Anomalous compression behaviour in Nd₂O₃ studied by x-ray diffraction and Raman spectroscopy Open Access

The polymorphism and structural properties of Rare earth sesquioxides (RE₂O₃, RE=Rare Earth) have been of great interest from both technological as well as fundamental point of view.^1–6 The electronic, optical, and thermodynamic properties are related to their polymorphism,^7,8 pressure could induce crystallographic and electronic changes in solid material, thus causing profound effects on physical and chemical properties.^9–11 It is important to study the phase stability of various RE₂O₃ under high pressures and temperatures.

Depending on the radius of cation in the oxides at ambient conditions, there exist three polymorphic modifications: for the large cations, such as La to Nd, a hexagonal phase, whose cations are in seven-fold coordination, is designated as the A-type with a space group (SG) P $3¯$m1 and Z = 1; for the medium cations, such as Sm to Gd, typically a monoclinic phase, whose cations are mixed with six or seven-fold coordination, is as the B type with a SG C2/m and Z = 6; and for the small cations, from Tb to Lu, a cubic phase is as C-type with a SG Ia $3¯$ and Z = 16. Moreover, the medium RE₂O₃ can adopt either the B or C-type structure depending on their thermal histories. At very high temperature, additional two phases designated as H (hexagonal, SG P63/mmc) and X (cubic, SG Im $3¯m$⁠) are formed.¹² Phase transitions of RE₂O₃ at various temperatures have been summarized by Zinkevich.¹³ At increasing of temperature, most of RE₂O₃ follow the transition sequence of C→B→A. The molecular volume of RE₂O₃ decreases with increasing cation coordination numbers in the order of C, B and A, and the phase transition sequence of C→B→A is usually expected for the most of RE₂O₃ compounds at elevated pressures.

Recently, the phase stability and transition sequences of RE₂O₃ under pressures have been the subject of many research groups. The pressure-induced C→B phase transition has been reported in C-type RE₂O₃ with small size cations, including Er₂O₃,¹⁴ Ho₂O₃,^15,16 Yb₂O₃,¹⁷ Lu₂O₃,^18,19 and Sc₂O₃.,²⁰ and the successive C→B→A phase transformation was investigated in Dy₂O₃,²¹ Er₂O₃²² and Y₂O₃.²³ In addition, a grain size-dependent crystalline-amorphous transition in Y₂O₃,²⁴ and a review of pressure induced structural changes in nanocrystalline RE₂O₃ were presented.²⁵ 

The C-type RE₂O₃ with medium size cations have attracted special attention in view of their unique pressure-induce phase transition sequences. The C-type Gd₂O₃ a was found to transform directly to the phase A at about 7.0 GPa, as well as a small discontinuity in the slope of P-V curve.²⁶ Later, this C→A phase transition was observed in the C-type Eu₂O₃ and Sm₂O₃ at 5.0 GPa and 4.2 GPa,^27,28 respectively, Moreover, Guo et al. carried out high pressure x-ray diffraction (XRD) measurements on Sm₂O₃ with mixture of C and B phases and the phase transitions from both C and B to A were identified.²⁹ Recently, a pressure induced C→A phase transition was investigated in nano-Eu₂O₃ at around 9.3 GPa,³⁰ higher than that of bulk Eu₂O₃ at a pressure of 5.0 GPa.²⁷ Furthermore, the pressure induced C→A phase transition of RE₂O₃ from density functional theory (DFT) calculations were presented.³¹ 

The high pressure behavior of RE₂O₃ with phase of A as initial material has been given much less attention compared with that of B or C type, most of previous studies focus on the C→B→A or C→A phase transformation in C type RE₂O₃ under high pressures, however, the high pressure A phase shows unique compression behavior and attracts great interest. The C→A structural transformation was verified in cubic Gd₂O₃ and anomalous compression behaviour of a-axis as well as a discontinuity in the volume change was observed within the high pressure hexagonal phase in the pressure range of 20.1–28.1 GPa.³² Similar compression anomaly of the a-axis has been investigated in high pressure A phase of Er³⁺ doped Gd₂O₃.³³ The abnormal lattice compressibility was also observed for the high pressure hexagonal phase of Eu₂O_3,³⁴ however, its volume compressibility maintain a similar value, this is different from that of Gd₂O₃,³² which exhibits a discontinuity in the volume change. In addition, Ce₂O₃ has been found to remain in the hexagonal phase up to 70 GPa, and a theoretical phase transition was not found.³⁵ Therefore, it is essential to investigate the structure evolutions of RE₂O₃ with A type structure as the starting material under high pressures.

