function values begins to fluctuate, which non-occupied electrons and can be used to characterize the light absorption behavior of the crystal. corresponds to the change of carrier concentration in the crystal. The imaginary part ε2 reflects the The first two peaks of the imaginary part of the dielectric function # are, respectively, at about 2.0 and transition between occupied and non-occupied electrons and can be used to characterize the light absorption behavior of the crystal. The first two peaks of the imaginary part of the dielectric function Appl. Sci. 2019, 9, x FOR PEER REVIEW 7 of 13 Appl. Sci. 2019, 9, 1267 7 of 13 ε2 are, respectively, at about 2.0 and 3.0 eV, which probably results from the electron transition from the top of the valence bands to the bottom of the conduction bands. 3.0 eV, which probably results from the electron transition from the top of the valence bands to the bottom of the conduction bands. Figure 5. Calculated complex dielectric function of MgBi O . 2 6 Figure 5. Calculated complex dielectric function of MgBi2O6. The calculated refractive index n, extinction coefficient k, absorption coefficient a, reflectivity R, The calculated refractive index n, extinction coefficient k, absorption coefficient α, reflectivity R, and electron energy loss function L of MgBi O are shown in Figure 6. As presented in Figure 6a, 2 6 and electron energy loss function L of MgBi2O6 are shown in Figure 6. As presented in Figure 6a, the the higher value of n is in the energy range of 1.5–5.8 eV and the corresponding wavelength range is higher value of n is in the energy range of 1.5–5.8 eV and the corresponding wavelength range is from 214 to 826 nm, indicating that MgBi O has a strong refractive effect in both ultraviolet (UV) and 2 6 from 214 to 826 nm, indicating that MgBi2O6 has a strong refractive effect in both ultraviolet (UV) visible light region. The value of k rapidly starts to increase from 2.0 eV, also showing a response in and visible light region. The value of k rapidly starts to increase from 2.0 eV, also showing a the visible and UV light region. The calculated in Figure 6c shows that the light absorption edge response in the visible and UV light region. The calculated α in Figure 6c shows that the light is about 1.6 eV and is comparable with the band gap calculated by the PBE0 method. The value of absorption edge is about 1.6 eV and is comparable with the band gap calculated by the PBE0 optical absorption edge also agrees with literatural values [18,20]. With the increase of energy, a also method. The value of optical absorption edge also agrees with literatural values [18,20]. With the gradually increases and a series of absorption peaks appear in the energy range from 1.6 to 27 eV. increase of energy, α also gradually increases and a series of absorption peaks appear in the energy Combining with the calculated dielectric function and density of states, we can find that the first two range from 1.6 to 27 eV. Combining with the calculated dielectric function and density of states, we absorption peaks at 4.5 and 6.0 eV are probably related to the electron migration of the O-2p, Bi-6s, can find that the first two absorption peaks at 4.5 and 6.0 eV are probably related to the electron Bi-5d, and Mg-2p states. The reflectivity R and the electron energy loss function L can be used to migration of the O-2p, Bi-6s, Bi-5d, and Mg-2p states. The reflectivity R and the electron energy loss represent the resonant frequency of the incident light and the resonant frequency of the plasma. As function L can be used to represent the resonant frequency of the incident light and the resonant shown in Figure 6d, the average value of R is about 13.8%, indicating that MgBi O can be used as a 2 6 frequency of the plasma. As shown in Figure 6d, the average value of R is about 13.8%, indicating light absorbing material. The calculated L presented in Figure 6e completely locates in the continuous that MgBi2O6 can be used as a light absorbing material. The calculated L presented in Figure 6e energy range of 0–45 eV, indicating that the characteristics of plasma oscillation in MgBi O are not 2 6 completely locates in the continuous energy range of 0–45 eV, indicating that the characteristics of obvious. This is strongly different from the behavior appearing in Bi Sn O [31]. 