Hydrothermal synthesis of Ce/Zr co-substituted BiFeO3: R3c-to-P4mm phase transition and enhanced room temperature ferromagnetism

A facile hydrothermal method was used for fabricating phase-pure Bi1−xCexFe1−xZrxO3 (x = 0.00, 0.03, 0.06) multiferroic ferrites, and the dependence of structural, optical, and magnetic properties on the composition have been investigated. The samples were investigated by X-ray diffraction, Raman and Fourier transform infrared spectroscopies, scanning electron microscopy, UV–Vis spectroscopy, and vibrating sample magnetometer at room temperature. Structural results show that the structure of Bi1−xCexFe1−xZrxO3 ferrites is indexed to a rhombohedral structure with the R3c space group. However, the weakening in the intensity, the expansion of the line-width of all bands, and some band shifts observed in Raman spectra indicate a structural transition from rhombohedral (R3c) to pseudo-tetragonal (P4mm) phase as the content of Ce/Zr increases. Also, a significantly enhanced intensity of the A1–2 mode in Raman spectra means that there is a novel behavior of magnetic anisotropy in the Ce/Zr co-substituted samples. A significant increase in optical bandgap with increasing of the Ce/Zr co-substitution suggests that the materials are suitable for technological applications. Magnetic properties of the samples show a magnetic transition from antiferromagnetic to ferromagnetic phase due to the presence of the rhombohedral to the tetragonal phase transition, and exchange interaction between the 4f orbitals of the Ce3+/Ce4+ and the 3d orbitals of the Fe3+/Fe2+.


Introduction
BiFeO 3 (BFO) is the most famous multiferroic material having the antiferromagnetic Néel temperature (= 370 K) and the ferroelectric Curie temperature (= 830 K) which simultaneously shows a saturation polarization and magnetic moment of 90 lC/cm 3 and 8-9 emu/cm 3 , respectively [1]. The ferroelectricity and G-type antiferromagnetic characteristics of BFO come respectively from the lone-pair distortion on the 6s 2 of Bi 3? ions and spin-exchange coupling between half-filled 'd' orbital of Fe 3? ions [2,3].
Arora et al. [20] reported successfully the substitution of Fe 3? with Zr 4? pure-phase Zr-substituted BiFeO 3 prepared with the hydrothermal method by several techniques. Our group recently reported that the A-site (Nd, Y, Gd) and B-site (Mn, Zr) co-substitution of BFO have a result to reduce the particle size to less than 62 nm which will destruct or suppress the magnetic spiral structure [6,7]. However, in the present work, the hydrothermal method was used for the synthesis of pure single-phase Bi 1-x Ce x Fe 1-x Zr x-O 3 (x = 0.00, 0.03, 0.06) at a low temperature of 180°C without a further calcination step. Since, r Ce 3þ CN : 12 ð Þ¼1:34Å is closer to the r Bi 3þ CN : 12 ð Þ (1.4 Å , 6 s lone pair), the Ce substitution results in a low symmetry distorted rhombohedral structure with R3c space group accompanied by a large polarization along the hexagonal [001] or the pseudocubic [111] direction [21][22][23]. Furthermore, it highly expects that Bi 3? substitution with Ce 3? can reduce the leakage current density accompanied by a further improvement in the ferroelectric properties of BFO [23]. On the other side, the Ce 4? ions act as a donor because of their higher valance than that of Bi 3? ions, where the substitution of Ce 4? for Bi 3? requires charge compensation