The neodymium oxide, Nd₂O₃, with A type as the initial phase, is recognised as a highly active catalyst for many organic reactions and excellent liquid laser medium.³⁶ Temperature-induced phase transition of Nd₂O₃ at ambient pressure have been summarized.¹³ Raman spectra of the A-type Nd₂O₃ at ambient conditions have been reported and a complete assignment of Raman modes was given.^37–40 Recently, high pressure investigations on A type Nd₂O₃ using energy dispersive x-ray diffraction (EDXD) and Raman scattering suggested a phase transition at around 25 GPa,⁴¹ due to the limited resolution of EDXD system, some diffraction peaks have not been indexed, and the high pressure phase was not determined, in addition, only two of the four predicted Raman modes in A type Nd₂O₃ were given. It is the goal of this study to investigate the structure evolution of A type Nd₂O₃, and gain an insight into the anomalous compression behaviour of A type RE₂O₃.

In this work, we present the results of high pressure study on Nd₂O₃ with phase of A as the starting material by using the angle dispersive x-ray diffraction (ADXD) and Raman spectroscopy. The ADXD data indicate the initial hexagonal structure is retained as the pressure compressed to 53.1 GPa, whereas it undergoes an isostructural phase transition in the pressure range from 10.2 to 20.3 GPa, accompanied by anomalous compression in lattice parameters and pressure-volume curve. This phase transition is verified by Raman scattering measurements.

The Nd₂O₃ sample is a polycrystalline in powder form with purity of 99.99%. The starting material was ground with alcohol for 30 minutes and heated at 900 °C for 6 hours to eliminate the possible hydroxide and adsorptive water. A Mao-Bell type diamond anvil cell (DAC) with culet sizes of 300μm was used to generate high pressures. The powder sample with a ruby chip was loaded into the sample hole with a diameter of 100μm drilled in a stainless steel gasket. The in situ high pressure ADXD experiments were mainly performed at the 4W2 beamline of the Beijing Synchrotron Radiation Facility (BSRF) by angle-resolved measurements with a wavelength of 0.6199 Å. The pressure was determined by the wavelength shift of ruby R1 luminescence line.⁴² Silicone oil was used as the pressure-transmitting medium. The diffraction patterns were recorded by using a Mar3⁴⁵ image plate detector. CeO₂ powder was used to calibrate the distance and orientation of the detector. The collected images were integrated into one-dimensional diffractions patterns by software of FIT2D.⁴³ 

High pressure Raman spectroscopy measurements were carried out at room temperature using the self-established confocal Raman spectrometry system in back scattering geometry. The 488 nm line of an Ar ion laser was used as the Raman excitation source. A Mitutoyo 20x long working distance objective was employed for focusing the laser on the sample and collecting the Raman scattering spectra. A holographic notch filter was used for laser rejection. The Raman signals were dispersed by the Acton sp-500i monochromator with 1800gr/mm grating and detected by a liquid-nitrogen-cooled CCD detector (Princeton Instrum. Inc.), giving a spectral resolution of 0.5 cm⁻¹. As the x-ray diffraction experiments, a DAC with the culet size of 300μm was used and the pressure was also calibrated by ruby fluorescence.²⁶ 

The schematic crystal structure of hexagonal Nd₂O₃ is shown in Fig. 1. The primitive cell has one formula unit, with two Nd cations in 2d positions (C_3v); oxygen atoms are distributed over two different sites, O₁ in 1a (D3d symmetry), O₂ in 2d (C3v) symmetry. The Nd atom is in seven fold coordination with oxygen atoms, three oxygen atoms, O₁(3) are on the corner of the unit cell, three oxygen atoms (numbers in the brackets represent the number of bonds in the unit cell), O₂(3) are nearly in the same plane paralleling to the a-b plane, and the seventh oxygen O₂(1) is in the neighbouring layer.

