Microwave-Driven Hexagonal to Monoclinic Transition in BiPO4: An In-depth Experimental Investigation and First-Principles Study

Present theoretical and experimental work provides an in-depth understanding of the morphological, structural, electronic, and optical properties of hexagonal and monoclinic polymorphs of BiPO4. Herein, we demonstrate how microwave irradiation induces the transformation of the hexagonal to a monoclinic phase one in a short period of time and thus, the photocatalytic performance of BiPO4. To complement and rationalize the experimental results, first-principle calculations have been performed within the framework of the density functional theory. This was aimed at obtaining the geometric, energetic and structural parameters as well as vibrational frequencies; further, electronic properties (band structure diagram and density of states) of the bulk and the corresponding surfaces of both hexagonal and monoclinic surfaces of BiPO4 were also acquired. A detailed characterization of the low vibrational modes of both hexagonal and monoclinic polymorphs is key in explaining the irreversible phase transformation from hexagonal to monoclinic. Based on the calculated values of the surface energies, a map of the available morphologies of both phases was obtained by using the Wulff construction and compared with the observed SEM images. The BiPO4 crystals obtained after 16-32 min of microwave irradiation provided excellent photodegradation of Rhodamine B under visible light irradiation. This enhancement was found to be related to the surface energy and the types of clusters formed on the exposed surfaces of the morphology. These findings provide details of the