which can be achieved by the suppression of oxygen vacancies and Fe 2? [21]. the A-site Bi 3? ion of the BFO film shows a valence electron configuration of 6s 2 6p 0 ; the lone 6s 2 electrons of the Bi 3? ion hybridize with both the empty 6p 0 orbits of the Bi 3? ion and the 2p 6 electrons of the O 2ion to form a Bi-O bond [24]. As for the Ce-substituted BFO film, the A-site Ce 3? and Ce 4? ions show valence electron configurations of 4f 1 5d 0 6s 0 and 5p 6 4f 0 5d 0 6s 0 , respectively [25,26]. The 4f 1 electron of the Ce 3? ion hybridizes with the empty 5d 0 and 6s 0 orbits of the Ce 3? ion and the 2p 6 electrons of the O 2ion; meanwhile, the 5p 6 electrons of the Ce 4? ion hybridize with the empty 4f 0 , 5d 0 , and 6s 0 orbits of the Ce 4? ion and the 2p 6 electrons of the O 2ion to form Ce-O bonds, leading to a noncentrosymmetrically distorted structure and a suppressed spiral spin structure, probably improving the ferroelectric and magnetic properties of the Ce-substituted BFO. Previous reports on Zr 4? substitution for Fe 3? showed that lattice strains and defects originated from a mismatch in ionic radii prevent the growth of the grain sizes as the substitution increases and all the samples show the antiferromagnetic behavior [27]. While in A/Zr co-substitution for Bi/ Fe, the particle sizes go down and a weak ferromagnetic behavior with an improvement of microwaves properties are observed [7,28]. Detailed studies of structural, optical, and magnetic properties indicate novel behaviors of the pure single-phase Bi 1-x To ensure accurate and  reproducible results, the high purity reagents and chemicals were used which were purchased from Sigma-Aldrich. The crystal phase of the Bi 1-x Ce x Fe 1-x Zr x O 3 (x = 0.00, 0.03, 0.06) nanoparticles was identified by powder X-ray diffraction (XRD, D8-Advance Bruker AXS diffractometer) with a Cu-Ka radiation (k = 1.54048 Å ). The patterns were analyzed using the Fullprof program [29]. Raman spectra were performed in a Renishaw 1000 confocal Raman microscope using a 532 nm diode-pumped solid-state laser (Cobolt) with a laser power of 10 mW. The Fourier transform infrared (FTIR) spectra of the samples were obtained from a Perkin-Elmer FT-IR spectrometer. The surface morphology images of the samples were recorded by field-emission scanning electron microscopy (FESEM, HITACHI S-4160 model) with the accelerating voltage of 10 kV. The absorption spectra of the samples were recorded by a UV-Vis system (Agilent8453, Palo Alto, CA). The direct-transition bandgap energy of the samples was estimated through Tauc's equation [30]. The hysteresis loops of the samples were recorded using the VSM 7407 Lake Shore's vibrating sample magnetometer at room temperature and a maximum magnetic field of 2 T.

Results and discussion
3.1 Structural analysis Figure 1 shows XRD patterns of a single-phase perovskite structure of Bi 1-x Ce x Fe 1-x Zr x O 3 (x = 0.00, 0.03, 0.06) nanoparticles. It reveals the presence of a rhombohedral crystal structure with R3c space group for BFO which is in accordance with the JCPDS card (no. 86-1518) [7]. After Ce 3? /Zr 4? ions doping into BFO, the doublet diffraction peaks (104) and (110), (006) and (202), (116) and (112), (118) and (300) of the rhombohedral structure are merging to the singlet peak as shown in Fig. 1. Also, the location of all the diffraction peaks shifted toward a higher angle.
