Here we have prepared good quality crystalline sample MgBi2O6 employing the solid-state reaction technique. The synthesized material was characterized by XRD and SEM (scanning electron microscopy). The structural study confirmed that MgBi2O6 possesses a tetragonal crystal configuration (JCPDS PDF#, No. 86-2492) with outstanding crystallinity and a grain size between 200 to 350 nm. The temperature dependence electrical resistivity and conductivity were measured by two probe methods and ensured the semiconducting nature of this material. Using the impedance analyzer and UV-visible spectrophotometer we studied the experimental electronic and optical properties of this material. To explore the hypothetical features of MgBi2O6 we have used first-principles methods that depend on CASTEP code. The band structure analysis also ensured the semiconducting nature of MgBi2O6 with a small band gap of 0.12 eV. The semiconducting behavior of MgBi2O6 with a band gap of 0.12 eV was also observed by the band structure analysis. The Borns stability criteria were fulfilled by the investigated elastic constants and ensured the stable nature of MgBi2O6. The response of structural and mechanical properties with the pressure of MgBi2O6 was discussed in detail. We have also studied the hypothetical optical properties of MgBi2O6 by CASTEP code.
Nowadays, semiconductor photocatalysis has attar-cted a lot of attention in view of the fact that it offers a profitable and environmentally secure option for pollution purification, high efficiency, energy saving and conversion (Zou et al., 2011; Kudo and Miseki, 2009; Chen et al., 2010; Linic et al., 2011). Fujis-hima and Honda, (1972) was first reported about the photocatalytic activity of TiO2 which is one of the most popular photocatalysts, has been broadly studied due to its nontoxicity, outstanding oxidative power, high stability, low cost and photostability (Tang et al., 2007; Matsuda and Hatano, 2005). Unfortunately, due to the wide band gap of about 3.2 eV, TiO2 is only active in the UV region which only involves in about 4% of the incident solar radiation. Therefore, it is severely limits the efficient usage of solar energy. Moreover, TiO2 reveals low quantum efficiency due to the high recombination rate of photo-induced electron-hole pairs (Long et al., 2006; Jiang and Wang, 2007). Hence, in order to make full utilize of sunlight it is urgently essential to discover more efficient materials with visible-light-driven photocatalytic activity. In present years, numerous bismuth-based semi-conductors have received extra-ordinary attention due to their high photocatalytic activity (Meng and Zhang, 2016). In these compounds, bismuth normally presents in trivalent or pentavalent states. Recently, some Bi3+ containing materials for example BiVO4 (Kudo et al., 1999), Bi2WO6 (Fu et al., 2005), and BiOCl (Wang et al., 2017) have been broadly explored as new candidates for visible-light-responsive photo-catalysts due to the exceptional electronic configuration essentially arising from the hybridization of O-2p and filled Bi-6s orbitals. Additionally, the empty 6s orbital of Bi5+ also leads to some Bi5+ including compounds having tremendous photo-catalytic activity. Alternatively, a number of Bi oxides having remarkable pentavalent state (Bi5+) have received a lot of attention for their research interest. Among these bismuth oxides a famous example is NaBiO3 which show as a strong absorber of visible light and has significant application in photo-oxidation of organic materials (Kako et al., 2007).
Recently Gong et al. (2017) proposed that the compound AgBiO3 has the ability to create large quantity of reactive oxygen species with no light illumination and has an exceptional oxidizing activity. The compound BaBiO3 having both Bi3+ and Bi5+ states, can be used as a potential absorber of all-oxide photovoltaic (Chouhan et al., 2018) and show photocatalyst behavior in the case of visible-light irradiation (Liu et al., 2019). With trirutile structure the compound MgBi2O6 shows outstanding photo-catalytic manners for methylene blue degradation (Takei et al., 2011). This compound was first synthe-sized by Kumada et al. (2003) employing the hydro-thermal method. In 2003, Mizoguchi et al. (2011) investigated the electrical and optical features of MgBi2O6 and mentioned that it is a degenerate n-type semiconductor with relatively narrow band gap of about 1.8 eV. Having special band configuration, the compound MgBi2O6 can be used as visible light-sensitive photocatalysts for disintegration of carbo-nic species. The theoretically investigated band gap of MgBi2O6 is found to be1.10 eV carried out by Heyd-Scuseria-Ernzerhof (HSE) functional method (Zhang et al., 2018).
