Structure and Lattice Dynamics of Bi_1−xNd_xFeO₃ and Bi_1−xGd_xFeO₃ Ceramics near the Morphotropic Phase Boundary

Abstract

The crystal structures of Bi_1−xNd_xFeO₃ and Bi_1−xGd_xFeO₃ solid solutions (0 ≤ x ≤ 0.2) with chemical compositions across structural transformations from the polar rhombohedral phase to the orthorhombic phase with an antipolar distortion and then to the nonpolar orthorhombic phase have been investigated using X-ray diffraction and infrared reflective spectrometry. The obtained results clarify details of the structural transitions assuming the changes that occurred in the crystal lattice dynamics of the compounds. Increase in the dopant content causes a notable change in the intensity and position of the reflectance lines at 18.2 μm and 22.6 μm (550 cm⁻¹ and 440 cm⁻¹) ascribed to the transverse optical phonon modes associated with Bi (Nd, Gd)–O and Fe–O bonds. In the concentration region attributed to the dominant rhombohedral phase, the chemical substitution leads to an increase in intensity of the modes A₁ for solid solutions of both systems. Meanwhile, in the case of Gd doping, the mode A₁ shifts towards the red side of the spectrum, but there is an opposite tendency in the case of Nd doping; the intensity of the modes E decrease regardless of both the dopant-ion type and concentration. This behavior is discussed assuming the change in mass for the chain of chemical bonds caused by different dopant ions and the structural transformations occurring in the compounds upon chemical doping.

1. Introduction

Ceramics based on iron complex oxides (ferrites) attract the attention of researchers due to their fundamental significance and potential for practical applications mainly associated with multiple concentration-driven structural transitions accompanied by a notable change in physicochemical parameters of the compounds [1,2,3,4,5]. In the vicinity of the phase transitions, bismuth-ferrite-based solid solutions are characterized by a notable improvement in physical properties caused by the formation of a metastable structural state in such compounds [6,7,8,9,10]. It is assumed that the metastable state is conditioned by a coexistence of the adjacent structural phases and is accompanied with a decrease in the characteristic sizes of these phases down to the nanoscale level. This structural state assumes the presence of a quantity of different structural defects, inhomogeneous distribution of mechanical stresses, local fluctuations in chemical composition, vacancies of oxygen and cations, etc. [6,7,8], which reduce the thermodynamic stability of the compounds and increase sensitivity to external influences—temperature, electric field, magnetic field, pressure, etc.

In the pristine BiFeO₃, the substitution of Bi ions by rare earth elements with similar ionic radii (La, Pr, Nd, Sm, Eu, Gd) leads to a concentration-driven structural transformation from the rhombohedral to the orthorhombic phase, and the mentioned structural modification assumes a formation of an intermediate antipolar orthorhombic phase [11,12]. The most favorable physical parameters were found for solid solutions with chemical compositions near the morphotropic phase boundary (MPB) between the polar active rhombohedral phase (R-phase) and the antipolar orthorhombic (O^*-phase) phase [13]. The concentration region specific to the MPB consisting of the R- and O- phases essentially depends on the sort and concentration level of the rare-earth elements. Thus, the chemical substitution by lanthanum ions causes a formation of the mentioned MPB region in the concentration range 15–20 mol. % of the La ions; doping by praseodymium ions shifts the two-phase region to 13–17 mol. %; further decrease in the ionic radius of the substituting ion leads to a contraction of the MPB region along with a reduction in its concentration level [12]. Despite the obvious role of size effect, the mentioned structural transition from the R- to the O- phases is also determined by the oxygen stoichiometry, electronic configuration of the dopant ions and features of the chemical bonds’ character, lattice dynamics, local defects caused by the vacancies in A- and B- perovskite sublattices, and other factors [12].