Although the intensity of XRD peaks located at the higher angles is increasing, the intensity of singlet peak (012) R at about 22°becomes smaller. Besides, an enlarged view of (012) R and (024) R reflections is plotted inset of Fig. 1 to show the structural change as Ce 3? /Zr 4? content increases up to x = 0.06. As seen from Fig. 1, a splitting in both the parallel (012) R and (024) R reflections of the rhombohedral structure which are singlet peaks, occur with the addition of Ce 3? /Zr 4? content. The singlet (012) R peak is split into two sub-peaks, a larger peak at about 22.50°and a smaller peak at about 22.75°which are respectively corresponded to the reflection planes (001) T and (100) T of tetragonal structure. Similarly, the singlet (024) R peak is split into two sub-peaks, a larger peak at about 45.90°and a smaller peak at about 46.40°F ig. 1 XRD pattern and Rietveld analysis with rhombohedral (space group R3c) structural model for Bi 1-x Ce x Fe 1-x Zr x O 3 (x = 0.00, 0.03) and a mixed-phase tetragonal (P4mm) ? rhombohedral (R3c) structural models for x = 0.06. Red circles and black solid lines represent the raw data and the calculated profile, respectively. Green vertical lines indicate the position of Bragg peaks for rhombohedral structure. The blue lower trace shows the difference between the observed (the raw data) and the calculated patterns (Color figure online) which are respectively corresponded to the reflection planes (002) T and (200) T of the tetragonal structure. It should be noted that the intensity of the (001) T and (002) T reflections of the tetragonal structure is smaller than the (100) T and (200) T , respectively [31]. Since the structure of sample x = 0.06 is a mixture of the tetragonal (P4mm) and rhombohedral (R3c) phases, the peak overlap of the (012) R with the (001) T and the peak overlap of the (024) R with the (002) T occurs. These findings could be related to the fact that the lower symmetry rhombohedral structure of BFO gradually transforms into a higher symmetry tetragonal structure due to the changes of bond lengths Bi-O and Fe-O after the Ce 3? /Zr 4? doping into BFO, which is discussed further below.
The Rietveld refinement of the XRD patterns of the samples using Fullprof software confirms the formation of the rhombohedral structure with R3c space group (see Fig. 1). The refined lattice parameters and error bars of parameters in parentheses, as well as R-factors values related to the quality of Rietveld refinement (R p , R wp , R exp ) and v 2 (goodness of fitting), are listed in Table 1. The difference between observed and calculated curves can be due to noisy data observed over the whole angle range which results in the high values of R factors (R p , R wp , R exp ), while v 2 value shows the best goodness of fitting. Generally, the major factors causing a noisy XRD pattern are poorly crystalline sample, the measurement conditions, Cu-Ka X-rays.
The factor of the poorly crystalline sample is related to the amorphous sample having an XRD pattern with broad and low-intensity peaks. However, the height of XRD peaks in our samples is very high compared to the noisy background. If there is an impurity phase of ZrO 2 or CeO 2 in the samples, it needs to be at least the preferred peaks belonged to the impurity phases of ZrO 2 or CeO 2 in the XRD pattern of our samples. However, there are no preferred peaks from oxides ZrO 2 and CeO 2 in our samples. Also, the presence of a potassium line in the EDS spectrum of all the samples can suggest the formation of a small impurity phase containing K element (already, we cannot find any trace) which may be contributed to the noise background. As can be seen, all the Raman peaks were been completely belonged to BFO rhombohedral structure with no trace of the Raman peak of the impurity phase containing the K, Zr, or Ce elements. It should be noted that previous reports showed successfully the substitution of Bi 3? /Fe 3? with Ce 3? /Zr 4? into BiFeO 3 [7,13,21,[24][25][26][27][28][32][33][34]. Also, the successful synthesis of pure-phase BiFeO 3 and Zr-substituted BiFeO 3 prepared with hydrothermal method were investigated by several techniques [20,35].
The sample fluoresces is most pronounced when the source Cu-Ka radiation energy is only slightly greater than the characteristic X-rays of the sample (that are rich in Fe, Cr, Mn). In Cu diffractometer, the energy of the Cu-Ka (1.54 Å ) is sufficiently high to excite the Fe atoms (which conjointly stimulates the Table 1 The lattice parameters of conventional hexagonal (a H , c H ), primitive rhombohedral (a R , a R ) structures, the crystallite size (D W-H ) and microstrain (e) obtained from the Williamson-Hall method for Bi 1-x Ce x Fe 1-x Zr x O 3 with their error bars in parentheses and R-factors values related to the quality of Rietveld refinement (R p , R wp , R exp ,) and v 2 (goodness of fitting) Rhombohedral Tetragonal 13.87 (9) 13.83 (8) 13 124.9 (7) 123.9 (0) 123.6 (7) 61.18 ( FeKa (1.94 Å ) line and consequently engenders X-ray fluorescence) and the Fe-rich samples will fluoresce under the incident Cu-Ka beam which creates a combination of both Cu-Ka and Fe radiations with different wavelengths plus the continuum radiation entering the detector. It can lead to strange shaped and elevated backgrounds causing a noisy XRD pattern. Since the sample x = 0.06 contains more Fe than sample x = 0.00, the diffraction patterns of the sample x = 0.06 tend to feature a greater background. Potential resolutions of this issue are to utilize Co-Ka radiation (1.79 Å ) or to shield the front of the detector with a PVC filter, which will absorb the low energy fluorescence. Sometimes the noise/signal ratio can be reduced by going to lower scan rates or by opening up the slit size to allow a greater X-ray flux. Finally, the feature of noisy data observed in XRD patterns of all the samples over the whole angle range was due to the low-qualified measurement system which results in the high values of R factors (R p , R wp , R exp ).