In this work we have investi-gated the detailed physical properties of MgBi2O6 by first-principles method with GGA and PBE and have seen that this phase shows metallic behavior (Rahman et al., 2016). The characteristic has also been found by Lin Liu, Dianhui Wang et al. in 2019. Therefore to obtain the band gap of this compound they have used HSE functional scheme instead of GGA, PBE route. But fortunately in our present work we have successfully observed the band gap of MgBi2O6 by using the GGA and PBE route. In this work, we have also synthesized the high quality MgBi2O6 crystals via the solid-state reaction method and characterized the as-prepared sample by XRD, SEM, impedance analyzer and UV-visible spectrophoto-meter. Furthermore, using first-principles method we have calculated the structural and mechanical properties of this compound under different pressures for the first time.
2.1 Experimental methodology - In this research work, the pure MgBi2O6 crystal was produced through the usual solid-state reaction method with the high purity (purity > 98 %) powders of MgO and Bi2O5. In order to begin the synthesizing process of MgBi2O6, initially we have studied the phase development of this phase using a thermobalance (TG/DTA 630). A stoichiometric mixture of MgO and Bi2O5 was heated in an air atmosphere through a heating program as shown in the inset of Fig 1. A characteristics TG curve attained from the mixture of raw materials (MgO and Bi2O5) is also revealed in Fig 1.
Fig 1: Thermogravimetric (TGA) curve (with heat program) for phase formation process of MgBi2O6.
From this TG curve, it was noticed that the weight loss at 100-580°C is too large. This result confirm that at temperature lower than 100°C, the chemical reaction between the raw materials may not be active so far and there is no weight change above 600°C where the phase formation is done. At the primary step of synthesis, the reactants were dried in air an oven at 100 °C for 12 h. The powder mixture of MgO and Bi2O5 was mixed well in an agate mortar with ethanol then dried and calcined at 800 °C for 12 h at ambient. Before the next heat treatment the mixture was grounded again to ensure homogeneity. The powder was calcined second time at 850 °C for 12 h at atmosphere. After the second heat conduct, the powder was grounded and pelletized in 12 mm diameter under the pressure of 80 KN by using pressure gauze. At atmosphere the pellet was sinte-red at 900°C for 12 h. During the heat treatment process the raising- cooling rates of temperature were fixed to 3 °C/min. The powder sample of MgBi2O6 was analyzed by using the X-ray powder diffraction spectroscopy with CuKα (λ = 0.15418 nm) radiation source at room temperature in Centre for Advanced Research in Sciences (CARS), in Bangladesh. The sample was scanned at the diffraction angle (2θ) within the range of 5° and 85°. The structural and morphological investigation of the prepared sample was carried out by scanning electron microscopy (SCM). For investigating the FTIR spectrum of the powder sample, we have used Fourier transform infrared (FTIR) spectrophotometer (Spectrum 100, Perkin Elmer). The Agilent Precision impedance analyzer (Agilent technologies, Model 4294A Japan) was used for the measurement of frequency-dependent ac conductance, impedance, dielectric constant, capacitance, inductance and reactance.
2.2 Theoretical methodology - The detailed phy-sical properties of magnesium bismuth oxide, MgBi2O6 has been carried out through the CASTEP computer code (Clark et al., 2005) within the frame of density-functional theory (DFT). By employing the Perdew-Burke-Ernzerhof (PBE) method (Perdew et al., 1996) we have treated the exchange-correlation energy within the genera-lized gradient approximation (GGA). For pseudo atomic computations, Mg-2p6 3s2, Bi- 6s2 6p3 and O- 2s2 2p4 have been taken as the valence electron states. The plane wave basis set with cut-off energy 480 eV is employed to expand the wave functions. For sampling the Brillouin zone a Monkhorst-Pack grid of 10105 k-points was used for compound MgBi2O6. In order to obtain the equilibrium crystal structure of MgBi2O6 the Broyden-Fletcher-Goldfarb- Shanno (BFGS) mini-mization scheme was used. The succeeding crite-ria for the geometry optimization were sited to 5.0×10-5 eV/atom for total energy, 0.01 eV/Å for maximum force, 0.02 GPa for maximum stress and 5.0×10-4 Å for maximum atomic displacement. The stress-strain system was used to find out the single independent elastic constants of MgBi2O6 (Kang et al., 2003; Mostari et al., 2020). We have used the Voigt-Reuss-Hill approximations to compute the poly-crystalline elastic constants of MgBi2O6.