2 2 7 plasma oscillation in MgBi2O6 are not obvious. This is strongly different from the behavior appearing in Bi2Sn2O7 [31]. Appl. Sci. 2019, 9, x FOR PEER REVIEW 8 of 13 Appl. Sci. 2019, 9, 1267 8 of 13 Figure 6. Calculated optical properties of MgBi O : (a) complex refractive index n, (b) extinction 2 6 coefficient k, (c) absorption coefficient a, (d) reflectivity R, and (e) electron energy loss function L. Figure 6. Calculated optical properties of MgBi2O6: (a) complex refractive index n, (b) extinction coefficient k, (c) absorption coefficient α, (d) reflectivity R, and (e) electron energy loss function L. 3.4. Mechanical Properties of MgBi O 2 6 To investigate the mechanical properties of tetragonal MgBi O , the six independent elastic 3.4. Mechanical Properties of MgBi2O6 2 6 constants C are calculated by applying finite distortions of the lattice. The results are listed in Table 3. ij To investigate the mechanical properties of tetragonal MgBi2O6, the six independent elastic For the tetragonal system, the mechanical stability criterion [32] is given by the following relationships: constants Cij are calculated by applying finite distortions of the lattice. The results are listed in Table 3. For the tetragonal system, the mechanical stability criterion [32] is given by the following (C C ) > 0, (C + C 2C ) > 0, 11 12 11 33 13 relationships: C > 0, C > 0, C > 0, C > 0, 11 33 44 66 (C11 − C12) > 0, (C11 + C33 − 2C13) > 0, (2C + C + 2C + 4C ) > 0, (2) 11 33 12 13 C11 > 0, C33 > 0, C44 > 0, C66 > 0, The calculated values of C in Table 3 satisfy the stability criterion mentioned above, indicating ij that the tetragonal MgBi O has mechanical stability. As listed in Table 3, C is significantly smaller (2C11 + C33 + 2C12 + 4C13) > 0, (2) 2 6 11 Appl. Sci. 2019, 9, 1267 9 of 13 than C , indicating that the chemical bonding strength in the (100) and (010) directions is significantly weaker than the bonding strength in the (001) direction. In addition, C is obviously smaller than C , which demonstrates that it is easier for shear deformation to occur along the (001) direction in comparison with the (010) direction. The shear elastic anisotropy of the material can be estimated by the relation A = 2C /(C C ). Typically, if A has a value of 1, meaning that the material is 66 11 12 isotropic. The more the value of A deviates from 1, the elastic anisotropy would be more prominent. For MgBi O , the calculated A value is 4.6, indicating that MgBi O is highly anisotropic. 2 6 2 6 Table 3. Calculated elastic constants C , bulk modulus B, shear modulus G, Young’s modulus E, and ij Poisson’s ratio u of MgBi O . 2 6 Elastic Constants (GPa) Mechanical Moduli (GPa) u C C C C C C B G E 11 12 13 33 44 66 171.8 110.4 98.1 280.3 66.2 141.9 137.7 76.2 193.0 0.27 For the tetragonal system, the bulk modulus B and the shear modulus G are calculated as follows: B = (2C + C + 2C + 4C )/9, (3) 11 33 12 13 G = (2C + C C 2C + 6C + 3C )/15, (4) 11 33 12 13 44 66 Young’s modulus E and Poisson’s ratio u can be estimated from the bulk and shear moduli E = 9BG/(G + 3B), (5) u = (3B 2G)/[2(3B + G)], (6) The calculated B, G, E, and u are listed in Table 3. The B/G value is about 1.81. According to Pugh’s criteria of brittleness and ductility [33], MgBi O exhibits some toughness, but it is not obvious, 2 6 which