INTRODUCTION
Bismuth phosphate (BiPO 4 ) is a promising photocatalyst that is activated by visible light. It demonstrates double the activity of TiO 2 (P25, Degussa) for the degradation of organic dyes under ultraviolet (UV) light 1 ; further, it exhibits enhanced photocatalytic activity toward NO purification 2,3 . BiPO 4 presents hexagonal and monoclinic polymorphs that comprise both distorted tetrahedral [PO 4 ] and octahedral [BiO 6 ] clusters, which are the primary building blocks of the polymorph. However, both polymorphs present different photocatalytic activity, which is highly dependent on the structure, electronic properties, morphology of these phases; consequently, it is reliant its exposed surfaces as well 2,[4][5][6][7] . In particular, Fu et al. 8 have reported that the monoclinic phase of BiPO 4 is the preferred crystalline structure for the degradation of benzene; this is due to the structural distortion of the tetrahedral [PO 4 ] cluster and the large band gap structure [9][10][11] . The preparation of BiPO 4 polymorphs (hexagonal and monoclinic) has been successfully carried out by several methods. The pure hexagonal phase of BiPO 4 has already been obtained by conventional hydrothermal 12 , microwave assisted hydrothermal (MAH) 13 , and sonochemical 14,15 methods under mild synthesis conditions. In turn, the pure monoclinic phase is usually obtained by the conventional hydrothermal method, which exhibits long synthesis periods (2h-96h) and temperatures up to 200 °C 1, 2, 16-18 . Wang et al. also observed the formation of the monoclinic phase using the MAH method, but with the addition of an ionic liquid in the reaction medium 19 . Few studies in the literature also show the conversion of the hexagonal phase to the monoclinic phase by the hydrothermal method 12 through the incorporation of compression 20 or doping processes 21,22 . Chen et al. observed complete conversion by employing the time frame of 1 to 3h at a temperature of 200 °C 23 . Further, Zhu et al. required up to 12h of synthesis at 150 °C to complete the conversion of the hexagonal phase to monoclinic 24 . In these studies, it is evident that complete conversion from one phase to the other was directly proportional to the temperature employed during the synthesis.
Among the different solution-based synthesis techniques, microwave irradiation has garnered a widespread scope of remarkably new opportunities to explore its applications in the area of material science. Microwave irradiation in a suitable solvent has been widely applied for the rapid synthesis of inorganic solids at relatively lower temperatures within a short reaction time (within minutes) as compared to conventional heating [25][26][27] ; further, it has received special attention owing to its interesting advantages, which include rapid, uniform, and selective heating, reduced processing costs, better production quality, and the possibility of modifying the phase stability and the morphology beyond thermodynamic equilibrium. This has led to the fabrication of new materials that are technologically important such as meta-stable phases, which are not accessible by conventional methods [28][29][30] . Further, microwave heating is an inexpensive, facile, and relatively fast method for the preparation of crystalline samples, which exhibit unique or enhanced properties; further, these can be used to fabricate products with narrow particle size distribution and increased phase purity [30][31][32][33][34] . However, microwave-specific thermal effects and microwave non-thermal effects are still poorly understood, especially during synthesis procedures 35 .
Recently, the structures and energetics of four low index stoichiometric surfaces ((001), (010), (011), and (100)) of monoclinic monazite BiPO 4 have been studied from a theoretical point of view by using density functional theory (DFT) calculations 36 . Fun et al. 37 showed that monoclinic BiPO 4 exhibits a dendritic morphology, and performs well as a photocatalyst for the degradation 5 process of benzene; this is due to the presence of highly energetic (002), (012), and (031) surfaces and the oxygen vacancies (). However, the role of the exposed surfaces and morphology on the photocatalytic activity are still unrevealed. To the best of our knowledge, reports on the direct visualization of the transition process between hexagonal and monoclinic phases have been very limited; in addition, deep insight into the surface-dependent photocatalytic activity of both hexagonal and monoclinic polymorphs of materials based on BiPO 4 has not been yet carried out.
An attractive alternative, but yet underexplored strategy to gain control over phase transition is provided by regulating the microwave irradiation while keeping all other parameters constants.
Therefore, understanding the phase transition process, at the atomic scale, can allow an efficient phase-controlled synthesis that leads to crystal structure with improved properties and thus may have new materials with potential for various technological applications. Inspired by the above considerations, we report a novel study on the gradual transformation of hexagonal BiPO 4 to the monoclinic polymorph upon microwave irradiation without the addition of any surfactants and templates; the BiPO 4 microcrystals initially exhibit a hexagonal structure and are obtained by a simple co-precipitation (CP) method. Our principal aim was to understand the fine effects of the microwave irradiation on the morphology and photoluminescence (PL) emissions of the assynthesized BiPO 4 crystals, and to investigate the role of the electronic structure on their photocatalytic activity. Herein, we elucidate these points by performing a detailed theoretical and experimental study on the photocatalytic activity in the degradation process of Rhodamine B (RhB) under visible irradiation. The synthesized materials were characterized by X-ray diffraction (XRD) with Rietveld refinement, scanning electron microscopy (SEM), and micro-Raman spectroscopy. Moreover, their optical properties were investigated by using ultraviolet-6 visible (UV-vis) spectroscopy and PL measurements at room temperature. First-principles theoretical calculations within the framework of density functional theory (DFT) were employed to obtain atomic level information of the geometry and electronic structure, local bonding, band structure, density of states (DOS), and vibrational frequencies. The morphologies of the assynthesized samples are obtained by SEM images, and their corresponding transformations are rationalized; this is achieved by using the Wulff construction and altering the relative values of the surface energies of the different surfaces. The effect of time on the formation of hexagonal and monoclinic phases and on their structural, morphological, and absorption properties was investigated. Furthermore, by combining the results obtained from first-principle calculations and experimental measurements, the crystal structure, electronic properties, and surface energies characteristics of BiPO 4 were analysed; this was aimed at achieving deep insights into the morphology characteristics, optical properties, and photocatalytic activity toward RhB. The accurate prediction of the structure, stability, electronic structure, and morphologies of BiPO 4 is an essential prerequisite for tuning their electronic properties and functions. Characterization. The BiPO 4 samples were structurally characterized by XRD using a D/Max-2500PC diffractometer (Rigaku,) with Cu Kα radiation (λ = 1.5406 Å) in the 2θ range of 10 -110° and a scanning speed of 1°min -1 in the Rietveld routine. The Rietveld refinement method was employed to understand the structural differences and the phase composition of the BiPO 4 . In this analysis, the refined parameters were: the scale factor, background, shift in the lattice constants, profile half-width parameters (u, v, w), isotropic thermal parameters, lattice parameters, strain anisotropy factor, preferred orientation, and atomic functional positions.
Further, micro-Raman spectra were recorded using the iHR550 spectrometer (Horiba Jobin-Yvon) coupled to a Silicon CCD detector and an argon-ion laser (Melles Griot, USA), which operated at 514.5 nm with a maximum power of 200 mW; moreover, a fiber optic microscope was also employed. UV-Vis diffuse reflectance measurements were obtained using a Varian Cary spectrometer model 5G in the diffuse reflectance mode, with a wavelength range of 200 to 800 nm and a scan speed of 600 nm min -1 . Photoluminescence measurements were performed at room temperature by using a 355 nm laser (Cobolt/Zouk) as an excitation source, which was The accuracy of the Coulomb and exchange integral calculations (TOLINTEG) was controlled by five parameters set to 10 −7 , 10 −7 , 10 −7 , 10 −7 and 10 −14 , the reciprocal space was considering in a 6x6 mesh (SHRINK) corresponding to 6 independent k-points in the Brillouin zone according to the Pack-Monkhorst method 42 . The band structure and DOS were obtained for 100 k-points along the appropriate high symmetry paths of the adequate Brillouin zone.
The equilibrium morphology of a crystal was calculated based on the classic Wulff construction 43 , by minimizing the total surface energy () at a fixed volume, providing a simple relationship between the of the plane (hkl) and its distance in the normal direction from the center of the crystallite 44 . is defined as the energy per unit area required to form the surface relative to the bulk and is calculated according to equation: Where is the energy of the relaxed slab, is the number of BiPO 4  In addition, the broken bonding density (), which is defined as the number of bonds broken per unit cell area when a surface is created can be calculated by using Eq. 5 54,55 : Eq. 5 Where is the number of broken bonds per unit cell area on a specific surface and A is the area unit of the surface. From the values derived from , we can predict the order of surface stability as we know that higher values are related to larger quantities of defects present on the surface 56 .
The polyhedron energy () was calculated with Eq. 6 and energy profiles were constructed, allowing us to associate the ideal morphology with the final experimental morphology.