3.1. Experimental and Theoretical Structural Properties - The structural analysis of MgBi2O6 has performed by X-ray diffractometer (XRD) (Rigaku Ultima IV X-Ray Diffractometer) with CuKα radiation (λ = 0.15418 nm) from 10º-80º, with a scan speed of 5º/min. The unit cell refinement has been performed by Cell Call program employing the XRD data. The X-ray diffraction pattern of MgBi2O6 is displayed in Fig 2 which ensured the single phase tetragonal crystal structure of this material with space group of P42/mnm (No. 136) and lattice parameters a = b = 4.841, c = 9.721 Å (JCPDS PDF#, No. 86-2492) (Kumada et al., 1997). The experimental, theore-tically investigated lattice parameters and atomic co-ordinates of MgBi2O6 are listed in Table 1. From Table 1, we have seen that our experimental lattice parameters are approximately equal to the standard lattice parameters obtained from the stated JCPDS data and satisfied the previous work. The optimized lattice parameters are very close to our experimental data which insured the reliability of the DFT based simulation. The sharp and strong diffraction peaks (Fig 2) reveals the excellent crystallinity of MgBi2O6. The larger value of inten-sity ratio reveals the better crystallinity (Hu et al., 2007). Here, the intensity ratio of the highest peaks (110) and second highest peak (103 ) is 2.21 which is large than the critical value 1.2 (Hao et al., 2005) and confirms the better crystallinity of MgBi2O6. The higher crystallinity would promote to yield higher photocatalytic activity (Zhong et al., 2018).
Fig 2: X-ray diffraction patterns of MgBi2O6.
To study the effect of external pressure on the crystal structure of MgBi2O6, we have studied the variations of the lattice parameters, unit cell volume and bulk modulus of MgBi2O6 with differ-rent pressures up to 50 GPa. For this investigation we have used generalized gradient approximation depend on DFT based calculations implement in CASTEP code. The variations of the cell volume, lattice parameters and bulk modulus of MgBi2O6 with pressure are presented in Fig 3. From Fig 3 we have seen that the lattice parameters and the cell volume of MgBi2O6 are decrease with increa-ses of pressure, consequently the bulk modulus, B0 increased with the increase of pressure. However, the atomic distance is reduced with increasing pressure. For this reason, the repulsive attraction between atoms becomes string, which guides to the complexity of compression of the material under pressure (Rahman et al., 2016). The lattice parameters, cell volume and bulk modulus with different pressures are listed in Table 2.
Table 1: Lattice parameters and atomic positions of MgBi2O6.
Table 2: Lattice parameters a, c (Å), cell volume, V (Å3) and bulk modulus, B0 (GPa) under different pressures of MgBi2O6.
FT-IR Analysis - The FTIR analysis is an investi-gative scheme which offers elementary information about the chemical bonding and phase formation of materials, whether organic or inorganic (Fairooz and Imran, 2013). This analysis also provides the information about the vibration frequency of efficient groups, network configurations of sample and cation situation in oxides (Amdouni et al., 2003: Khatun et al., 2014). The FTIR absorption spectrum of crystalline sample MgBi2O6 in the range of 225-4000 cm-1 is displayed in Fig 4. All spectra are typically distributed in two wave number ranges 400-950 cm-1 in the far-infrared region and 1000-2000 cm-1 in the infrared region. The main absorption bands are observed at 468.70, 677.01, 844.82, 1101.35, 1395.53, 1475.54, 1624.06, 1717.65, 2854.65, 2922.16, 3435.22, 3689.88 and 3774.69 cm-1. These results verify the XRD examinations viewing that the vibration bands for precursors vanished and the vibration bands for the oxide network are built up. In the far-infrared region, we have seen a single well-resolved band at 468.70 cm-1 in MgBi2O6 due to an asymmetric stretching motion of MgO6 octahedron which is distorted enormously (Kim et al., 2012: Julien et al., 2004). It is the unique finger of Mg site occupancy in the MgBi2O6 crystal arrangement. The absorption bonds at 677.01 and 844.82 cm-1 are attributed due to the symmetric and asymmetric stretching of BiO5 units, respectively (Tang et al., 2013). The sharp absorption bands at 1101.35 cm-1 in MgBi2O6 are consigned to Bi = O stretching mode (Song et al., 2009). The absorption bands in the region of 500-800 cm-1 are due to the asymmetric or sym-metric stretching of Bi-O-Bi bonds (Gao et al., 1994). Furthermore the bands at around 420 cm-1 can be assigned to the stretching modes of Mg-O. A sharp medium absorption peak at 1624.65 cm-1 is found because of the stretching (vibrations) of magnesium bismuth crystal lattice. Two weak peaks are also detected at 2854.56 and 2922.16 cm-1 that was related to O-H bond stretching into the sample. The structural deformation is mainly shown by the existence of new broad bands at 1395.53, and 3435.22 cm-1 (Janjua et al., 2014).