Representative high pressure XRD patterns upon compression and decompression are illustrated in Fig. 2(a) and (b), respectively. At ambient pressure, the diffraction patterns can be indexed within the hexagonal structure with space group P $3¯$m1, the diffraction peaks are marked with the corresponding (hkl) values. As the pressure up to 10.2 GPa, no obvious changes occur in the diffraction patterns except for a shift in the diffraction peaks to higher 2θ angles attributed to lattice contraction. It is noticeable that the (100) and (110) diffraction peaks show a movement to lower 2θ angles or higher interplanar spacing in the pressure range from 10.2-20.3 GPa, however, other diffraction peaks shift to higher 2θ angles in this pressure range. To obtain further insight into the effect of pressure on the (100) and (110) diffraction peaks, the local diffraction peaks are magnified in the plot (Fig. 3). As the (100) and (110) planes are perpendicular to the a-b plane in A type Nd₂O₃, the shifts of the diffraction peaks to lower 2θ angle of these peaks mean that the a-axis expanses with increasing pressure. This is clear evidence of the anomalous compression of the hexagonal lattice, because it is in contrast to normal compression behaviour which shows a uniform decrease in all dimensions of the unit cell. This anomalous compression behaviour could be attributed to an isostructural phase transition, as was observed in Gd₂O₃,³² Er⁺doped Gd₂O₃,³³ and CrAs.⁴⁴ Above 20.3 GPa, the compression of the hexagonal lattice parameters could be considered normal, as all diffraction peaks move to higher angle.

The XRD patterns were refined by the Rietveld method up to 37.4 GPa using GSAS package, above 37.4 GPa, the lattice parameters were obtained by using Lebail refinement.⁴⁵ The refined unit cell parameters at ambient conditions are: a=3.829(1) Å, c=5.996(1) Å, which is in good agreement with the values in literature,⁴⁶ the refined atomic coordinates are listed in Table I. Upon compression and decompression, all diffraction patterns can be refined by hexagonal structure with SG P $3¯$m1, which reveal that the Nd₂O₃ retains hexagonal to the highest of 53.1 GPa as well as during decompression process. Fig. 4 shows the results of a typical Rietveld refinement of hexagonal Nd₂O₃ at 33.9 GPa, the good refinement indicate that the structural symmetry of Nd₂O₃ at the pressure is the same at that of ambient conditions. The Rietveld refinement results indicate this isostructural phase transition is driven by an electronic phase transition, the hexagonal displays a small distortion in the pressure range of electronic phase transition(10.2-20.3 GPa), and it became normal above the critical pressure, as have also been investigated in Gd₂O₃,³² Er³⁺ doped Gd₂O₃,³³ and Eu₂O₃.³⁴ 

The pressure dependence of Nd-O₂ (1) and Nd-O₂ (3) bond lengths are shown in Fig. 5, the Nd-O₂ (1) is correlated to c-axis, and that Nd-O₂ (3) is associated with a-axis. It is seen from Fig. 5 that both the Nd-O₂ (1) and Nd-O₂ (3) bond lengths decrease with pressure up to 10.2 GPa, then Nd-O₂ (3) bond distance increases subtly, which reveals a-axis expansion, whereas the Nd-O₂(1) bond length decrease more rapidly, indicating the contraction of c-axis. Above 20.3 GPa, the lattice parameters display normal compression behaviour. This phenomenon can be explained by the band model,⁴⁷ the layerlike structure of hexagonal Nd₂O₃ means that the ions are arrange far along the c-axis, thus their wave function of electrons overlap slightly, and the electron repulsion is weak along this axis, as the pressure increase up to 10.2 GPa, the c-axis is much more compressible compared with the a-axis, when the applied pressure is increased up to the critical pressure range (10.2-20.3 GPa), an extremum in the electronic band structure crosses the Fermi level, which induces the electronic phase transition, thus an anomalous compression. Above 20.3 GPa, the strong electron repulsion cause the c-axis less compressible.