The available studies, e.g., Refs. [9,10,11,12] dedicated to the crystal structure of Bi_1−xRE_xFeO₃ ceramics are mainly focused on the size effect (n.b. r(Bi³⁺)_CN8 = 1.17 ų, r(Nd³⁺)_CN8 = 1.109 ų, r(Gd³⁺)_CN8 = 1.053 ų [2]) and electronic configuration of the dopant ions as the key factors affecting the structural phase transitions. Along with the mentioned factors, the present paper highlights the effect of the ionic masses of the dopant ions—Nd and Gd (m(Nd) = 144.24 u, m(Gd) = 157.2 u, m(Bi) = 208.98 u)—on the structural stability of the polar rhombohedral phase and the structural transformation to the antipolar or the nonpolar orthorhombic phases. Such chemical doping scheme has allowed us to itemize the factors governing the structural transitions across the phase boundary regions ‘rhombohedral—antipolar orthorhombic’ and ‘antipolar orthorhombic—nonpolar orthorhombic’ located in the dopant concentration ranges x ≤ 0.2 for both solid solutions. The relationship between the crystal structure of the solid solutions and the perovskite lattice dynamics of the respective phases has also been analyzed using a combination of results obtained by X-ray diffraction and FT-IR spectroscopy methods.

2. Experimental Section

Ceramic compounds Bi_1−xNd_xFeO₃ and Bi_1−xGd_xFeO₃ (x = 0–0.2 with a step of 5 mol. %) were prepared using the solid-state reaction method from stoichiometric mixtures of the simple oxides Bi₂O₃, Fe₂O₃, Nd₂O₃, Gd₂O₃ [9,14]. The powders were rigorously mixed in a planetary ball mill using ethanol as a medium, then pressed in pellet form and calcined at ~700 °C for 3 h, then ground again, pressed and synthesized at 800–900 °C for 8 h (temperature increases with the dopant’s concentration); the ceramics were furnace cooled to room temperature from the synthesis temperature. The structure of the cermic compounds was studied based on the diffraction results obtained at room temperature using a DRON-3M laboratory diffractometer with λ = 1.5406 Å in 2θ range of 20°–70° with a scanning rate of 5 deg./min and a step of 0.02 deg. The diffraction data were refined by FullProf software using the Rietveld method [15]. The reflectance FT-IR spectra in the mid-IR region were obtained at room temperature using an FT-IR spectrometer (VERTEX 80 v, Bruker). The samples were prepared in the form of cylindrical pellets 8 mm in diameter and 1.4 mm in height obtained under a pressure of ~5 GPa, the surface was polished to an optical quality (class 12, rms roughness ~0.2 µm), the incident angle of the testing radiation beam was ~1.2 rad. An aluminum mirror (R = 97 %) and a single crystal silicon wafer were used for calibrating the absolute values of the reflection coefficient.

3. Results

3.1. Analysis of the Crystal Structure by Diffraction Measurements

The results of diffraction measurements obtained for Bi_1−xNd_xFeO₃ ceramics with a dopant concentration x < 0.10 indicated the formation of compounds with a single-phase rhombohedral structure described by the space group (s. g.) R3c (R-phase, metric √2a_p · √2a_p · 2√3a_p, where a_p—a parameter of pseudocubic unit cell) (Figure 1). An increase in the dopant content leads to the formation of the antipolar orthorhombic phase refined using the s. g. Pbam (O^*-phase, metric √2a_p · 2√2a_p · 2a_p). The most characteristic reflections ascribed to the rhombohedral and antipolar orthorhombic phases are marked, as seen in the insets of the Figure 1. The XRD pattern recorded for the compound with x = 0.15 was refined using the single-phase model assuming an antipolar orthorhombic structure. The compound with x = 0.2 remains in the single phase orthorhombic structure (O^*-phase).

The concentration range of the rhombohedral structure solely for the solid solutions Bi_1−xGd_xFeO₃ is reduced compared with that estimated for the compounds Bi_1−xNd_xFeO₃. The structure of the 10 mol. % Gd solid solution is characterized by the presence of a minor amount (~10 %) of the antipolar orthorhombic phase simultaneously with the dominant rhombohedral phase (Figure 1). The XRD pattern of the solid solution with x = 0.15 was refined assuming a dominance of the nonpolar orthorhombic phase refined using the s. g. Pnma (O-phase, metric √2a_p · 2a_p · √2a_p), while careful analysis of the XRD patterns revealed the presence of a small amount (~5–10%) of the antipolar orthorhombic phase (O^*-phase, s. g. Pbam). The concentration region specific for the dominance of the antipolar orthorhombic phase is placed in the concentration region 0.1 < x < 0.15 which is in accordance with previous data [11]. The solid solution with x = 0.20 is assumed to be single-phase orthorhombic (O-phase, s. g. Pnma).