Fig 3: (a) Variations of lattice parameters, (b) cell volume, and (c) bulk modulus of MgBi2O6 with different pressure.
Fig 4: FT-IR spectrum of sample MgBi2O6.
SEM Analysis - The morphology and microstru-cture of the as-prepared pure sample MgBi2O6 was measured by scanning electron microscopy (SEM) at different magnifications as shown in Fig 5. From Fig 5, it can be seen that the photocatalyst material MgBi2O6 was composed of cuboid-like particles with the grain size of about 200 to 350 nm. In Fig 5(c), MgBi2O6 particles show better crystallinity and closer arrangement and look more regular and compact (Zhong et al., 2018). The higher cryst-allinity would promote to yield higher photocatalytic activity, since the recombination of photogenerated electron-hole pairs can be suppressed in the highly crystalline photocatalysts (Hudo et al., 1999).
3.2. Experimental Electronic Properties - Using the two probe methods from room temperature to 600 K, we have measured the electrical resistivity and dc conductivity of MgBi2O6 which are shown in Fig 6 (a, and b). From Fig 6(a), we have seen that the values of resistivity of compound MgBi2O6 are decreased with increasing the temperature. For this reasons the conductivity of this material is increased with increasing temperature as shown in Fig 6(b).
This analysis ensured the semiconducting manner of this material. Our results coincide with the previous study of MgBi2O6 (Takei et al., 2011). Impedance spectroscopy is relatively a new and powerful routine of analyzing many of the electrical features of electrolyte materials and their interfaces. The frequency dependent dielectric constant, conduct-ance, resistance, capacitance, reactance and imped-ance of MgBi2O6 are displayed in Fig 7 which was measured within the range 100 Hz to 2 MHz at ambient temperature with the oscillating voltage 500 mV. For this measurement silver paste was coated on both surface of the sample MgBi2O6. From the dielectric property analysis, we have seen that the value of the dielectric constant of MgBi2O6 is measured to 0.75 at 100 Hz which ensure the semiconducting nature of this phase. This charact-eristic is also observed from the resistivity analysis shown in Fig 6(a).
In the high frequency region the dielectric constant is decreased because the dipoles are not capable to rotate rapidly with the increase of frequency. For this reason their oscillations begin to lag behind to the applied field. As the frequency is further increased, the dipole will be totally unable to follow the field and the orientation polarization will be stopped (Sarkar et al., 2016).
Fig 5: SEM images of MgBi2O6 at different magnifications.
Fig 6: The temperature dependent electrical (a) resistivity and (b) conductivity of MgBi2O6.
The frequency-dependent ac conductance of the synthesized sample MgBi2O6 was measured by precision impedance analyzer within the frequency range 100 Hz to 2MHz with applied oscillating voltage of 500 mV. From Fig 7(b) we have seen
that the conductance is increased rapidly with the increase of frequency. The mobile charge carriers contribute to this conductivity. Following the ion-hopping rules, the ionic conduction of MgBi2O6 is created from the transfer of exchangeable channels and cavities of the grains. The mobile charge carriers face some displacement between the two minimum potential energy states when they jump to a new site from its original position. This is due to the polarization of dipoles (Usha et al., 2007). The maximum conductance is observed at the high frequency (~2 MHz). Fig 7(c) represents the frequency dependent resistance of MgBi2O6 measured with oscillating voltage 500 mV. At 100 Hz the value of the resistance of MgBi2O6 is approximately 3236.65 MΩ. Due to semiconducting manner the value of the resistance decreases with the increase of frequency in the low frequency region and approaching a constant value at above 0.08 MHz.
Fig 7: Frequency dependent (a) Dielectric constant, (b), Conductance, (c) Resistance, (d) Capacitance, (e) Reactance and (f) Impedance of MgBi2O6 material.