is consistent with the Poisson’s ratio u = 0.27. In addition, the elastic anisotropy of MgBi O 2 6 can be directly determined by the direction-dependent Young’s modulus. The Young’s modulus in a specific direction can be expressed by the elastic compliances (s ): E = , (7) with s = A A A A s , (8) 1i 1j 1k 1l ijkl where A is the matrix associated with the change of axes: A = cos q sin j, A = sin q sin j, A = cos j, (9) 11 12 13 Using the reduction of s for the tetragonal crystal class [34], the reduced Young’s modulus with ijkl orientation can be expressed as follows: E = n o , (10) sin 2j sin q 4 s + s 2 s s sin q + s cos q + 2s + s [ ( )] ( ) 11 66 11 12 33 13 44 4 4 The calculated directional dependence of Young’s modulus depicted in Figure 7 is a significantly distorted spherical shape. The calculated values along the [001], [110], and [-110] directions are obviously larger than those along the [100] and [010] directions. Tetragonal MgBi O exhibits the 2 6 highly elastic anisotropy. Appl. Sci. 2019, 9, x FOR PEER REVIEW 10 of 13 Appl. Sci. 2019, 9, 1267 10 of 13 Figure 7. Directional dependence of Young’s modulus (in GPa) of MgBi O . 2 6 Figure 7. Directional dependence of Young’s modulus (in GPa) of MgBi2O6. 3.5. Lattice Dynamical Properties of MgBi O 2 6 3.5. Lattice Dynamical Properties of MgBi2O6 The phonon dispersion curves along high symmetry directions and the phonon density of states are shown in Figure 8. There are 18 atoms in MgBi O cells, so there is a total of 54 vibration modes in The phonon dispersion curves along high symmetry directions and the phonon density of states 2 6 the are phonon shown in spectr Figuum, re 8. The including re are thr 18 at eeoacoustic ms in MgB modes i2O6 cell and s, 51 so t optical here ismodes. a total o The f 54 vibr calculated ation modes in phonon spectrum shows no imaginary frequency, indicating the dynamical stability of MgBi O . Along F-Q the phonon spectrum, including three acoustic modes and 51 optical modes. The calculated phonon 2 6 and spect Qr-um Z paths show in s no the im Brillouin aginaryzone, frequenc the vibration y, indicatmodes ing the dyn are double amical degenerate. stability of MgBi The acoustic 2O6. Alomodes ng F-Q phonons reflect the vibration of the centroid of the original cell and occupy the 0–3 THz frequency and Q-Z paths in the Brillouin zone, the vibration modes are double degenerate. The acoustic modes rphonons ref egion. Among lect t the he vibrat three acoustic ion of the cen modes troid of passing the o thrroug iginh althe cellG an point, d occupy the longitudinal the 0–3 THz fre mode quency has higher frequency in comparison with the other two transverse acoustic modes. There is no gap at region. Among the three acoustic modes passing through the Γ point, the longitudinal mode has the higher frequency frequency range in comp of about aris3 on wi THzth the other two tr between the longitudinal ansverseacoustic acoustic mode and transverse s. There is no optical gap modes. at the Thus, phonons can transition from the acoustic mode to the optical mode without any momentum frequency range of about 3 THz between the longitudinal acoustic and transverse optical modes. transfer Thus, phono [35]. n Further s can transit combining ion from with the the acoustic calculated mode to the opti PDOS shown cain l mode wi Figure 8thout a , we can ny momentum find that the coupled vibrations of Bi, Mg, and O atoms including the O-Bi-O and O-Mg-O bending vibrations in transfer [35]. Further combining with the calculated PDOS shown in Figure 8, we can find that the BiO coupled and vibr MgO ations octahedr of Bi, Mg, and ons within O at the oms frequency includin range g the O-B from i-O 3 to and O 9.8 THz -Mg-O and bending v the Bi-O iand brations Mg-O in 6 6 str BiO etching 6 and Mg vibrations O6 octahedrons wi in the frequency thin the f range requency range from 12 to 16.4 from 3 THz ar to e9.8 obvious. THz an The d the phonon Bi-O abranch nd Mg- es O above stretching v 16.4 THz ibrations in are completely the frequency ascribedrange from to the vibrations 12 to 16 of.4 O THz a atoms. re obvious. The phonon branches above 16.4 THz are completely ascribed to the vibrations of O atoms. Appl. Sci. 2019, 9, x FOR PEER REVIEW 11 of 13 Appl. Sci. 2019, 9, 1267 11 of 13 Figure 8. Calculated phonon dispersion curves and phonon density of states of MgBi O . 