The unit cell parameters calculated based on the diffraction measurements are presented in Figure 2 for the compounds of both systems. For the solid solutions Bi_1−xNd_xFeO₃ in the rhombohedral phase, the a- parameter slightly decreases but the c- parameter barely increases thus resulting in a decrease of the unit cell volume. The structural parameters of the antipolar orthorhombic phase (O^*-phase) also show gradual reduction thus demonstrating the formation of a continuous solid solution. The unit cell volume decreases from ~62.0 ų for the rhombohedral compound with x = 0.05 down to ~61.28 ų for the compound with x = 0.15 and then to ~61.08 ų for the solid solution with x = 0.2 which are considered to be single-phase orthorhombic (O^*-phase). The structural parameters estimated for the compounds Bi_1−xGd_xFeO₃ show more drastic changes along the phase transition to the orthorhombic structure, viz. the unit cell volume decreases from ~61.97 ų for the rhombohedral compound x = 0.05 down to the average unit cell volume ~60.86 ų for the two-phase compound x = 0.15 and ~59.51 ų for the solid solution with x = 0.2 with single-phase nonpolar orthorhombic structure (s.g. Pnma) (Figure 2). The bond lengths Fe–O and RE–O estimated from the diffraction data show gradual decrease in the average magnitudes with the dopant concentration, while the accuracy of the obtained values is insufficient to obtain precise values for all different chemical bonds due to limitations of the X-ray diffraction method, the reliability factors are quite low for all refined patterns (R_f < 8, chi² < 5). An evolution of the chemical bond lengths as a function of the dopant type and concentration is discussed in the next section based on the FT-IR data.

3.2. FT-IR Spectroscopy Analysis

Reflection spectra (Figure 3) show the activation of the optical oscillator caused by a growth in the dopant content against the background of a general decrease in the refractive index in accordance with normal dispersion. In the region of low wavelengths, the spectra show a decrease in the intensity of the reflection coefficient which is related to the decrease in the permittivity for high energy radiation, while this tendency is violated upon chemical doping. Figure 3 shows an evolution of two main vibrational modes at λ = 18.2 μm and 22.6 μm (550 cm⁻¹ and 440 cm⁻¹) from 12 total modes (4 A and 8 E types) usually observed within the spectral range 50–700 cm⁻¹ [16,17]. The vibrational mode at 18.2 μm is symmetrical transverse optical phonon mode noted as A₁(TO4), while that at 22.6 μm is doubly degenerated transverse optical phonon mode E(TO8). These bands are caused by stretching vibrations of the Fe–O chemical bond–A₁(TO4) and bending vibrations of the Fe–O bond occurring in the oxygen octahedra FeO₆–E(TO8), while the E(TO8) band is also related to Bi–O group vibrations corresponding to BiO₁₂ polyhedra thus overlapping the modes ascribed to vibrations of Fe–O bonds [16,18,19,20].

According to the published data [21,22], in undoped bismuth ferrite the band A₁(TO4) is located at 17.5 μm (~570 cm⁻¹) at a temperature of 5 K and the band shifts towards lower frequencies with an increase in temperature reaching ~18.1 μm (~550 cm⁻¹) at room temperature. Temperature increases also causes a notable broadening of its linewidth accompanied by a decrease in its intensity [22]. Chemical substitution by the rare-earth elements also causes a shift of the A₁(TO4) and E(TO8) bands towards higher wavelengths. This is caused by a decrease in the mass of the chain of the chemical bonds—Bi–Bi(Nd, Gd)–Bi—and structural distortions, specific to the rhombohedral phase. An increase in the dopant content causes drastic changes of the observed IR bands. In the case of the solid solutions Bi_1−xNd_xFeO₃, the A₁(TO4) band notably decreases in intensity and shifts towards lower wavelengths for the compounds with x > 0.1 [23,24].