The frequency dependent capacitance of MgBi2O6 is shown in Fig 7(d) measured at 500 mV with a precision impedance analyzer. The high value of capacitance is observed in the low frequency region (Fig 7d) which is due to the due to the involvement of all kinds of polarizations at low frequency region. The capacitance is decreased with the increase of frequency and come close to almost constant value at above 1.0 MHz. This is due to the change of space charge, ionic and orientation polarizations at higher frequencies. Fig 7(e) and (f) represent the frequency dependent reactance and impedance of MgBi2O6 sample respectively within 100 Hz to 2 MHz. All these parameters are high in the low frequency region and gradually decrease in the high frequency region. The reactance is almost independent of frequency at higher frequencies (above 0.4 MHz) which is due the resistance effect.
3.3. Experimental Optical Properties - The analy-sis of optical function of material is very crucial due to the fact that it has some vital applications in optical coatings, reflectors, absorbers and various optoelectronic devices. The reported results on optical absorption and transmission of MgBi2O6 crystals are not available in literature. In this study, the UV–visible absorption spectrum and the transmittance of MgBi2O6 crystal were recorded using a UV-visible spectrophotometer (Shimazu: UV-1650 PC) within the photon wavelength 200 to 800 nm.
Fig 8: The wavelength dependent (a) absorption spectrum, and (b) transmittance of MgBi2O6.
Fig 8 (a, and b) illustrate the absorption spectra and transmittance of compound MgBi2O6. From Fig 8(a) we have seen two absorption peaks in the ultraviolet region which ensures the absorption criteria of this material in this region. No absorption peaks are found in the visible site. However the absorption increases and the transmittance decreases with the increase of wavelength in the visible region. The optical band gap energy can be calculated by using the following equation -
E_g=hc/λ
Where ‘Eg is the optical band gap, ‘h is the Planks constant, ‘c is the velocity of light and λ is the wavelength at the edge of the absorption peak.
Here, λ = 522 x10-9 m
Therefore, E_g=(6.626×10^(-34)×2.99×10^8)/(520×10^(-9) ) joule
Or, E_g=(3.8×10^(-19))/(1.6×10^(-19) ) eV
Therefore, E_g= 2.39 eV
This band gap indicates that the sample is a semiconductor material. This feature has also found from the dielectric and resistivity analysis. The same results ensured the reliability of our present work.
3.4 Theoretical Mechanical Properties - Elastic constants are incredibly exceptional parameter of any crystalline material. These constants provide a relation between the mechanical features and dynamic information regarding the nature of the forces working in solids, particularly for the stability and hardness of materials (Wang and Zhou, 2004). The elastic constants provide fundamental information about solid-state phenomenon for example rigidity, fragility, ductile feature, anisotropy and stability behavior of a material. So it is very essential to study the stiffness constants of a material and also essential to know how the elastic feature varies with different pressures. The elastic constants of MgBi2O6 are calculated from a linear fit of the stress-strain function as said by Hooks law. Since our synthesized material is belong to tetra-gonal crystal system, it has six independent elastic constants which are listed in Table 3. We are unable to compare our results due to absence of experi-mental measurement of elastic constants data in literature. However our investigated results are in well accord with the previous theoretical work (Liu et al., 2019). There some slide variation in our investigated results from the previous study which is due to the use of different calculation methods.
Table 3 also included the elastic constants of MgBi2O6 at different pressures which are totally new investigation about this material. For mechanical stability the single independent elastic constants of a tetragonal system should convince the recognized Born stability criteria which are as follows:
C11 > 0, C44 > 0, C33 > 0, C66 > 0
C11 + C33 – 2C13 > 0, C11 – C12 > 0 (1)
2(C11 + C12) + C33 + 4C13 > 0
From Table 3 we have observed that the investigated independent elastic constants of our synthesized compound are positive and fulfill the above stability conditions which demonstrating that MgBi2O6 is mechanical stable in nature. From Table 3 we have observed that C33 is higher than C11 signifying that the chemical bonding strength in the (001) direction is considerably stronger than bonding strength in the (100) and (010) directions. Additionally, C44 is clearly smaller than C66 indicating that it is very easy to occurs shear deformation in (001) direction than (010) direction (Liu et al., 2019).
Table 3: The calculated elastic constants Cij (in GPa) of MgBi2O6 at different pressures.
Fig 9 represents the variation of the elastics Cij, the elastic modulus and the Borns criteria under the effect of pressure of MgBi2O6. We evidently detect a linear dependence in all curves of elastic constants and bulk modulus of MgBi2O6 in the considered range of pressure while C44 varies little under the pressure effect.
Fig 9: The calculated pressure dependence of (a) elastic constants, Cij, (b) elastic modulus and (c) Borns criteria of MgBi2O6 structure.