2 6 Figure 8. Calculated phonon dispersion curves and phonon density of states of MgBi2O6. 4. Conclusions 4. Conclusions In this work, we have investigated the structural, electronic, optical, mechanical, and lattice dynamical In this wo properties rk, we h of the ave trir inv utile-type estigated t MgBi he struct O u inral detail , electroni usingc, optica the first-principles l, mechanicacalculations. l, and lattice 2 6 dynamical properties of the trirutile-type MgBi2O6 in detail using the first-principles calculations. The calculated band gap of MgBi O from the Heyd-Scuseria-Ernzerhof hybrid functional PBE0 2 6 electrical The calculated is aboutban 1.62 d gap eV of MgB and consistent i2O6 from with ththe e Hey experime d-Scuser ntal ia-Er data nzerho (1.6~1.8 f hybr eV). id funct The calculated ional PBE0 electrical is about 1.62 eV and consistent with the experimental data (1.6~1.8 eV). The calculated effective masses show that the mobility of holes at conduction band is obviously slower than that of electr effect ons ive ma at valence sses show t band, hat indicating the mobilit high y of hole separation s at conduct efficiency ion bof and electr is obviou ons and sly slow holeser t in h MgBi an that O of . 2 6 electrons at valence band, indicating high separation efficiency of electrons and holes in MgBi2O6. The calculated results of optical parameters clearly show that MgBi O has strong light response in 2 6 the The calc visible ul light ated resu region lts of o and can ptical be p used arame asters cle a lighta absorbing rly show that Mg material. BiThe 2O6 has stro calculated ng light resp elastic constants onse in the visible light region and can be used as a light absorbing material. The calculated elastic constants and phonon dispersion clearly show that MgBi O is mechanically and dynamically stable. Moreover, 2 6 MgBi and phonon O exhibits disper significantly sion clearly elastic show anisotr that MgBi opy. 2O6 is mechanically and dynamically stable. 2 6 Moreover, MgBi2O6 exhibits significantly elastic anisotropy. Author Contributions: Conceptualization, C.H. and Y.Z.; methodology, D.W.; software, D.W.; validation, L.L., D.W. and Y.Z.; formal analysis, L.L.; investigation, L.L.; resources, C.H.; data curation, L.L.; writing—original draft Author Contributions: conceptualization, C.-H.H. and Y.Z.; methodology, D.-H.W.; software, D.-H.W.; preparation, L.L.; writing—review and editing, D.W., Y.Z., C.H.; visualization, L.L.; supervision, C.H.; project validation, L.L., D.-H.W. and Y.Z.; formal analysis, L.L.; investigation, L.L.; resources, C.-H.H.; data curation, administration, C.H.; funding acquisition, C.H. L.L.; writing—original draft preparation, L.L.; writing—review and editing, D.-H.W., Y.Z., C.-H.H.; Funding: This research was funded by the National Natural Science Foundation of China, grant number 11464008, visualization, L.L.; supervision, C.-H.H.; project administration, C.-H.H.; funding acquisition, C.-H.H. the Natural Science Foundation of Guangxi Zhuang Autonomous Region, Grant Number 2014GXNSFGA118001 and 2016GXNSFGA380001, the Talents Project of Guilin University of Electronic Technology, and Guangxi Key Funding: This research was funded by the National Natural Science Foundation of China, grant number Laboratory of Information Materials, Grant Number 1210908-215-Z and 171034-Z. 11464008, the Natural Science Foundation of Guangxi Zhuang Autonomous Region, Grant Number Conflicts of Interest: The authors declare no conflict of interest. 