The pressure dependence of O-Nd-O band angles is illustrated in Fig. 6, the O₁-Nd-O₁ bond angle increases in the entire compression process, however, it displays a noticeable slope change in the pressure range from 10.2-20.3 GPa, where it increases more rapidly, similar phenomenon is also observed in O₂(1)-Nd-O₂(3) bond angle. The increase in the O₁-Nd-O₁ and O₂(1)-Nd-O₂(3) bond angles during the compression process indicate that the Nd and O₂ move towards to the nearby a-b plane, it is clear evidence of a layerlike structure in Nd₂O₃.

The change in normalized lattice parameters a and c-axis of Nd₂O₃ determined by GSAS refinements with increasing pressure is shown in Fig. 7, the result is consistent with the pressure dependence of bond length. It is shown that the a and c-axis displays a steep decrease up to a pressure of 10.2 GPa, the a-axis displays an increase in the pressure range from 10.2-20.3 GPa, whereas the c-axis shows a rapid decrease. A further increase in pressure above 20.3 GPa results in a decrease in a and c-axis and a normal compressibility that continues up to the highest pressure of 53.1 GPa. Such an anomalous axial compressibility was also observed in A type Eu₂O₃ in the pressure range of 15-25 GPa,³⁴ and that of 20-28.1 GPa in A-type Gd₂O₃.³² It is worthwhile to note the ionic radii decrease in the sequence of Nd₂O_3, Eu₂O₃, and Gd₂O₃, the ionic radii are affected by number of f-electrons, larger number of f-electrons, the smaller radii, which is called lanthanide contraction, consequently, the higher transition pressure is required. It is concluded the lanthanide contraction also play a role in the anomaly compressibility and electronic phase transition of the A type RE₂O₃.

It is noticeable that the compressibility along the c-axis is larger than that along the a-axis. The relative change along the c-axis is about 15.3% and that along the a-axis is about 2.6% from 0 to 53.1 GPa, the relative change along the c-axis is about 5.8 times larger than that along the a-axis, this anisotropic compressibility of lattice parameters in hexagonal Nd₂O₃ is correlated to layered structures, which have weak van der Waals bonds between the atoms in neighboring layers, as was confirmed by change of the pressure dependence of the O-Nd-O bond angles, and was also observed in A type Gd₂O₃³² and Eu₂O₃.^27,34

The Rietveld refinements permit us to obtain the pressure dependences of the lattice parameters. The Nd₂O₃ displays anomalous lattice compressibility in the pressure range from 10.2 to 20.3 GPa, which is typical characteristics of a pressure-induced isostructural phase transition. Such as in Gd₂O₃,³² Er³⁺ doped Gd₂O₃,³³ and CrAs.⁴⁴ In addition, GSAS refinements of the XRD patterns for Nd₂O₃ at different pressures display good refinement, which indicates that the structural symmetry of Nd₂O₃ at the pressure is the same as that of ambient conditions, confirming the occurrence of pressure-induced isostructural transition.

However, the direct evidence of electronic phase transition would be the calculated band structure of Nd₂O₃ at pressures, the energy band model would satisfactorily address the pressure-dependency curve of the lattice parameter and the electronic responses to high pressure, which is important in understanding the pressure-induced isostructural phase transition of Nd₂O₃, as have been done in the CrAs,⁴⁴ by combining the experimental results and first principle calculation.

The pressure dependence of the unit-cell volume for the hexagonal Nd₂O₃, is shown in Fig. 8, it displays an anomalous compression behaviour, similar phenomenon was observed in Gd₂O₃.³² This anomalous compressibility is attributed by an isostructural transition caused by an extremum in the electronic band structure crossing the Fermi level, as was determined in AuIn₂ by first principle calculation,⁴⁸ The anomaly separates two regions of the compression curve, each is characterized by a distinct pressure dependence of the bulk modulus, and is fitted to the third-order Birch–Murnaghan equation of state.⁴⁹ 

where B₀ and B₀^′ correspond to bulk modulus and its pressure derivative, V₀ is zero-pressure volume, the pressure derivative B₀^′ is fixed at 4, then by fitting the two regions of the P-V curve yield B₀=142(4) GPa for the pressure region of 0-10.2 GPa; and B₀=183(6) GPa for the pressure region of 20.3-53.1 GPa. The values of B₀ are listed in Table II, previous experimental and theoretical results for some RE₂O₃ with phase of A are also presented for comparison, our results is similar to Wu’s theoretical calculation on Nd₂O₃.⁵⁰ 