Eq. 6
Where is the percentage contribution of the surface area to the total area of polyhedron () and is the surface energy 57 .

RESULTS AND DISCUSSION
X-Ray Diffraction. Figure 1 shows the XRD patterns of the BiPO 4 samples obtained by the CP method and also of those subjected to microwave irradiation at different times. XRD analysis were performed to demonstrate the order/disorder transition at long-range, or to determine the periodicity and arrangement of the crystalline lattice. All samples exhibit well defined diffraction peaks, indicating a good degree of structural order at long-range in the crystalline lattice.

<INSERT FIGURE 1>
The samples synthesized by the CP method and irradiated by microwave at 2 and 4 min correspond to BiPO 4 with hexagonal structure and space group P3 1 21; this was in accordance with card no. 67986 58 Tables SI-1 and Table SI-2 (in the Supporting Information, SI).

<INSERT FIGURE 2>
The parameters obtained in the Rietveld refinements of BiPO 4 powders are shown in Table SI-3 and Table SI-4, and their structural results are presented in Figure 3, in which the statistic fitting parameters (R wp and GOF see Table SI-3, Supporting Information) indicate that the quality of structural refinement data is acceptable ( Figure SI-1). The calculated equilibrium lattice parameters of the two phases of BiPO 4 are also shown in Table SI-4. An analysis of the results presented in Table SI-1 and Table SI-2 renders slight differences between the calculated and experimental data of bond distances and angles, which can be attributed to differing synthesis conditions. Following the proposal of Xu et al. 36 , and Zhu et al. 59 we assumed that both polymorphs can be described by [BiO 6 ] and [PO 4 ] clusters.
Thus, more specifically, the [BiO 6 ] clusters correspond to a distorted octahedron in the hexagonal phase with the Bi-O bond length in the range of 2.368 Å to 2.558 Å (see Table SI-3) and a distorted oblique triangular prism in the monoclinic phase with the bond length of Bi-O in the range of 2.326 Å to 2.523 Å (see Table SI Table SI-5 and SI-6