The hexagonal cell is no longer primitive and has three times the volume of the rhombohedral cell. When the XRD pattern of a rhombohedral sample is indexed, i.e., with reference to hexagonal axes and the true nature of the lattice determined, we usually want to know the lattice parameters a R and a R of the rhombohedral unit cell. But the dimensions of the rhombohedral cell can be determined from the dimensions of the hexagonal cell and this is an easier process than solving the rather complicated planespacing equation for the rhombohedral system. The first step is to analyze and index the XRD pattern based on the hexagonal axes using the Fullprof program. Then, the parameters a H and c H of the hexagonal cell are calculated in the usual way. Finally, the parameters a r and a R of the rhombohedral cell are determined from the refined parameters a H and c H of the hexagonal cell using the Fullprof program [6].
Primitive rhombohedral and hexagonal structures in a stable perovskite structure of BiFeO 3 are shown in Fig. 2. The values of the ion radius of the cations used in this work which are located at the sixfold coordination site (octahedron site) and the 12 [36,37]. According to these values, substituting the smaller Ce 3þ for larger Bi 3þ , will reduce the unit cell volume. Simultaneously, it is expected that Zr 4þ replacement instead of Fe 3þ will increase the unit cell volume. For better discussion, we calculated the difference in ion radii of the host ions with the substituted ions as follows: Therefore, it is expected that the lattice volume will increase with the Ce 3? /Zr 4? co-substitution in BFO. However, a shift of the XRD peaks to the larger angles with an accompanying decrease of the lattice volume suggests the presence of various cations of Ce 3? and Ce 4? in the samples (see Table 1). It should be noted that it is harder to enter the Zr 4? ions having an ionic radius larger than Fe 3? , which may results in the oxidation of Ce 3? to Ce 4? . Since the electronic configuration of Ce is 4f 1 5d 1 6s 2 (atomic number of 58), one among the lanthanides, Ce 3? ions having the configuration 4f 1 5d 0 6s 0 can easily lose an electron to acquire the configuration 4f 0 and attains the stable configuration of Xenon. The Ce has two stable valence states, ? 3 and ? 4 indicating that Ce 4? ion substituting Bi 3? ion plays a role of a donor in the oxygen octahedron because of its higher valance than that of Bi 3? ions, charge compensation which can be achieved by the suppression of the inherent oxygen vacancy concentration, thus resulting in the restrained reduction of Fe 3? to Fe 2? [24]. Since the ionic radii of Ce 4? ions are smaller than that of Bi 3? ions, and the valence of Ce 4? ions is higher than that of Bi ions, the substitution of Ce 4? for Bi 3? may induce structural distortion (or even structural transition) and change local electron density in the lattice [25].
The increase in the angle of a R near to 60°and decreasing of the lattice parameters given in Table 1 with the doping amount of (Ce 3? -Ce 4? )/Zr 4? ions indicates a slight contraction of the FeO 6 octahedral along the body diagonal [111] of rhombohedral (111) axis (c axis of hexagonal) or the c-axis [001], which is accompanied with a transition to a higher symmetry structure (see Fig. 2) [6,7].
