Cite this Article
Zhang Ji, Zhang De-Ming, Zhang Ran-Ran. Temperature-dependent Raman spectroscopic study of ferroelastic K2Sr(MoO4). Chinese Physics B, 2018, 27(11): 117801  
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Temperature-dependent Raman spectroscopic study of ferroelastic K2Sr(MoO4)
Zhang Ji1, †, Zhang De-Ming2, Zhang Ran-Ran3
An Hui Xin Hua University, Hefei 230088, China
Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Hefei 230031, China
High Magnetic Field Laboratory of the Chinese Academy of Sciences, Hefei 230031, China

 

† Corresponding author. E-mail: 18956063545@189.cn

Abstract

Raman scattering measurements of K2Sr(MoO4)2 were performed in the temperature range of 25–750 °C. The Raman spectrum of the low-temperature phase α-K2Sr(MoO4)2 that was obtained by first-principle calculations indicated that the Raman bands in the wavenumber region of 250–500 cm−1 are related to Mo–O bending vibrations in MoO4 tetrahedra, while the Raman bands in the wavenumber region of 650–950 cm−1 are attributed to stretching vibrations of Mo–O bonds. The temperature-dependent Raman spectra reveal that K2Sr(MoO4)2 exhibits two sets of modifications in the Raman spectra at ∼150 °C and ∼475 °C, attributed to structural phase transitions. The large change of the Raman spectra in the temperature range of 150 °C to 475 °C suggests structural instability of the medium-temperature phase β-K2Sr(MoO4)2.

PACS: 78.30.-j;81.70.-q;63.70.+h
Keyword:ferroelastics;K2Sr(MoO4)2 crystal;Raman spectroscopy;phase transition
1. Introduction

In recent years, various active dielectric materials and ferroelectrics have been extensively investigated in terms of their synthesis methods, crystal structures, and phase transitions owing to their applications in acoustoelectric devices, logic and memory elements, optic shutters, and so on. These applications are based on adjustment of crystal orientations and control of their domain structures by small mechanical and thermal deformations.[1] A large promising family of ferroelastics with general formulas of M3(XO4)2 (M = Sr, Ba, Pb; X = P, As, V, Cr), A2M(XO4)2 (A = K, Rb, Cs, Tl; M = Sr, Ba, Pb; X = S, Se, Cr, Mo, W), and A5R(Mo4)4 (A = K, Rb, Tl; R = RE, Y, Bi, Fe) is characterized by tetrahedral XO4 anions in their structures.[2–6] Among the ferroelastics, double molybdate K2Sr(MoO4)2 containing MoO4 tetrahedra is a new ferroelastic compound with the same palmierite-like structure as that of Pb3(MoO4)2 and B2Pb(MoO4)2 (B = K, Rb, Cs).[7] According to the study of Galiba,[8] K2Sr(MoO4)2 crystallizes in a monoclinic phase (referred to as α-phase with a space group of C2/c) at a low temperature, which is similar to that of Pb3(MoO4)2. At a high temperature of approximately 744 K, K2Sr(MoO4)2 transitions to the K2Pb(SO4)2-type phase (referred to as γ-phase with a space group of ). In addition to the low- and high-temperature phases, a medium-temperature phase has been demonstrated by x-ray diffraction (XRD) of K2Sr(MoO4)2 at 573 K. However, the crystal structure change is continuous and complex. To understand the crystallographic changes with temperature, further studies on the transformation of the crystal structure upon temperature variations are required.

Because Raman spectroscopy is an efficient method to investigate crystal structures, temperature-dependent Raman spectroscopy is frequently used to study phase transitions.[9–11] In this study, the Raman spectrum of K2Sr(MoO4)2 was calculated by density functional theory (DFT) to help us assign the vibration modes. Temperature-dependent Raman spectra were then measured to study the structural changes of the K2Sr(MoO4)2 system at different temperatures.