<INSERT FIGURE 4>
These findings seem to indicate that the energetic stimuli, provided by the microwave irradiation, is capable to active these low vibrational modes to enhance the phase transformation, from the hexagonal to the monoclinic polymorph. At the local coordination, the distorted octahedron [BiO 6 ], at the hexagonal phase, undergoes a structural rearrangement to distorted oblique triangular prism [BiO 6 ] in the monoclinic polymorph. This monoclinic BiPO 4 phase presents low vibrational modes at 71.3 and 78.28 cm -1 , but the corresponding movements are not associated to the transformation from monoclinic to hexagonal polymorph. Therefore, these results seem to indicate that the phase transition from hexagonal to monoclinic, induced by microwave irradiation, corresponds to an irreversible process.
A note of caution is mandatory here, our previous analysis is based on the low vibrational modes of the hexagonal phase to explain the initial vibrational modes responsible for the phase transition, but a correct explanation need to be obtained by characterizing transition state, and in particular their transition vector, i.e, their unique imaginary vibration mode that controls this phase transition.

Photoluminescence (PL) Emissions. PL measurements were also performed in order to
investigate the influence of structural ordering of defects of BiPO 4 samples. Figure 5A shows the PL emissions under a UV laser excitation (λ = 355 nm). All samples show PL emission in the range of the visible spectrum with a broad-band profile, which is characteristic of multi-phonon processes, ruled by the presence of high density of electronic levels within the band gap [67][68][69][70] . In order to verify the whole PL emission, an analysis by Commission Internationale de l´Éclairage (CIE) coordinates was performed by SpectraLux software 71 . Figure 5B shows the CIE chromaticity diagram for PL spectra of all samples. Although there are slight differences in the color shades, all samples presented emissions in the green region of the visible spectrum.

<INSERT FIGURE 5>
The PL emissions were deconvoluted using the Voigt function, to quantify the contributions of each defect to the PL emission, as shown in Figure SI In the case of the monoclinic phase ( Figure SI-7), the top of the VB is located mainly between D and C points and the bottom of the CB is located at the region between  and Γ points. The band gap calculated is 4.60 eV corresponding to an indirect transition and the experimental value report in this work was 3.80 eV. Band gap experimental values between 3.5-4.6 eV have been reported, which depend on the size of the particle and the method of synthesis 59,66,78 .  Figures 6B-D), the hexagonal phase is predominantly observed, and there is an increase in the size of the needles that form the rod microstructure, and well-defined hexagonal rods appear. When the monoclinic phase is predominant, at 16 and 32 min of microwave irradiation, (Figures 6E-F), the microstructures change into beveled tetragonal rods. This effect is due to the continuous dissolution/recrystallization processes that occur in BiPO 4 induced by the microwave irradiation, and thus, structural changes take place at short, medium and longdistance, as discussed above.

<INSERT FIGURE 8>
Thus, for the hexagonal phase the and , surfaces, present only one kind of under-coordinated cluster , it is worth noting that all studied surfaces present this kind of under-coordinated cluster, with exception for the surface which present only an under-coordinated cluster . In surface, under-coordinated cluster of and is present. The surface is formed by , and clusters. The most unstable surfaces, and , are formed by under-coordinated and clusters which are common to both surfaces, while on the surface, the clusters appear, and in surface, and clusters are found.
In the case of the monoclinic phase, under-coordinated Bi cation, and and clusters, can be observed, and under-coordinated and clusters centered around the P cation can be sensed. More specifically, , , and surfaces are characterized for present only the under-coordinated cluster.
In the case of surface can be observed , clusters as well as cluster. On the other hand, surface presents four kind of under-coordinated cluster: , , and . The surface displays the and clusters, while surface, is formed for the under-coordinated and clusters, and it is the only surface that present clusters. Table SI-8 and Table SI-9. It is possible to establish an order of thermodynamic stability for these surfaces, thus, to BiPO 4 hexagonal the following order of decreasing stability is established: > > > > > > while for BiPO 4 monoclinic of decreasing order of stability is: > > > > > > > .