In the Williamson-Hall (W-H) method (Fig. 3), the bcosh (y-axis) plot versus 4sinh (x-axis) corresponding to the three parallel reflection planes (012), (024), (036) has a positive slope for BFO, while it indicates a negative slope for Ce/Zr co-substituted BFO. The crystallite size (D) is calculated by the inverse of the y-intercept of linearly fitted data and microstrain (e) is obtained from the slope [38]. The results of Table 1 show the remarkable changes in the crystallite size and the microstrain contribution from the broaden X-ray profile for the Ce/Zr co-substituted BFO. With the increase of the Ce/Zr co-substitution in BFO, the value of the D decrease and the e become negative due to the presence of compressive stress. This compressive stress created into the BFO lattice can be related to the following reasons: First, ionic radii mismatch between Ce 3? /Ce 4? and Zr 4? ions with the Bi 3? and Fe 3? , respectively, causes the stresses and defects in the lattice of BFO that prevent further the growth of the crystallite sizes [28,29]. Second, the evaporation of Bi for sintering the BFO at 750°C induces vacancies due to the low melting point of Bi (271°C). By increasing the replacement of rare-earth ions such as Ce (795°C) instead of Bi, the oxygen vacancies will be reduced, which prevents the migration of the oxygen ions between the particles and thus the decrease in growth and the size of the crystallites or nanoparticles [5]. Third, since the Zr-O bond is stronger than the Fe-O bond, substituting the nonmagnetic Zr 4? ion for Fe 3? in BFO leads to a decrease in the concentration of the oxygen vacancies. This prevents the formation of oxygen vacancies and slows down their motion between particles, which results in a reduction in the crystallite size by increasing the Zr 4? substitution [24].

Raman and FTIR spectroscopies
Many reasons are indicating that the local structure analysis of substituted BFO nanoparticles can be explained more clearly by the IR and Raman spectroscopies: (1) The structural analysis of BFO nanoparticles by XRD is hampered by the reflection broadening so that splitting the XRD peaks of BFO just covered by the broadening [6]. (2) In particular, the presence of Fe in combination with Cu-Ka radiation leads to significant X-ray fluorescence and high measured backgrounds [38]. These easily can cover the presence of low-level impurities. Figure 4a shows the Raman spectra measured at room temperature for Bi 1-x Ce x Fe 1-x Zr x O 3 . According to group theory, distorted rhombohedral BiFeO 3 have 18 optical vibration modes (= 4A1 ? 5A2 ? 9E), which A1 (TO) and E (LO) are Raman and infrared active vibration modes, respectively, and 5A2 are Raman inactive vibration modes. So, the 13-point Raman active phonons (= 4A1 ? 9E) of distorted rhombohedral perovskite structure (R3c space group) can propagate in longitudinal and transverse directions as following [39]: Four A1 modes propagating along the c-direction, A1-1, A1-2, A1-3, and A1-4 and nine E modes propagating along the x-y plane. Generally, the A1-1 and A1-2 modes show strong scattering intensities, whereas the A1-3, and A1-4 modes show weak scattering intensities [32,35,[40][41][42][43]. By comparison, the scattering intensity of nine E modes is medium. However, the resonance frequency and the shape of the spectral line depend on the characteristics of the samples. According to previous reports [35,[40][41][42], the polar phonon modes of A1-1, A1-2, and E1 are mainly contributed to spin-phonon coupling, magnetic anisotropy, and magnetoelectric coupling, respectively. In this research, a slight shift of the A1-1, A1-2, and A1-3 modes (assigned to the Bi-O bonds) to higher frequencies and a significant change in their intensities with the increase of the Ce and Zr co-substitution indicate that the Ce 4? ions of smaller size are substituted for the Bi 3? ions. Figure 5 shows two strong peaks near 132, and 168 cm -1 assigned to the A1-1, and A1-2 phonon modes and two weak peaks at 224, and 426 cm -1 assigned to A1-3, and A1-4 phonon modes. Also, the Raman spectra indicate a significant decrease in the scattering intensity of A1-1 mode and an obvious increase in the scattering intensity of A1-2 mode