2. Experimental and computational methods

K2Sr(MoO4)2 polycrystalline powder was prepared by conventional solid-state reactions. K2CO3, SrCO3, and MoO3 (analytic grade) were homogeneously mixed with appropriate proportions in an agate mortar and packed into a Pt crucible. The sample was heated slowly to 580 °C and maintained at this temperature for 80 h with several intermediate grindings and mixings. Powder-XRD measurements were performed in the range of 10°–70° with a step of 0.02°.

Room- and high-temperature Raman spectroscopy measurements were performed in the range of 100–1100 cm−1. The sample was heated in a home-made heating furnace. The temperature was monitored by a thermocouple attached to the metal sample holder and controlled by a temperature controller within 1 °C. Raman spectra were acquired with a Horiba Jobin Yvon Raman spectrometer (LabRam800HR) in a backscattering configuration. An ultraviolet light pulse with a wavelength of 355 nm and repetition frequency of 10 kHz from a coherent Innova ultra-laser was focused onto the sample using a Raman microprobe with a 4× objective lens. An intensified charge coupled device (CCD) was used to collect the scattering light. The sample was steadily heated from room temperature to 750 °C in a platinum boat placed in the center of the chamber. Each spectral acquisition (accumulation mode) was performed for 10 s, the average power of the laser operation was fixed to 800 mW, and the slit width was set to 300 nm for all measurements under different temperatures.

Structure optimization and calculations of the band structure, density of states, and Raman spectrum were performed using the CASTEP code[12] based on density functional theory (DFT). Conserving pseudopotentials were employed; the exchange–correlation was modeled using the Perdew–Burke–Ernzerhof (PBE)[13] functional, based on generalized gradient approximation (GGA).[14,15] The cut-off energy for the plane-wave basis set and k-point separation were chosen based on the criterion of fine precision. The structure optimization was performed until the forces on the atoms were smaller than 0.01 eV/Å, the energy change per atom smaller than 10−5 eV, and the stress components smaller than 0.05 GPa. Pseudo-atomic calculations were performed for O 2s22p4, K 3s23p64s1, Sr 4s24p65s2, and Mo 4d55s1. The other parameters used in the calculations had the default values of the CASTEP code.[16]

3. Results and discussion
3.1. Structures and factor group analyses

The XRD pattern of the sample is shown in Fig. 1. Comparison with the results of Galiba[8] shows that the obtained structure is α-K2Sr(MoO4)2. The α-K2Sr(MoO4)2 structure has a space group of C2/c with lattice parameters of a = 14.318 Å, b = 5.933 Å, c = 10.422 Å, and β = 105.83 °C. The structure of α-K2Sr(MoO4)2 is shown in Fig. 1. The K and Sr atoms are located at the M1 and M2 positions with distances of M1–O in the range of 2.578–2.789 Å and M2–O in the range of 2.605–3.161 Å. In addition, MoO4 tetrahedra with Mo–O bond lengths of 1.747–1.767 Å[8] share vertices and edges with M1 and M2 polyhedra. These polyhedra alternatively arrange to form a layered structure parallel to the (100) plane.

Fig. 1. (color online) Powder-XRD pattern and structure (inset) of the α-K2Sr(MoO4)2 crystal.

The α-K2Sr(MoO4)2 crystal is monoclinic, with a space group of C2/c and two molecular formulae per unit cell (Z = 2). A group theoretical analysis of the normal modes of vibration of the α-K2Sr(MoO4)2 structure at q = 0 predicts the following decomposition for the two formula units of the crystal in the primitive cell, according to the irreducible representations of the point group .[17] Excluding acoustic modes Au+2Bu, the Raman spectrum should contain 37Au+40Bg normal modes of vibration.