Furthermore, C44 rises firstly and then decreases with pressure. The outcome is consistent with other hypothetical inquiry on a tetragonal crystal system (Benmakhlouf and Bentabet, 2015; Zhai et al., 2012). The linear response of the elastic constants with pressure fulfills the Borns stability criteria (Fig 9c) and confirms the stability nature of MgBi2O6 up to 50 GPa. Consequently, the bulk modulus, shear modulus and Youngs modulus definitely shows an increasing tendency as pressure increases (Fig 9b) (Zheng et al., 2015).
For estimating the mechanical features of any material the most significant parameters such as the bulk modulus, shear modulus, Youngs modulus, anisotropy factor, poissons ratio of MgBi2O6 are determined through the Voigt-Reuss-Hill approxi-mations from the investigated elastic constants Cij. Depend upon the Voigt-Reuss-Hill approximations; the bulk modulus BV and shear modulus GV for tetragonal structure are given as:
B_V= (2C_11+ 2C_12+C_33+4C_13)/9 (2)
B_R= C^2/M (3)
G_V= (M+3C_11-3C_12+ 12C_44+ 6C_66)/30 (4)
G_R= 15/[(18B_V)/C^2 + 6/((C_11- C_12))+ 6/C_44 + 3/C_66 ] (5)
Where,
M= C_11+C_12+2C_33-4C_13
And C^2=(C_11+C_12 ) C_33- 2C_13^2
According to Hill the average value of B and G is given by,
B= 1/2 (B_R+ B_v ) (6)
G= 1/2 (G_v+ G_R ) (7)
Now to find out the values of Youngs modulus (E) and Poissons ratio (ν) we have used the following relations,
E= 9GB/(3B+G) (8)
ν= (3B-2G)/(2(3B+G)) (9)
The Universal anisotropic factor of a material can be calculated by the following equation Ranganathan and Ostoja-Starzewski, 2008,
〖 A〗^U= (5G_V)/G_R + B_V/B_R - 6 (10)
The calculated polycrystalline elastic constants at different pressures of MgBi2O6 by using the Eq. 2 to Eq. 10 are charted in Table 4. The ratio of bulk to shear modulus B/G is a sign of ductile and brittle manner of any material. The bulk modulus B indicates the resistance to volume changes via applied pressure, whereas the shear modulus G denotes the resistance to plastic deformation. The high value of B/G ratio ensures the ductility, whereas a low value corresponds to brittle manner. If B/G > 1.75, the material will behaves ductile manner; or else, the material will behaves brittle activities. From the value of B/G as shown in Table 4, we can say that this material has some toughness at ambient condition. The nature of B/G with pressure in MgBi2O6 is depicted in Fig 10(c). It has been seen that when pressure increases from 0 to 50 GPa, the value of B/G changes from 1.81 to 4.07. It indicates that the compound MgBi2O6 is strongly prone to ductility at high pressure. Another recognized parameter is the Poissons ratio, ʋ which is used to separate the brittle solids from the ductile once proposed by Frantsevich et al. (1983). The larger value of Poissons ratio (ν>0.26) indicates ductile manner and the compound will be brittle when the value of Poissons ratio is (ν<0.26).
According to the value of ν as evident from Table 4 this material shows ductile behavior which consistent with the result of Pughs criteria B/G. Our results are very similar to the previous study (Liu et al., 2019). Fig 10(b) also ensures that MgBi2O6 has little bit ductile manner at zero pressure and is strongly prone to higher ductility with increasing pressure.
Table 4: The calculated bulk modulus B (GPa), shear modulus G (GPa), Youngs modulus E (GPa), B/G values, Poissons ratio ʋ and anisotropy factor AU of MgBi2O6 compound at 0 to 50 GPa pressure.
It is well recognized that elastic anisotropy associates with anisotropic plastic deformation and activities of micro cracks in solid materials. Therefore it is very essential to determine the elastic anisotropy in super hard materials due to realized these properties and expectantly find mechanisms which will develop their hardness and mechanical durability. An appropriate explanation of anisotropic manners has a significant impact in engineering discipline as well as in crystal physics. For a pure isotropic material, AU is zero and for other case the material will be anisotropic. The value of AU at 0 to 50 GPa of MgBi2O6 is shown in Table 4 which is greater than zero and ensures that this compound shows anisotropic behavior. From Fig 10(a) it is observed that the value of AU increases sharply with increasing pressure due to reason that that the elastic constants C11, C33, C66, C12 and C13 are increased with pressure.