as the Ce/Zr co-substitution increase. The relatively reduced intensity of the A1-1 mode with the degree of the Ce/Zr co-substitution indicates a decrease in the spin-phonon coupling. The relatively enhanced intensity of A1-2 Raman mode with increasing the Ce/Zr co-substitution in BFO indicates that two predominant scattering mechanisms controlling the magnetic anisotropy are the spin-dependent and spin-phonon scattering, so that the Raman intensity of a magnetically ordered phase can be Here, R and M are the spin-independent, and the magnetic moment parameters, respectively, and S i S j =S 2 is the nearestneighbor spin-spin correlation function. The increase in the intensity of A1-2 mode is due to different contributions from the correlation function S i S j =S 2 , in different directions, which is the result of a change in the magnetic ordering due to the spin-reorientation phase transitions. According to our structural results, it may be attributed to the presence of (001) T and (002) T peaks oriented in the c-axis direction of the Ce/Zr co-substituted BFO. The positions of all the observed Raman peaks for samples Bi 1-x Ce x Fe 1-x Zr x O 3 are given in Table 2. The atomic mass also plays a very important role in a  . Nevertheless, at a replacement of less than 15%, the calculated average molar mass does not have much effect [40].
The Raman spectra (Fig. 4c-d) show remarkable changes in some band shifts, the expansion of the line-width of all bands, and the weakening in the intensity of the BFO structure with the increases of Ce/Zr content. It indicates an intensity change in A1 modes and the shift in the E modes. As seen, the intensity of the A1-1 mode decreases, while A1-2 phonons increases after Ce/Zr ions are incorporated. When Ce/Zr co-substitution increases up to 0.06, E4 mode at 299 cm -1 shifts to a lower wavenumber, followed by merging with the phonon mode E3 at 263 cm -1 . At the same time, the E7 mode at 471 cm -1 shifts to a higher wavenumber, followed by merging with the phonon mode E8 at 518 cm -1 . According to our structural results, an increase in the intensity of the E7 mode may be attributed to the presence of peaks (100) T and (200) T oriented in an a-axis direction in the Ce/Zr co-substituted BFO. Also, the E5 and E6 modes at 343 and 367 cm -1 , respectively, become gradually weak and finally disappear. On the other hand, the mean radius of the Ce 3? /Ce 4? ions is smaller than that of the Bi 3? ions, which a decrease in d spacing yields a compressive force into the A-sites of the BFO lattice as seen from Fig. 3. As seen from our structural analysis given in Table 1, it suggests an incomplete structural transition from a rhombohedral structure to a higher symmetry pseudo-tetragonal by Ce/Zr substitution up to x = 0.06. which its structure is a mixture of rhombohedral and tetragonal phases. When the induced microstrain by the Ce/Zr co-substitution causes the BFO structure to transits to tetragonal (P4mm space group), the Raman active modes can be expressed by the following irreducible representation: 3A1 ? B1 ? 4E [43]. Figure 4b shows normalized FT-IR spectrum of Bi 1-x Ce x Fe 1-x Zr x O 3 (x = 0.00, 0.03, 0.06). It is known that the absorption frequencies observed in the range of 400 to 700 cm -1 are related to metal-oxygen vibrations of the perovskite structure [44][45][46]. The strong absorption frequencies found at wavenumbers 475 and 618 cm -1 of the BFO are related to the asymmetric bending and the symmetric stretching vibrations of the iron-oxygen bond in the FeO 6 octahedral iron sites. The former frequency only appears in the high-distortion rhombohedral structure of the perovskite oxides [32]. As seen from Fig. 4b, there is no absorption peak at about 446 cm -1 for x = 0.06, indicating a structural phase transition from R3c low symmetry rhombohedral structure to P4mm high-symmetry tetragonal structure occurs as obtained from XRD and Raman analysis. However, we can observe that the position of absorption peak located at 618 cm -1 shifts to a lower wavenumber located at 558 cm -1 , indicating successful substitution of the Fe 3? ion by a bigger Zr 4? ion. Figure 5 shows FESEM images for the Bi 1-x Ce x-Fe 1-x Zr x O 3 (x = 0.00, 