3.2. Raman spectrum at room temperature

The measured Raman spectrum of α-K2Sr(MoO4)2 at room temperature in the range of 100–1100 cm−1 is presented with the black line in Fig. 2, while the calculated (with the first-principles method) Raman spectrum of α-K2Sr(MoO4)2 is presented with the red line. The calculated spectrum fits well with the experimental one. In the Raman spectrum, the bands can be grouped into three regions. The wavenumber region of 100–250 cm−1 consists of four bands at 110 cm−1, 138 cm−1, 180 cm−1, and 235 cm−1, which are fundamental transitions for translational and rotational lattice vibrations. The low-frequency bands in this region are assigned to external modes, related to translations of Sr2+, K+, and MoO4 clusters. The assignments of the external modes are based on the previous studies about Raman spectra of acousto-optic NaBi(MoO4)2, ferroelastic orthorhombic Gd2(MoO4)3, and multilayer KY(MoO4)2 crystal with Raman active external modes below 200 cm−1, 300 cm−1, and 270 cm−1, respectively.[18–20] To provide insights into the vibrations, Figure 3 illustrates representative vibration modes calculated by DFT. Figure 3(c) illustrates the lattice vibration for the Raman band at 124 cm−1, where Sr2+ and K+ ions exhibit strong vibrations.

Fig. 2. (color online) Experimental and calculated Raman spectra of the K2Sr(MoO4)2 crystal at room temperature.
Fig. 3. (color online) Illustration of representative vibration modes: (a) Raman band at 899 cm−1 with Mo–O stretching vibration, (b) Raman band at 320 cm−1 with Mo–O bending vibration, and (c) Raman band at 124 cm−1 with lattice vibration.

The Raman bands around 250–500 cm−1 and 650–950 cm−1 are assigned to internal modes corresponding to the Mo–O vibrations of MoO4 tetrahedra. It is well known that a MoO4 tetrahedron molecule with a Td symmetry has four normal vibrational modes: v1 (symmetric stretching mode), v2 (bending mode), v3 (asymmetric stretching mode), and v4 (bending mode).[21,22] It is commonly observed that the stretching modes have higher vibration frequencies than the bending modes. For example, Mo–O bending vibrations were observed in the frequency regions of 320–404 cm−1 and 277–465 cm−1 in the spectra of NaBi(MoO4)3 and KY(MoO4)2 crystals, respectively, while the Raman bands of stretching vibration modes were observed at above 700 cm−1. Therefore, in the Raman spectrum of α-K2Sr(MoO4)2, the Raman bands at 315 cm−1, 363 cm−1, and 384 cm−1 are related to Mo–O bending vibrations, while the Raman bands at 711 cm−1, 795/810 cm−1, 844/858 cm−1, 887 cm−1, and 899/904 cm−1 are attributed to Mo–O stretching vibrations. Figures 3(a) and 3(b) illustrate representative vibration modes of the Raman bands at (a) 899 cm−1 (Mo–O stretching vibration) and (b) 320 cm−1 (Mo–O bending vibration). Therefore, the calculated results are valuable in the assignment of the vibration modes. The assignments of the observed vibrational wavenumbers at room temperature are presented in Table 1.

Table 1.

Raman shifts and assignments for the α-K2Sr(MoO4)2 crystal at room temperature.

.

It is worth noting that a considerable splitting of the vibration levels corresponding to the Mo–O stretching vibration is observed. The frequency difference between the v1 and v3 modes is as large as 200 cm−1 in the Raman spectrum of α-K2Sr(MoO4)2. These frequency differences are also observed in the Raman spectra of KY(MoO4)2 (280 cm−1) and NaBi(MoO4)2 (230 cm−1); however, the difference for the tetrahedral molybdate ions does not exceed 150 cm−1.[23–26] The stretching frequency region exhibits a large broadening owing to additional interactions between ions through relatively short (3.42 Å) bridge bonds in the unit cell, as shown in Fig. 1.

3.3. High-temperature Raman spectra

The K2Sr(MoO4)2 crystal melts incongruently at 900 °C and has two distinct phase transitions at temperatures of and corresponding to polymorphic first-order transitions α (low-temperature) (medium-temperature) (high-temperature). To better understand the structure changes of K2Sr(MoO4)2, temperature-dependent Raman spectra of the K2Sr(MoO4)2 crystal were recorded from room temperature to 750 °C, as presented in Fig. 4.