Whereas in the case of the compounds Bi_1−xGd_xFeO₃ the direction of shift is opposite, the band A₁(TO4) becomes even more intensive, wherein the band shifts towards higher wavelengths, viz. from λ ~18.0 μm for compound with x = 0.05 to λ ~18.5 μm for x = 0.2. It should be noted that the concentration-driven modification of the vibrational mode E(TO8) is quite similar for both systems, viz. the band decreases in intensity and becomes insignificant for the compounds with x ≥ 0.15. The evolution of the mode E(TO8) is associated with the rhombohedral distortion of the perovskite lattice, thus a decrease in the volume fraction of the rhombohedral phase followed by its disappearance causes a disappearance of the related vibrational mode.

The evolution of the vibrational modes as well as the crystal lattice dynamics are tightly related to the symmetry changes occurring in the solid solutions upon chemical doping. It is known that the total number of vibration modes and their type depend on the number of ions in the unit cell and their local symmetry. These can be represented through the combinations of normal coordinates corresponding to the symmetry elements of the structure, that is, by means of irreducible representations of local symmetry for groups of equivalent atoms. In vibrational spectroscopy, each vibrational normal mode consisting of stretches, bends, and other motions conform to the irreducible representation of a symmetry species in the point group of the lattice. So, it is possible to determine the motion of the crystal lattice in the terminology of formalism of the so-called factor-group.

For a rhombohedrally distorted perovskite lattice, the local symmetry of Bi and Fe atoms corresponds to C₃ (or 3, in ITA notations) symmetry, and oxygen ions correspond to C₁ (1, ITA) symmetry. Accordingly, the characters of these complexes in the Schoenflies terminology of the designation can be represented as presented in

Table 1. Symmetry operations and symmetry species * for the Wyckoff positions 6a (left side columns) and 18b.

WP: 6a		E	C3	$C_3^2$		WP: 18b		E
	A	6	0	0			A	18

* symmetry species are presented using Mulliken symbols.

and

Table 2. Character table for the C_3v (3m, ITA) point group.

	E	2C3 (3, ITA)	3Cv (m1–10, ITA)
A1	1	1	1
A2	1	1	−1
E	2	−1	0

.

The factor group as the space group reduced to the translation group defines the symmetry of directions and is isomorphic to the C_3v point group. This group has the following tabular characters.

Accordingly, the motion of the atoms can be written in the form of a sum of irreducible representations in terms of the types and symmetry of the vibrations of the group C_3v. Namely, there are two ordinary A₁, A₂ and one two-dimensional E vibration type belonging to Bi, Fe and O ions in the lattice

a^{Bi, Fe} = A₁ + A₂ + 2E;

a^O = 3A₁ + 3A₂ + 6E.

In accordance with the selection rules there are 12 IR active modes, viz. 4 A₁ modes and 8 E modes (A₂ modes are silent in the mentioned rhombohedral structure). The chemical doping causes the phase transformation to the orthorhombic structure in both studied systems. The solid solutions of both systems with the dopant concentration level of 10 mol. % contain a small amount of the antipolar orthorhombic phase (point group D_2h or mmm in ITA notations), while in the case of the Nd-doped system its amount is nearly negligible; however, in the case of the Bi_1−xGd_xFeO₃ system its volume fraction reaches a value of ~10%. The compound Bi_0.85Nd_0.15FeO₃ is single-phase orthorhombic (O^*- phase) and its IR spectrum shows a notable shift of the A₁ band to a lower wavelength (higher frequency) as compared to the compound with x = 0.10 which is in agreement with the reduced average mass in the ionic chains—Bi–Bi(Nd)–Bi. An additional phonon band appears at ~14.8 μm associated with a new stretching vibration band of FeO₆ octahedra caused by the antipolar alignment of dipole moments in the O^*- phase [23]. The band at ~14.8 μm is specific to the antipolar orthorhombic distortion, and it becomes less pronounced in the compound with x = 0.2 thus pointing at gradual reduction of the antipolar orthorhombic distortion. It should be noted that the mentioned band can hardly, if possible, be distinguished using Raman spectroscopy data as confirmed in the previous study [24], thus highlighting the advantages of FT-IR spectroscopy over the Raman measurements for analysis of the ‘rhombohedral—orthorhombic’ structural transition in BiFeO₃-based solid solutions.