In order to verify the pressure effect on the structure of Nd₂O₃, in situ Raman scattering measurements were performed. The A type Nd₂O₃ belong to space group P $3¯$m1 and the factor group analysis predicts 4 Raman active modes: two stretching mode (E_g +A_1g) and two bending modes (E_g +A_1g).³⁸ Fig. 9 displays the four Raman active modes in a unit cell in projection on the (110) plane.³⁹ Raman spectroscopy measurements were carried out at room temperature up to 37.0 GPa. Fig. 10 shows some collected Raman spectra under high pressures.

The A_1g stretching mode involves the medium Nd-O₂(1) length (2.392 Å) and that the E_g stretching mode is associated with the short Nd-O₂(3) length (2.308 Å), the force constant is inversely proportional to the bond length, thus the E_g stretching mode should have higher frequency than the A_1g stretching mode. In addition, the stretching modes are expected to have higher values than those of the bending vibrations.³⁹ Based on the analysis above and previous Raman measurements on single crystal Nd₂O₃,³⁹ the observed Raman peaks can be identified as E_g bending (106.6 cm^-1), A_1g bending (192.6 cm^-1), A_1g stretching (426.5 cm^-1), E_g stretching (437.0 cm^-1), respectively. At low pressures, the A_1g stretching and Eg stretching partially overlaps. The overlapping bands were fitted via the Peakfit software. With increasing pressure up to 9.7 GPa, the two stretching Raman modes can be distinguished easily, this change is in agreement with the slope change of the bond length of Nd-O₂. Upon further increasing pressure, all Raman bands shift to high frequencies and remain up to 37.0 GPa.

The pressure dependences of Raman phonon frequencies in the compression process from 0 to 37.0 GPa is shown in Fig. 11. Linear least-square fittings were performed on these data as shown by the solid lines. Table III lists the ambient pressure phonon frequencies ω₀, their pressure derivatives (k=∂ω/∂p) and mode Grüneisen parameters γ. The mode Grüneisen parameters were calculated using the formula:

where B₀ is the bulk modulus, which is 142 GPa and 183 GPa for low pressure and high pressure region, respectively, and ω₀ is the ambient pressure phonon frequencies.

Since the stretching modes are directly affected by the bond length, whereas the bending modes are influenced by more complex factors,³⁹ analyses were focused on the two stretching modes. As shown in Fig. 11, the slopes of stretching modes versus pressure exhibit discontinuities in the pressure range from 9.7-20.9 GPa, including a decrease of slope in the frequency-pressure plot of the E_g stretching mode and an increase of slope in the A_1g stretching, which correlate to the rapid decrease of the Nd-O₂ (1) bond, and the less compressibility of Nd-O₂ (3) band length in the pressure range of about 10-20 GPa, respectively.

In summary, the high pressure behaviours of Nd₂O₃ have been investigated by in situ ADXD and Raman spectroscopy up to 53.1 and 37.0 GPa, respectively. The XRD data reveals anomalous compressibility effects in the pressure range from 10.2-20.3 GPa, which is attributed to an isostructural transition. By fitting the Pressure–Volume data into the third-order Birch–Murnaghan equation, the zero pressure bulk moduli of 142(4) and 183(6) GPa for low and high pressure hexagonal phases are obtained. This isostructural phase transition is verified by Raman spectroscopy and the mode Grüneisen parameters of different Raman modes have also been determined.

Financial support from the National Natural Science Foundation of China (11775292, 11104307 and U1530134) are gratefully acknowledged. This work was mainly performed at 4W2 beamline of Beijing Synchrotron Radiation Facility (BSRF), and Partial work was carried out at the BL15U1 beamline, Shanghai Synchrotron Radiation Facility (SSRF).