0.06) on a scale of 500 nm and 1 lm. It is seen that the morphology of BFO (Fig. 5a,  b) is completely different from the morphology of Ce/Zr co-substituted BFO (Fig. 5c, d). As the concentration in the substitution increases, the elongated polyhedral and hexagonal grains cease to exist, and granular structures of rounded shape emerge. This result suggests the presence of two different structural phases in accordance with the rhombohedral-totetragonal structural phase transition observed by the structural results. In addition, the observed microand nano-size grains of BFO has a hexagonal basal plane with a nonhomogeneous distribution. It is clear that Ce/Zr co-substitution increases the grain size and the platelet hexagons show lower porosity and higher density than that for BFO. According to the structure results, further reduction in the internal microstrain with increasing the Ce/Zr co-substitution accompanied by a reduction in internal energy and pressure can only be achieved by a decrease of the grain boundary or increase of the grain size [7]. An X-ray energy-dispersive spectroscopy (EDS) connected to the FE-SEM was used for the elemental analysis of the samples x = 0.00 and x = 0.06 as shown in Fig. 5e and f, respectively. In the spectra, the energy lines are observed for composition ele- However, our non-conducting specimens for SEM should be coated with a conductive material such as Au which is one of the most common coatings. The presence of K lines in EDS spectra of the samples shows that the washing process of the samples with water was not enough to remove (NO 3 ) -1 and K ? ions.

Morphological analysis
The uncertainty in the concentrations can vary over a wide range, and large uncertainties are usually observed when the concentration of an element is low. Also, large uncertainties are expected when the sample contains elements with large differences in the Z number (such as oxygen, carbon, and significantly heavier metals). One can realize such large uncertainties by repeating measurements at the same spot of the sample. The background profile and overlap of a given spectral line may affect the results significantly. The best results can be obtained when the spectral line of the element does not overlap with other lines, and when the background is fitted accurately and subtracted from the spectral area. Also, lower uncertainty is expected from high-intensity spectra (obtained by long acquisition times). Above discussion suggest that EDS analysis shows a few percentages error in major concentration elements but up to several ten percentages error in minor or trace elements.
The values of weight percentages of composition elements for x = 0.00 are 67.22% Bi, 14   the electronic charge transfer from O 2p states (valence band) to Fe-3d states (conduction band) which were increased with Ce/Zr co-substitution up to 2.55 eV for x = 0.06.

Optical characterization
Zhou et al. [47] have reported an increase in optical bandgap in Sm and Mn co-doped BFO which may be due to Burstein-Moss effect. A similar increase in optical bandgap is also reported for Y and Co codoping of BFO due to a decrease in the density of state in the valence band [48]. However, there are contradictory reports on the effect of Ce substitution on the bandgap energy of BFO [33,34,49]. Here, the increase of the gap energy cannot be originated from the quantum confinement phenomenon (see the SEM images). It can be attributed to the following reasons: (1) the synergetic effect of Ce and Zr co-substitution on the band structure of BFO is due to the change of the Fe-O and the Bi-O length bonds and the Fe-O-Fe bond angles which may cause a decrease in the density of state in the valence band. (2) According to Burstein-Moss effect, some states close to the conduction band being populated would result in a blue shift of the optical bandgap, with increasing Ce content (Ce acts as a donor) [7,24,33,34,47,48]. These will lead to a shift in the fundamental absorption edge towards higher photon energy. A significant increase in optical bandgap energy with increasing of the Ce/Zr co-substitution suggests that the materials are suitable as UV and blue-green-driven photocatalysts, or for optoelectronic devices.

