Synthesis, Characterization and Pressure Effect on Structural and Mechanical Properties of MgBi2O6: Solid-State Route and DFT Study

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 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 which depend on CASTEP code. The band structure analysis also ensured the semiconducting nature of MgBi2O6 with small band gap of 0.12 eV. The semiconducting behavior of MgBi2O6 with band gap of 0.12 eV was also observed by the band structure analysis. The Born’s stability criteria were fulfilled by the investigated elastic constants and ensured the stable nature of MgBi2O6. The response of structural and mechanical properties with pressure of MgBi2O6 was discussed in details. We have also studied the hypothetical optical properties of MgBi2O6 by CASTEP code.

or pentavalent states. Recently, some Bi 3+ containing materials for example BiVO 4 (Kudo et al., 1999), Bi 2 WO 6 (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 Bi 5+ also leads to some Bi 5+ including compounds having tremendous photo-catalytic activity. Alternatively, a number of Bi oxides having remarkable pentavalent state (Bi 5+) have received a lot of attention for their research interest. Among these bismuth oxides a famous example is NaBiO 3 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 AgBiO 3 has the ability to create large quantity of reactive oxygen species with no light illumination and has an exceptional oxidizing activity. The compound BaBiO 3 having both Bi 3+ and Bi 5+ states, can be used as a potential absorber of alloxide 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 MgBi 2 O 6 shows outstanding photocatalytic manners for methylene blue degradation (Takei et al., 2011). This compound was first synthesized by Kumada et al. (2003) employing the hydrothermal method. In 2003, Mizoguchi et al. (2011) investigated the electrical and optical features of MgBi 2 O 6 and mentioned that it is a degenerate ntype semiconductor with relatively narrow band gap of about 1.8 eV. Having special band configuration, the compound MgBi 2 O 6 can be used as visible lightsensitive photocatalysts for disintegration of carbonic species. The theoretically investigated band gap of MgBi 2 O 6 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 MgBi 2 O 6 by first-principles method with GGA and PBE and have seen that this phase shows metallic behavior . 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 MgBi 2 O 6 by using the GGA and PBE route. In this work, we have also synthesized the high quality MgBi 2 O 6 crystals via the solid-state reaction method and characterized the as-prepared sample by XRD, SEM, impedance analyzer and UV-visible spectrophotometer. Furthermore, using first-principles method we have calculated the structural and mechanical properties of this compound under different pressures for the first time.

METHODOLOGY:
2.1 Experimental methodology -In this research work, the pure MgBi 2 O 6 crystal was produced through the usual solid-state reaction method with the high purity (purity > 98 %) powders of MgO and Bi 2 O 5 . In order to begin the synthesizing process of MgBi 2 O 6 , initially we have studied the phase development of this phase using a thermobalance (TG/DTA 630). A stoichiometric mixture of MgO and Bi 2 O 5 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 Bi 2 O 5 ) is also revealed in  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 Bi 2 O 5 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 sintered 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 MgBi 2 O 6 was analyzed by using the X-ray powder diffraction spectroscopy with CuK α (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.

Theoretical methodology -
The detailed physical properties of magnesium bismuth oxide, MgBi 2 O 6 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 generalized gradient approximation (GGA). For pseudo atomic computations, Mg-2p 6 3s 2 , Bi-6s 2 6p 3 and O-2s 2 2p 4 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 10105 k-points was used for compound MgBi 2 O 6 . In order to obtain the equilibrium crystal structure of MgBi 2 O 6 the Broyden-Fletcher-Goldfarb-Shanno (BFGS) minimization scheme was used. The succeeding criteria 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 MgBi 2 O 6 (Kang et al., 2003;Mostari et al., 2020). We have used the Voigt-Reuss-Hill approximations to compute the poly-crystalline elastic constants of MgBi 2 O 6 .

Experimental and Theoretical Structural
Properties -The structural analysis of MgBi 2 O 6 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 MgBi 2 O 6 is displayed 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 MgBi 2 O 6 . 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 MgBi 2 O 6 . The higher crystallinity would promote to yield higher photocatalytic activity (Zhong et al., 2018). To study the effect of external pressure on the crystal structure of MgBi 2 O 6 , we have studied the variations of the lattice parameters, unit cell volume and bulk modulus of MgBi 2 O 6 with differrent 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 MgBi 2 O 6 with pressure are presented in Fig 3. From Fig 3 we have seen that the lattice parameters and the cell volume of MgBi 2 O 6 are decrease with increa-ses of pressure, consequently the bulk modulus, B 0 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 . The lattice parameters, cell volume and bulk modulus with different pressures are listed in Table 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 MgBi 2 O 6 which are shown in 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).  The frequency-dependent ac conductance of the synthesized sample MgBi 2 O 6 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 ionhopping rules, the ionic conduction of MgBi 2 O 6 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).  The frequency dependent capacitance of MgBi 2 O 6 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 MgBi 2 O 6 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.   Fig 8 (a, and b) illustrate the absorption spectra and transmittance of compound MgBi 2 O 6 . 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 -