2014GXNSFGA118001 and 2016GXNSFGA380001, the Talents Project of Guilin University of Electronic Technology, and Guangxi Key Laboratory of Information Materials, Grant Number 1210908-215-Z and 171034-Z References Conflicts of Interest: The authors declare no conflict of interest. 1. Wang, J.; Neaton, J.; Zheng, H.; Nagarajan, V.; Ogale, S.; Liu, B.; Viehland, D.; Vaithyanathan, V.; Schlom, D.; Waghmare, U. Epitaxial BiFeO multiferroic thin film heterostructures. Science 2003, 299, 1719. [CrossRef] References [PubMed] 2. Jeen, H.; Singh-Bhalla, G.; Mickel, P.R.; Voigt, K.; Morien, C.; Tongay, S.; Hebard, A.; Biswas, A. Growth and 1. Wang, J.; Neaton, J.; Zheng, H.; Nagarajan, V.; Ogale, S.; Liu, B.; Viehland, D.; Vaithyanathan, V.; Schlom, characterization of multiferroic BiMnO thin films. J. Appl. Phys. 2011, 109, 074104. [CrossRef] D.; Waghmare, U. Epitaxial BiFeO3 multiferroic thin film heterostructures. Science 2003, 299, 1719. 2. Jeen, H.; Singh-Bhalla, G.; Mickel, P.R.; Voigt, K.; Morien, C.; Tongay, S.; Hebard, A.; Biswas, A. Growth and characterization of multiferroic BiMnO3 thin films. J. Appl. Phys. 2011, 109, 074104. Appl. Sci. 2019, 9, 1267 12 of 13 3. Subramanian, M.A.; Torardi, C.C.; Calabrese, J.C.; Gopalakrishnan, J.; Morrissey, K.J.; Askew, T.R.; Flippen, R.B.; Chowdhry, U.; Sleight, A.W. A new high-temperature superconductor: Bi Sr Ca Cu O . 2 3 x x 2 8+y Science 1988, 239, 1015. [CrossRef] [PubMed] 4. Tallon, J.L.; Buckley, R.G.; Gilberd, P.W.; Presland, M.R.; Brown, I.W.M.; Bowden, M.E.; Christian, L.A.; Goguel, R. High-Tc superconducting phases in the series Bi (Ca, Sr) Cu O . Nature 1988, 333, 153. 2.1 n+1 2n+4+ [CrossRef] 5. Shaddad, M.N.; Cardenas-Morcoso, D.; Arunachalam, P.; García-Tecedor, M.; Ghanem, M.A.; Bisquert, J.; Al-Mayouf, A.; Gimenez, S. Enhancing the optical absorption and interfacial properties of BiVO with Ag PO nanoparticles for efficient water splitting. J. Phy. Chem. C 2018, 122, 11608. [CrossRef] 3 4 6. Meng, X.; Zhang, Z. Bismuth-based photocatalytic semiconductors: Introduction, challenges and possible approaches. J. Mol. Catal. A Chem. 2016, 423, 533. [CrossRef] 7. Xu, D.; Yang, H.; Zhang, X.; Zhang, S.; He, R. Bi O cocatalyst improving photocatalytic hydrogen evolution 2 3 performance of TiO . Appl. Surf. Sci. 2017, 400, 530. [CrossRef] 8. Kudo, A.; Omori, K.; Kato, H. A novel aqueous process for preparation of crystal form-controlled and highly crystalline BiVO powder from layered vanadates at room temperature and its photocatalytic and photophysical properties. J. Am. Chem. Soc. 1999, 121, 11459. [CrossRef] 9. Fu, H.; Pan, C.; Yao, W.; Zhu, Y. Visible-light-induced degradation of rhodamine B by nanosized Bi WO . 2 6 J. Phys. Chem. B 2005, 109, 22432. [CrossRef] 10. Wu, J.; Huang, F.; Lü, X.; Chen, P.; Wan, D.; Xu, F. Improved visible-light photocatalysis of nano-Bi Sn O 2 2 7 with dispersed s-bands. J. Mater. Chem. 2011, 21, 3872. [CrossRef] 11. Shang, S.L.; Sheng, G.; Wang, Y.; Chen, L.Q.; Liu, Z.K. Elastic properties of cubic and rhombohedral BiFeO from first-principles calculations. Phys. Rev. B 2009, 80, 052102. [CrossRef] 12. Zhai, L.J.; Wang, H.Y. The magnetic and multiferroic properties in BiMnO . J. Magn. Magn. Mater. 2017, 426, 188. [CrossRef] 13. Kako, T.; Zou, Z.; Katagiri, M.; Ye, J. Decomposition of organic compounds over NaBiO under visible light irradiation. Chem. Mater. 