By comparison of the calculated values shown in
With the reported in Table SI-8

<INSERT FIGURE 10>
The ideal morphology of the hexagonal phase is characterized by a six-fold geometry (see Figure 9) that is controlled by , and surfaces. Starting from the ideal morphology and aiming to obtain a similar morphology to the experimental SEM images, which present a six-fold pyramidal geometry, the values of the surface energy for the and were decreased and the 23 surface energy for was increased, simultaneously. On the other hand, a similar morphology of experimental geometry can also be obtained through stabilization of the (1012) surface.
However, we associated the experimental morphology with the controlled morphology for the surface, as reported by Li et al. 13 in which the HR-TEM image of an individual BiPO 4 nanoparticle shows the presence of plane in the hexagonal phase.
In the case of the monoclinic phase of the BiPO 4 (see Figure 10 (top)), the ideal morphology is controlled by , , and surfaces. The experimental morphology was simulated by means of two paths: the first from shape A and by stabilizing surface to obtain shape A1 and subsequently by stabilizing and destabilizing simultaneously, obtaining shape A2. The second path was reached stabilizing surface which is theoretically the most unstable surface and surface, simultaneously to obtain shape B1 and destabilizing surface, to obtain shape B2. We have associated our experimental morphologies with the B1 and B2 shapes. The A2 and D morphologies generated are similar to that reported by Li et al. 21 Furthermore, the polyhedron energy () was calculated and also the energy profiles which allows to connect the ideal morphology with the final experimental morphology were constructed and are depicted in Figure 9 and 10 (bottom) for BiPO 4 hexagonal and monoclinic, respectively. The reaction diagram to obtain the final experimental morphologies of BiPO 4 hexagonal evidences a process barrier less thermodynamically favorable (Figure 9 (bottom)) while the reaction path for BiPO 4 monoclinic presents a minimum of energy via morphology B1 ( Figure 10 (bottom)). The parameters used to calculate are reported in Table SI-10  Here, k is the rate constant and t the reaction time. Therefore, if the reaction order is of pseudofirst order, the plot of -ln(C n /C 0 ) as a function of irradiation time gives a straight line in which the angular coefficient is the k value. The L-H plots were performed in order to verify the reaction order and to obtain the rate constant for all samples, as shown in Figure 11B.

<INSERT FIGURE 11>
The photodegradation behavior change is observed according to the time employed at the microwave irradiation. The hexagonal phase BiPO 4 synthesized by the CP method has an 85% rate of RhB chromophore photodegradation. After the sample was subjected to microwave irradiation for 2, 4 and 8 min, an inhibition of photodegradation activity is observed. This happens because the surfaces employed in the electron-hole recombination process of the hexagonal phase of BiPO 4 observed predominantly in these samples (2, 4 and 8 min) is different to that observed in the BiPO 4 sample obtained by the CP method. The surface stabilization of the obtained materials is intrinsically linked to the kinetic change in the balance of ordered and disordered [BiO 6 ] clusters due to microwave action. The sample obtained by CP method has no defined surfaces and may have several different types of oxygen vacancies () on its surface, both coming from Bi clusters and P clusters. When the hexagonal samples of BiPO 4 obtained at 2, 4 and 8 min by microwave irradiation are analyzed, we can observe the stabilization of the surfaces , which has two clusters with (), and ), which has three in the clusters and . The stabilized surfaces employed in the photodegradation process cannot perform electron-hole recombination, becoming ineffective in this process. Moving from the hexagonal phase to the monoclinic phase of the BiPO 4 , at the 16 and 32 min samples, an efficiency of 83 and 79% is observed for photodegradation respectively. This is due to the stabilization of the surfaces , which has two cluster with (), , which has two clusters with () and , which has six in the clusters , and .
Photocatalytic activity is dependent on the electron-hole recombination rate of the material.
The hexagonal structure of BiPO 4 obtained by CP has a high degree of order/disorder, so the electron-hole recombination rate is more effective, enabling RhB photodegradation. Analyzing the structures obtained in 2, 4 and 8 min, the hexagonal phase reorganization was observed, resulting in new morphologies of BiPO 4 . The results obtained for these samples at long-distance (XRD) correspond with an increase of material organization, creating new active sites and reducing electron-hole recombination. The transformation from hexagonal to monoclinic structure causes a structural reorganization, generating new active sites for electron-hole stabilization, making the photodegradation process of RhB effective again.
Due to these results, photocatalytic experiments using scavenger reagents were performed for the BiPO 4 CP and the BiPO 4 32 min samples, in order to understand the photodegradation mechanism. As a control for these experiments, tert-butyl alcohol (TBA), silver nitrate (SN), pbenzoquinone (BQ), and ammonium oxalate (AO) were used as scavengers for hydroxyl radicals, electrons, superoxide radicals, and holes, respectively. Figure 11C shows the photodegradation efficiency of samples of BiPO 4 with and without scavengers. All the experiments for both samples, i.e. the absence of hydroxyl radicals, electrons, superoxide radicals, and holes for reactions, presented inhibited or lower photodegradation efficiency compared to the BiPO 4 samples without scavengers. From these results, we propose a photodegradation mechanism, as given by Figure 12, which were constructed with Kröger-Vink notation 81 .