Fig 10: (a) The anisotropy factor A, (b) the Poissons ratio ʋ and (c) the B/G values of MgBi2O6 as a function of pressure.
3.5 Theoretical electronic and bonding properties
It is very essential to study to electronic properties of any material due to understanding the physical properties and bonding character of this material. For this reason in this study we studied the detailed electronic properties such as electronic band structure, density of states (total and partial) and the Mulliken atomic populations MgBi2O6 at zero pressure. The observed electronic band structure of this compound is depicted in Fig 11. A clear separation between the valence band and conduction band is observed from Fig 11 which ensures the semiconducting behavior of MgBi2O6. This characteristic is also observed from the resistivity analysis shown in Fig 6(a). The investigated electronic band gap of MgBi2O6 is about 0.121 eV which is differs from the experimental value of 1.6 eV (Mizoguchi et al., 2003). This happened because DFT based calculations skip the electrons excitation effects and therefore underrate the electronic band gap (Naefa and Rahman, 2020).
Fig 11: Electronic band structure of MgBi2O6 along high symmetry direction in the Brillouin zones.
The calculated partial and total density of states of tetragonal MgBi2O6 is exposed in Fig 12. The valance bands are located from -20 eV to the Fermi level and mostly created from Mg-2p, Bi-6s, O-2s and O-2p states. The conduction bands are located from 0 to 10 eV and chiefly created from Bi-6p states. However, near the Fermi level O-2p orbital contributes the most, which are the general features of oxide semiconducting materials. From Table 5 we have seen the total density of states of this material is 3.32 states/eV, where the contribution of O-2p states is dominated. In order to understand the chemical bonding nature in compound MgBi2O6 we have studied the Mulliken atomic populations which are listed in Table 6. A low value of the bond population refers to the ionic behavior (For perfect ionic bond the value of the bond population is zero) whereas a high value indicates increase of covalency level (Segall et al., 2003). The calculated bond populations of MgBi2O6 are shown in Table 6. From Table 6 we can see that Mg and Bi atoms carry the positive charges on the other hand O atoms carry the negative charges indicating the transfer of charge from Mg and Bi to O atoms.
Table 5: Mulliken atomic populations of semiconductor MgBi2O6.
Table 6: Total and partial density of states of MgBi2O6.
From Table 6 it is obvious that bond populations of bonds O-Mg and O-O are less than zero indicating the existence of ionic bond in MgBi2O6. On the other hand bond population of bonds O-Bi is greater than zero indicating the existence of covalent bond in this compound. To get comprehensible concept about the bonding features the total charge density map of MgBi2O6 is depicted in Fig 13. A covalent characteristic is observed in O-Bi bond due to the overlapping of charge distribution between the nearest O and Bi atoms. No overlapping of charge distribution is observed in O-Mg and O-O bonds ensure the ionic character of these bonds.
3.6 Theoretical Optical Properties
For understanding the optical properties of MgBi2O6 we studied the dielectric function, refractive index, loss function, absorption, conductivity and reflectivity by using the GGA and PBE approximations. Dielectric constants are calculated using the frequency dependent dielectric function iwhich is strongly consistent to the electronic structure. The imaginary part ε2() of this function is calculated through the following equation (Materials Studio CASTEP Manual © Accelrys, 2011):
Here w is the light frequency, e denotes the electronic charge, denotes the vector which defining the polarization of the incident electric field, and are the conduction band and valence band wave functions at k consecutively. The real part is determined via the Kramers-Kronig transforms. All the other functions are derived by Eqs., (Materials Studio CASTEP Manual © Accelrys, 2011).
The dielectric function of MgBi2O6 is shown in Fig 14(a) with photon energy up to 30 eV along [100] direction. From this figure it has been obvious that the static dielectric function of MgBi2O6 at 0 eV is found to be 9 eV which is contradict to the value 4.1 found by Lin Liu et al. (2019). The decrease of real part of the dielectric function with the increase of photon is due to the reasons that when the photon energy reaches to 0.121 eV which is the band width of this phase, the valence band electrons start to excite and move to conduction bands. Hence the carrier concentration is increases, the degree of polarization reduces and consequently the real part of the dielectric function decreases (Liu et al., 2019). The non-zero region of the imaginary part indicates the happening of light absorption of this material. The imaginary part comes to zero at about 13 eV indicating that this material would be transparent after this energy range. Refractive index is an important optical function which explains the nature of electromagnetic wave through a visual medium. From Fig 14(b) it is obvious that the refractive index is high in the infrared and visible regions and slowly decreases in the ultraviolet region demonstrating that MgBi2O6 has strong refractive effect in the infrared and visible regions.