2007, 19, 198. [CrossRef] 14. Gong, J.; Lee, C.S.; Kim, E.J.; Kim, J.H.; Lee, W.; Chang, Y.S. Self-generation of reactive oxygen species on crystalline AgBiO for the oxidative remediation of organic pollutants. ACS Appl. Mater. Interfaces 2017, 9, 28426. [CrossRef] [PubMed] 15. Chouhan, A.S.; Athresh, E.; Ranjan, R.; Raghavan, S.; Avasthi, S. BaBiO : A potential absorber for all-oxide photovoltaics. Mater. Lett. 2018, 210, 218. [CrossRef] 16. Tang, J.; Zou, Z.; Ye, J. Efficient photocatalysis on BaBiO driven by visible light. J. Phys. Chem. C 2007, 111, 12779. [CrossRef] 17. Kumada, N.; Takahashi, N.; Kinomura, N.; Sleight, A. Preparation of ABi O (A= Mg, Zn) with the 2 6 trirutile-type structure. Mater. Res. Bull. 1997, 32, 1003. [CrossRef] 18. Mizoguchi, H.; Bhuvanesh, N.S.P.; Woodward, P.M. Optical and electrical properties of the wide gap, n-type semiconductors: ZnBi O and MgBi O . Chem. Commun. 2003, 1084. [CrossRef] 2 6 2 6 19. Takei, T.; Haramoto, R.; Dong, Q.; Kumada, N.; Yonesaki, Y.; Kinomura, N.; Mano, T.; Nishimoto, S.; Kameshima, Y.; Miyake, M. Photocatalytic activities of various pentavalent bismuthates under visible light irradiation. J. Solid State Chem. 2011, 184, 2017. [CrossRef] 20. Zhong, L.; Hu, C.; Zhuang, J.; Zhong, Y.; Wang, D.; Zhou, H. AgBr/MgBi O heterostructured composites 2 6 with highly efficient visible-light-driven photocatalytic activity. J. Phys. Chem. Solids 2018, 117, 94. [CrossRef] 21. Zhang, C.; Kou, L.; He, T.; Jiao, Y.; Liao, T.; Bottle, S.; Du, A. First principles study of trirutile magnesium bismuth oxide: Ideal bandgap for photovoltaics, strain-mediated band-inversion and semiconductor-to-semimetal transition. Comput. Mater. Sci. 2018, 149, 158. [CrossRef] 22. Kresse, G.; Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 1996, 54, 11169. [CrossRef] 23. Kresse, G.; Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 1996, 6, 15. [CrossRef] 24. Blöchl, P.E. Projector augmented-wave method. Phys. Rev. B 1994, 50, 17953. [CrossRef] 25. Kresse, G.; Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 1999, 59, 1758. [CrossRef] Appl. Sci. 2019, 9, 1267 13 of 13 26. Perdew, J.P.; Burke, K.; Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 1996, 77, 3865. [CrossRef] [PubMed] 27. Paier, J.; Hirschl, R.; Marsman, M.; Kresse, G. The Perdew–Burke–Ernzerhof exchange-correlation functional applied to the G2-1 test set using a plane-wave basis set. J. Chem. Phys. 2005, 122, 234102. [CrossRef] 28. Paier, J.; Marsman, M.; Hummer, K.; Kresse, G.; Gerber, I.C.; Ángyán, J.G. Screened hybrid density functionals applied to solids. J. Chem. Phys. 2006, 124, 154709. [CrossRef] 29. Togo, A.; Tanaka, I. First principles phonon calculations in materials science. Scr. Mater. 2015, 108, 1. [CrossRef] 30. Zhang, H.J.; Liu, L.; Zhou, Z. Towards better photocatalysts: First-principles studies of the alloying effects on the photocatalytic activities of bismuth oxyhalides under visible light. Phys. Chem. Chem. Phys. 2012, 14, 1286. [CrossRef] [PubMed] 31. Hu, C.H.; Yin, X.H.; Wang, D.H.; Zhong, Y.; Zhou, H.Y.; Rao, G.H. First-principles studies of electronic, optical, and mechanical properties of
-Bi Sn O . Chin. Phys. B 2016, 25, 067801. [CrossRef] 2 2 7 32. Wu, Z.J.; Zhao, E.J.; Xiang, H.P.; Hao, X.F.; Liu, X.J.; Meng, J. Crystal structures and elastic properties of superhard IrN and IrN from first principles. Phys. Rev. B 2007, 76, 054115. [CrossRef] 2 3 33. Pugh, S.F. XCII. Relations between the elastic moduli and the plastic properties of polycrystalline pure metals. Philos. Mag. 1954, 45, 823. [CrossRef] 34. Authier, A. International Tables for Crystallography: Vol. D, Physical Properties of Crystals; Kluwer Academic Publishers: Dordrecht, The Netherland, 2003; pp. 83–84. 35. Shrivastava, D.; Sanyal, S.P. Structural phase transition, electronic and lattice dynamical properties of half-Heusler compound CaAuBi. J. Alloys Compd. 2018, 745, 240. [CrossRef] © 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
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