<INSERT FIGURE 12>
In Figure 16, the BiPO 4 surface clusters are represented for the general formula (where A = P and Bi, y = 2, 4 and 5, n = 1 and 2, to represent , and ). The presents in the clusters can become and according to the movement of electrons and holes in the BiPO 4 surface by cluster-cluster charge transfer (I, II and II in Figure 12). Losing electrons (I and II in Figure 12), the formation of and in the clusters favors the processes that lead to oxidation of H 2 O and reduction of O 2 (IV and V in Figure 12), which generate reactive oxygen species (ROS), the hydroxyl radical and the hydroperoxyl radical . This process can be observed for samples obtained by CP method and at 16 and 32 min of microwave irradiation. After ROS production, the clusters regenerate, continuing the oxidation processes (VI in Figure 12). The is generated by the reaction of the proton () with the superoxide radical 82 . Electron recovery for the formation of is not favorable 28 for photocatalysis oxidation processes, which probably occur for samples obtained at 2, 4 and 8 min of microwave irradiation (III and VII in Figure 12).

CONCLUSIONS
As has emerged from this work, microwave irradiation upon materials can be exploited for enhance phase transition. Here, we present a combined theoretical and experimental study dedicated to analyze the microwave-driven hexagonal to monoclinic transition in BiPO 4 . The study has been made possible by the combination of experimental techniques (XRD with Rietveld refinement, SEM, and micro-Raman and UV-vis spectroscopies, and PL measurements) and first principle calculations, at the DFT level. We have observed the phase transition of hexagonal to monoclinic BiPO 4 under microwave irradiation; in addition, by analyzing the structural ad electronic differences between these polymorphs and their exposed surfaces, the highest photocatalytic activity of monoclinic BiPO 4 exhibited when compared with the hexagonal BiPO 4 is disclosed.
The main conclusions of this work can be summarized as follows: (i) BiPO 4 crystals with hexagonal structure were successfully synthesized by the simple coprecipitation method and, for the first time, the effect the microwave irradiation to induce the irreversible phase transition from hexagonal into monoclinic BiPO 4 polymorph have been reported. Hexagonal BiPO 4 is unstable under microwave irradiation, spontaneously transforming to the monoclinic phase BiPO 4 in short time and thus, enhancing photocatalytic performance of (v) Based on the analysis of the geometry and electronic properties of the under-coordinated clusters (local coordination of P and Bi cations) appearing at the exposed surfaces of the morphology, we are capable to rationalize the mechanism of the photodegradation process of Rhodamine B under visible light irradiation.
Our findings elucidate the structural and electronic alterations along the phase transition between hexagonal and monoclinic phases of BiPO 4 , which are induced by microwaves; further, these results serve as guidelines for engineers to optimize the structure and performance of future photocatalysts for environmental remediation applications.