= ℎ
Where 'E g ' is the optical band gap, 'h' is the Plank's 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, = 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. 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 MgBi 2 O 6 are calculated from a linear fit of the stress-strain function as said by Hook's 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 experimental 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.

nm
2(C 11 + C 12 ) + C 33 + 4C 13 > 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 MgBi 2 O 6 is mechanical stable in nature. From Table  3 we have observed that C 33 is higher than C 11 signifying that the chemical bonding strength in the (001) direction is considerably stronger than bonding strength in the (100) and (010) directions. Additionally, C 44 is clearly smaller than C 66 indicating that it is very easy to occurs shear deformation in (001) direction than (010) direction (Liu et al., 2019).    9c) and confirms the stability nature of MgBi 2 O 6 up to 50 GPa. Consequently, the bulk modulus, shear modulus and Young's modulus definitely shows an increasing tendency as pressure increases (Fig 9b)  And 2 = ( 11 + 12 ) 33 − 2 13 2 According to Hill the average value of B and G is given by, Now to find out the values of Young's modulus (E) and Poisson's ratio (ν) we have used the following relations, The Universal anisotropic factor of a material can be calculated by the following equation Ranganathan and Ostoja-Starzewski, 2008, The calculated polycrystalline elastic constants at different pressures of MgBi 2 O 6 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 MgBi 2 O 6 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 MgBi 2 O 6 is strongly prone to ductility at high pressure. Another recognized parameter is the Poisson's ratio, ʋ which is used to separate the brittle solids from the ductile once proposed by Frantsevich et al. (1983). The larger value of Poisson's ratio ( > 0.26) indicates ductile manner and the compound will be brittle when the value of Poisson's ratio is ( < 0.26).
According to the value of ν as evident from Table 4 this material shows ductile behavior which consistent with the result of Pugh's criteria B/G. Our results are very similar to the previous study (Liu et al., 2019). Fig 10(b) also ensures that MgBi 2 O 6 has little bit ductile manner at zero pressure and is strongly prone to higher ductility with increasing 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 A U at 0 to 50 GPa of MgBi 2 O 6 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 A U increases sharply with increasing pressure due to reason that that the elastic constants C 11 , C 33 , C 66 , C 12 and C 13 are increased with pressure.

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 MgBi 2 O 6 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 MgBi 2 O 6 . This characteristic is also observed from the resistivity analysis shown in Fig 6(a). The investigated electronic band gap of MgBi 2 O 6 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 electron's excitation effects and therefore underrate the electronic band gap (Naefa and Rahman, 2020). The calculated partial and total density of states of tetragonal MgBi 2 O 6 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 MgBi 2 O 6 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 MgBi 2 O 6 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.    . 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 MgBi 2 O 6 has strong refractive effect in the infrared and visible regions. The loss function of fast moving electron would be used to represent the resonant frequency or bulk plasma frequency 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 MgBi 2 O 6 are obvious. This result is well agrees with our previous study  and did not agree with the study of Lin Liu et al. (2019). Therefore MgBi 2 O 6 shows transparent behavior when the incident photon has the energy higher than this plasma frequency. The calculated absorption spectrum of MgBi 2 O 6 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 MgBi 2 O 6 starts at about 0.14 eV (Fig 14e) confirming again the semiconducting nature of this phase. Since the material MgBi 2 O 6 has high absorption in the ultraviolet region as a result maximum conductivity is observed in this region. The reflectivity shape of MgBi 2 O 6 is shown in Fig 14(f). The high reflectivity is appeared at around 13 eV which corresponds to the energy where the conductivity falls to zero and absorption quality is good.
Since MgBi 2 O 6 shows good reflectivity in the high energy area this compound should be used as a possible shield for ultraviolet radiation.

CONCLUSION:
In summary, the pure single phase MgBi 2 O 6 crystal has been effectively prepared through solid-state reaction way. The polycrystalline sample MgBi 2 O 6 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 MgBi 2 O 6 , when it is used as a visible light-sensitive photocatalysts. The decrease of electrical resistivity and increase of electrical conductivity with temperature ensures the semi-conducting behavior of MgBi 2 O 6 . 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 configuration, mechanical, electronic and optical properties of MgBi 2 O 6 . 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 MgBi 2 O 6 . The existence of ionic and covalent features is observed from the Mulliken atomic population calculations. The investigated elastic constants satisfied the Born's stability criteria and ensure the mechanical stability of MgBi 2 O 6 . All the elastic constants show linear response with the external pressure in which C 33 shows more response compared to other constants. The calculated B/G ensures a little bit ductile manner of MgBi 2 O 6 at zero pressure but this phase is strongly prone to higher ductility at high pressure. The increased of Poisson's ratio and anisotropic factor are observed with increasing pressure. The large reflectivity in the ultraviolet site ensures that MgBi 2 O 6 should be used as a possible coating material for ultraviolet radiation.

ACKNOWLEDGEMENT:
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