The IR spectrum of the compound with x = 0.2 does not show any notable changes of the band at ~18 μm, while the band at ~22 μm completely vanishes thus confirming a total reduction of the R-phase even at a local scale level. An opposite trend in the modification of the vibrational modes was noted for compounds Bi_1−xGd_xFeO₃ with x ≥ 0.15 which bear a two-phase structural state (x = 0.15, O^* + O phases) and a single-phase orthorhombic state (x = 0.20, O^—phases), respectively. The bands at ~18 μm shift towards higher wavelengths caused by the formation of a nonpolar orthorhombic structure as compared to the antipolar orthorhombic structure in Bi_1−xNd_xFeO₃ compounds.

It should be noted, that for both orthorhombic structures only B (antisymmetric) modes are IR active, while these modes are similar for both structures (Γ_acoustic = B₁u + B₂u + B₃u modes for both space groups) as the point groups are the same for both structure (D_2h), the amount of the vibrational modes and their multiplicity are notably different (see

Table 3. IR selection rules of the selected Wyckoff positions (s.g. Pnma).

WP	Ag	Au	B1g	B1u	B2g	B2u	B3g	B3u
4a	·	·	·	3	·	3	·	3
4b	·	·	·	3	·	3	·	3
4c	·	·	·	2	·	1	·	2
8d	·	·	·	3	·	3	·	3

and

Table 4. IR selection rules of the selected Wyckoff positions (s.g. Pbam).

WP	Ag	Au	B1g	B1u	B2g	B2u	B3g	B3u
2a	·	·	·	1	·	2	·	2
2b	·	·	·	1	·	2	·	2
2c	·	·	·	1	·	2	·	2
2d	·	·	·	1	·	2	·	2
4e	·	·	·	1	·	2	·	2
4f	·	·	·	1	·	2	·	2
4g	·	·	·	1	·	2	·	2
4h	·	·	·	1	·	2	·	2
8i	·	·	·	3	·	3	·	3

). It should be noted that the rare-earth ions are located in the 4g and 4h Wyckoff positions in the lattice described by the s.g. Pbam while they occupy 4c Wyckoff position in the s.g. Pnma; the iron ions occupy 8i position in the s.g. Pbam and 4a position in the s.g. Pnma. The differences in the occupation sites attributed to the Bi(Nd,Gd) and Fe ions in the different orthorhombic lattices as well as the differences in the parameters of the chemical bond lengths Bi(Nd,Gd)–O and Fe–O determine the differences observed in the IR spectra of the orthorhombic compounds of both systems.

4. Conclusions

The X-ray diffraction results simultaneously with the data of IR reflective spectrometry measurements have allowed clarification of the correlation between the structural changes occurring in the solid solutions Bi_1−xNd_xFeO₃ and Bi_1−xGd_xFeO₃ across the structural phase transformations from the polar rhombohedral structure to the antipolar and then to the nonpolar orthorhombic structure, in addition to related changes in the crystal lattice dynamics. It is shown that regardless of the dopant-ion type, a growth in the dopant concentration leads to a growth in intensity of the reflectance lines at 18.2 μm and 22.6 μm (~550 cm⁻¹ and 440 cm⁻¹) ascribed to Bi (Nd, Gd)–O and Fe–O bonds. An opposite direction movement of the transverse optical phonon modes at ~18 μm observed for the cases of Nd- and Gd doping is caused by competitive contribution of two factors—mass of the ions in the chain of the bonds and—the changes occurring in the chemical bond parameters caused by chemical doping.

The chemical doping with Gd ions causes a stabilization of the nonpolar orthorhombic phase in the heavily doped solid solutions which presents a more symmetrical structure (O –phase, described by the s. g. Pnma, #62) as compared to the case of Nd-doped compounds characterized by the antipolar orthorhombic structure refined using the s. g. Pbam (#55) which demonstrates a dominance of the structural factor over the mass factor in the shift of the related vibrational modes.