Fig 14: The investigated optical functions of MgBi2O6: (a) conductivity, (b) absorption, (c) loss function, (d) dielectric function, (e) refractive index, and (f) reflectivity.
The loss function of fast moving electron would be used to represent the resonant frequency or bulk plasma frequency ω_P of the plasma (Xu et al., 2006). From Fig 14(c) it can be seen that the effective bulk plasma frequency is observed at 13 eV which ensures that the characteristics of plasma frequency in MgBi2O6 are obvious. This result is well agrees with our previous study (Rahman et al., 2016) and did not agree with the study of Lin Liu et al. (2019). Therefore MgBi2O6 shows transparent behavior when the incident photon has the energy higher than this plasma frequency. The calculated absorption spectrum of MgBi2O6 depicted in Fig 14(d) illustrates that the light absorption edge is stared at about 0.121 eV which is comparable with the band gap determined by PBE scheme. Only one major absorption peak is found at 9 eV in the absorption spectrum. Hence it is so interesting to notice that this material absorbs ultraviolet radiation quite efficiently. The optical conductivity of MgBi2O6 starts at about 0.14 eV (Fig 14e) confir-ming again the semiconducting nature of this phase. Since the material MgBi2O6 has high absorption in the ultraviolet region as a result maximum conductivity is observed in this region. The reflectivity shape of MgBi2O6 is shown in Fig 14(f). The high reflectivity is appeared at around 13 eV which corresponds to the energy where the conduct-ivity falls to zero and absorption quality is good. Since MgBi2O6 shows good reflectivity in the high energy area this compound should be used as a possible shield for ultraviolet radiation.
In summary, the pure single phase MgBi2O6 crystal has been effectively prepared through solid-state reaction way. The polycrystalline sample MgBi2O6 has been obtained after two times calcinations at 600 and 650 °C respectively. The powder XRD patterns reveal that the prepared sample is well crystallized and indexed to a trirutile-type tetragonal crystal structure. The large grain size of about 200-350 nm as observed from SEM images ensures the increase of efficiency of MgBi2O6, when it is used as a visible light-sensitive photocatalysts. The decrease of electrical resistivity and increase of electrical condu-ctivity with temperature ensures the semi-conducting behavior of MgBi2O6. This behavior is also observed from the electronic band structure calculations and from dielectric constant measurement. The high dielectric constant, high capacitance, high resistance, high impedance and low ac-conductance are observed at low frequency regions and consequently reverse characteristics are found in the high frequency regions. We have also performed the DFT based calculations to study the structural configu-ration, mechanical, electronic and optical properties of MgBi2O6. Furthermore we have observed the pressure effect on the structural and mechanical properties of the prepared product. The geometrical optimized lattice constants are very close to our experimental values which ensure the accuracy of our present work. The lattice parameters and cell volumes are decreased with the increase of pressure. The observed band gap of about 0.121 eV near the Fermi level confirms the semiconducting nature of MgBi2O6. The existence of ionic and covalent featu-res is observed from the Mulliken atomic population calculations. The investigated elastic constants satisfied the Borns stability criteria and ensure the mechanical stability of MgBi2O6. All the elastic constants show linear response with the external pressure in which C33 shows more response compared to other constants. The calculated B/G ensures a little bit ductile manner of MgBi2O6 at zero pressure but this phase is strongly prone to higher ductility at high pressure. The increased of Poissons ratio and anisotropic factor are observed with incre-asing pressure. The large reflectivity in the ultra-violet site ensures that MgBi2O6 should be used as a possible coating material for ultraviolet radiation.
We would like to thank Department of Physics, Rajshahi University, Bangladesh, and Centre for Advanced Research in Sciences, Dhaka University, Dhaka, Bangladesh for their lab support
The authors declared that there is no conflict of interests about this article.
Academic Editor
Dr. Wiyanti Fransisca Simanullang Assistant Professor Department of Chemical Engineering Universitas Katolik Widya Mandala Surabaya East Java, Indonesia.
Department of Physics, Pabna University of Science and Technology, Pabna, Bangladesh
Rahman MA, Rahman MA, and Sarker AR. (2020). Synthesis, characterization and pressure effect on structural and mechanical properties of MgBi2O6: solid-state route and DFT study, Int. J. Mat. Math. Sci., 2(5), 71-86. https://doi.org/10.34104/ijmms.020.071086