Magnetic measurements
The room temperature magnetization curves of Bi 1-x Ce x Fe 1-x Zr x O 3 (x = 0.00, 0.03, 0.06) are shown in Fig. 7. From the curves, we can extract the highest field magnetization (M H ), coercive field (H c ), magnetization at zero applied fields (M r , the remanent magnetization) for the samples as listed in Table 3.
According to the law of approach to saturation (LAS), anisotropy constant can be calculated by fitting the magnetization curves at the high sufficiently field regions (H ) Hc) with relation (see Fig. 8): where M H ð Þ is the magnetization at the applied field H [49][50][51]. Also, the parameters M s , a, b, and v are saturation magnetization, inhomogeneity parameter, factor proportional K 2 1 (K 1 anisotropy constant), and susceptibility, respectively. They are obtained from the fitting method and listed in Table 3. According to our structural results, the Fe 3? ion extracts an electron from Ce 3? to form Ce 4? and Fe 2? ions. However, the Fe 2? ion contributes to anisotropy, but the Fe 3? ion is expected to be isotropic based on its electron structure. Finally, the increase in the coercive field in Ce/ Zr-substituted samples with the substitution has been attributed to the increase of the Fe 2? /Fe 3? ratio and K 1 anisotropy constant.
An almost linear increase and small values of the magnetization curves indicate the antiferromagnetic nature of sample BFO which is changed to the weak ferromagnetic as Ce/Zr co-substitution increase (see Fig. 8). However, the presence of the paramagnetic nanoparticles or high magnetic anisotropy of the samples causes the magnetization curves to do not saturate even in the highest applied fields [7,51]. The increase of M r and M H with the Ce/Zr substitution can be related to three reasons: First, a mixture of the rhombohedral and tetragonal structural phases can destroy the spiral spin modulation with an increase of the magnetization [6,7,52,53]. Second, when magnetic ion Ce 3? having a large magnetic moment of 2.4 l B substitutes for nonmagnetic ion Bi 3? , an exchange interaction between 3d orbital of Fe 3? ion and 4f orbital of Ce 3? ion at the B-and A-sites, respectively, produce a local ferrimagnetic spin configuration accompanied by a magnetic enhancement [54]. Third, it is known that the reduction in the particle size of BFO below 62 nm (the period length of the spiral spin structure in bulk BFO) destroys the periodicity of the spin cycloid which makes the ferromagnetic order prevail over the antiferromagnetic order [7,51]. Furthermore, the larger ratio of the surface to the volume and mismatch in the ionic radii increases the uncompensated surface spins at the surface of nanoparticles, which can play a significant role in the enhancement of the particle's overall magnetization of the Ce/Zr-substituted BFO samples having smaller nanoparticles in compared with BFO (see Table 1).

Summary
We have summarized the key points from our work on the Ce/Zr co-substituted BFO as follows: (1) The XRD and Raman spectroscopy studies confirmed that the samples are single phase even for the highest doping of 6% of Ce and Zr accompanied by a rhombohedral-tetragonal phase structural transition.
(2) The lattice distortion observed in Ce/Zr co-substituted BFO accompanied by the anomalous enhancement of the A1-2 mode induces a magnetic anisotropy in BiFeO 3 . (3) Increasing the Ce/Zr cosubstitution decreases the values of crystalline size due to the increase of the compressive stress induced into the BiFeO 3 lattice, while it increases the particle size. (4) The bandgap energy significantly increases with the increasing of Ce/Zr co-substitution suggesting that the materials are suitable as UV and blue-green-driven photocatalysts, or optoelectronic devices. (5) The weak ferromagnetic behavior observed in Ce/Zr co-substituted samples is related to the following reasons: the destruction of a cycloidal antiferromagnetic structure of BFO due to the rhombohedral-tetragonal structural transition, and the exchange interaction between the 4f-and 3d magnetic orbitals of Ce 3? and Fe 3? ions. Table 3 The values of remanent magnetization (M r ), coercivity (H c ), and magnetization at the highest applied field (M H ) and the fitting parameters of LAS curve (M = M s (1 -a/Hb/H 2 ) ? vH) for Bi 1-x