Fig. 4. Temperature-dependent Raman spectra of K2Sr(MoO4)2 in the range of 25–750 °C.

To provide further insights into the Raman bands’ behaviors with the increase of the temperature, we analyzed the Raman wavenumber variations with the temperature (ω as a function of T).[27] The equation (α is the linear coefficient of the curve) was obtained in the first approximation as the dependences of ω on T. The curves for each mode are plotted in Figs. 5 and 6. The wavenumbers of the bands of 111 cm−1, 138 cm−1, and 180 cm−1 shift almost linearly toward higher values (Fig. 6), as these bands are attributed to the external vibrations related to motions of K and Sr atoms. However, the high-wavenumber bands at 711 cm−1, 795 cm−1, 810 cm−1, and 899 cm−1 become softened with smaller slope coefficients at the first transition point (approximately 150 °C).

Fig. 5. (color online) Wavenumber shifts of Raman bands in the spectral range of 100–350 cm−1 with the increase of the temperature.
Fig. 6. (color online) Wavenumber shifts of Raman bands in the spectral range of 700–950 cm−1 with the increase of the temperature.

Compared to the wavenumber shifts, the appearance of new bands better reflects the structure changes of K2Sr(MoO4)2. Local enlarged views of the Raman spectra are shown in Figs. 7 and 8. In order to clearly show the changes of the Raman bands, different line styles were used at different temperature ranges. In the low-wavenumber region of 300 cm−1 to 340 cm−1, the intensity of the shoulder band at 324 cm−1 began to increase at 150 °C, corresponding to the first phase transition. This shoulder band continued to increase and merged into a broadened band with a main band at 314 cm−1. However, with the increase in the temperature, the band at 314 cm−1 disappeared and only one band remained at 350 °C, represented by the blue dotted lines. After the temperature reached the second phase-transition point of 475 °C, the Raman spectra became stable. Band changes are also observed at the high-wavenumber region. The Raman band at 894 cm−1 in the plot at 300 °C disappeared when the temperature increased to 350 °C. A band at 890 cm−1 was generated and merged with the band at 880 cm−1 into a broadened band when the sample was heated to 450 °C. In particular, a larger change was observed between 350 °C and 475 °C. These changes of the spectra suggest that the crystal structure of the medium-temperature phase is not stable in the temperature range of 150 °C to 475 °C. It is worth noting that the Raman intensities of the low-wavenumber bands at 110 cm−1, 138 cm−1, and 180 cm−1 (related to the vibrations of K+ and Sr2+ cations) significantly decreased when the temperature increased above 475 °C. These bands were almost not observed at 600 °C. According to a study on a palmierite-related K5Yb(MoO4)4 crystal,[28] the occupations of M1 and M2 positions change from ordered type to statistical with the increase of the temperature. The disappearance of these low-wavenumber bands suggested further disordering of K+ and Sr2+ cations at high temperatures.

Fig. 7. (color online) Local enlarged image of the temperature-dependent Raman spectra in the range of 260–400 cm−1.
Fig. 8. (color online) Local enlarged image of the temperature-dependent Raman spectra in the range of 850–930 cm−1.
4. Conclusion

We performed a detailed investigation on the Raman spectrum of α-K2Sr(MoO4)2 using first-principle calculations. The structural changes were discussed based on the temperature-dependent Raman spectra. The calculated Raman spectrum of α-K2Sr(MoO4)2 was in good agreement with the experimental result. The Raman bands were mainly related to Mo–O vibrations in MoO4 tetrahedra. The temperature-dependent Raman spectra revealed that K2Sr(MoO4)2 exhibited two sets of modifications in the Raman spectra, at ∼150 °C and ∼475 °C. These modifications were attributed to structural phase transitions. The large change of the Raman bands in the temperature range of 150 °C to 475 °C showed that the structure of the medium-temperature phase β-K2Sr(MoO4)2 was not stable.

Acknowledgment

The authors thank the High-Magnetic-Field Laboratory of the Chinese Academy of Sciences for the use of their Raman spectrometer.

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