Floating zone growth and optical phonon behavior of corundum Mg₄Ta₂O₉ single crystals

Abstract

We demonstrate that corundum Mg₄Ta₂O₉ crystals, free of low-angle grain boundaries and bubbles, were prepared for the first time by the infrared heating optical floating zone method. The X-ray diffraction results showed that the crystals had corundum structure, cleaved parallel to the c plane and grew along the a-axis. The temperature-dependent optical phonon behavior of Mg₄Ta₂O₉ were also investigated in the range from 84 to 834 K.

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1. Introduction

Magnesium tantalates, which show favorable potential applications in optical and dielectric devices,^1–4 have received increasing attention from researchers and developers in recent years. The phase diagram of the MgO–Ta₂O₅ system, established in a previous study,⁵ indicates that it consists of three distinct forms: Mg₄Ta₂O₉, Mg₃Ta₂O₈, and MgTa₂O₆. Corundum Mg₄Ta₂O₉ has a hexagonal unit cell with space group P̄3c1 (165),⁶ a = 0.51611 nm, c = 1.40435 nm, and a unit cell volume of 0.32396 nm³. Mg₄Ta₂O₉ appears to be stable up to its melting point (2098 K) and is particularly favored as a candidate material for luminescent^7–9 and microwave dielectrics due to its low dielectric loss and high dielectric constant.¹⁰ Until now, Mg₄Ta₂O₉ has only been obtained in ceramic,¹¹ powders^12–14 and thin films^10,15,16 forms.

Many interesting properties make magnesium tantalates attractive, not only as far as basic physics, such as energy level, is concerned, but also for other possible applications that may effectively utilize its optical properties.^17–19 The crystal boundary and twin structure influence the material properties significantly; investigation of single crystals with well-defined crystallographic orientation can manage these extrinsic effects, significant to both applied and fundamental aspects. Raman scattering, for example, is a nondestructive and readily available optical spectral method that enable us to obtain spectra of vibration modes in various wavenumbers, providing invaluable information on lattice dynamics and describing the dielectric behavior of materials at microwave frequencies. The dielectric response in this region is determined primarily by the characteristics of the polar optical phonons.^20–23

To the best of our knowledge, no reports regarding Mg₄Ta₂O₉ crystals grown by any method have been published yet. The controllable atmosphere, crucible-free, and steep temperature gradients generated along the vertical direction allow for the rapid and stable growth of contaminant-free crystals. Furthermore, crystals grown by this method are usually large enough in size to be successfully measured in experimentations.^24–29 To this effect, the primary goal of this study is investigation of the growth and optical phonon behavior of Mg₄Ta₂O₉ single crystals with the optical floating zone method.

2. Experimental section

Crystal growth

The fabrication of Mg₄Ta₂O₉ supporting and feeding rods started with calcining grinded powders containing stoichiometric amounts of MgO (Alfa Aesar 99.99%) and Ta₂O₅ (Alfa Aesar 99.99%) at 1400 K for 20 h with intermediate grinding. The obtained Mg₄Ta₂O₉ powder was then packed into a cylindrically shaped rubber tube, evacuated via a vacuum pump, and then pressed up to 75 MPa hydrostatically in a cold isostatic presser forming a cylindrical rod of 0.6–0.8 cm in diameter and about 10 cm in length. Finally, the rods were sintered in air at 1700 K for 10 h.

Crystals were grown in a four 1000 W halogen lamps heated optical floating zone furnace (CSI FZ-T-10000 H-VI-VP, Crystal systems, Inc., Japan). The growth conditions were listed as follow: the growth speed was 6 mm h⁻¹, the support and feed rods were rotated with 10 rpm in opposite directions, respectively; the air flow was about 0.5 L min⁻¹ with a pressure of 0.2 MPa. At the initial stage of crystal growth, the melting zone is stable with an adequate shape. After about two hours, as the grown crystal reaches about 12 mm in length, the melting zone becomes suddenly thin and the material becomes highly viscous and dropped down. Usually, the liquid forms a solid solution at the outside of the crystal rod top. During our experiment, however, there was no solid-solution formation outside and the phenomenon is periodic.

To further examine the lack of outer solid solution, we shut down the heating lamp just when the melting zone became thin again, and observed that the crystal then separated along the crack. In the center of the crystal, we found that the solid solution had formed a cone shape with its axis along growth direction, as shown in Fig. 1a. The shape of the interface between the melted liquid and grown crystal is shown in Fig. 1a as a red dotted line. The solid solutions formed from the dropped liquid. Generally, the interface of a growing crystal can be illustrated as shown in Fig. 1-1, with crystal growth that has a positive wetting angle.³⁰ Negative wetting angle, which is a common problem in the growth of vanadate, niobate and tantalate crystals at the formed interface, is shown in Fig. 1-2, as well as detailed in Fig. 1a (the red arrow represents the crystal growth direction.)

Fig. 1 Photographs of (a) longitudinal cross section of the Mg₄Ta₂O₉ crystal obtained from suddenly shut down lamp powder after melting zone became thin; (b) the crystal wafer cut perpendicular to the growth direction; (c) the as-grown crystal wafer under polarizing microscope in cross transmission configuration and (d) the as-grown corundum Mg₄Ta₂O₉ crystal.

At the beginning of the process, a gas bubble formed at the center of the growing crystal where the oxygen ions in the feed rods were converted to oxygen gas (or the oxygen gas dissolved in the melt was re-boiled) as shown in Fig. 1-3. As the crystal grew, the bubble enlarged gradually due to its similarly negative wetting angle. The diameter of the bubble is grew as the amount of gas in the bubble remained constant, which reduced the concentration of air in the bubble as shown in Fig. 1-4. Once the diameter of the bubble was large enough, the reduced air concentration in the bubble made the surface tension unable to maintain the melted liquid, as shown in Fig. 1-5. As a result, the liquid dropped down into the bubble forming the cone-shaped solid solution that resulted in a thin melting zone as shown in Fig. 1-6. This processes is illustrated in Fig. 1-3 to 6.

The shape of the interface is usually modified by changing rotational speed.³⁰ Based on our experience, a high rotational speed results in a large number of bubbles in the crystal rods, especially in niobate and tantalate crystals. In this study, we modified the shape of the interface by moving the feeding rods and changing the melting zone's shape.^28,29,31,32 Moving the feeding rods also changed the amount of melting liquid in the floating zone and the radio of the grown crystal, and the radio of the grown crystal can be obtained according to the following equation (where the densities of the feeding rods and grown crystal are ignored):

R_g and R_f are the radius of the grown crystal and feeding rod, respectively; v₁ and v₂ are the crystal growth speed and the shift speed of the feed rod, respectively. Fig. 1-7 depict the feed rod shifting down the shape of the melting zone and interface. Though the feed rod shifted up in this case, Fig. 1-8 illustrate the shape of the melting zone and interface theoretically.

For further tests of the above argument, the parameters were set as follows: 79% lamp power, growth speed of 6 mm h⁻¹, feeding rod shifted between −2 and +2 mm h⁻¹ (negative values indicate upward feeding rod shift). Mg₄Ta₂O₉ crystals were grown by spontaneous nucleation. Multiple nucleation sites were observed at the beginning of the growth process. The rod was composed of several large grains post-optimization, as shown in Fig. 1d. The boule was a cylindrical rod 5–8 mm in diameter and 65 mm in length, and the largest crystal grain was Φ 4 mm × L 12 mm obtained under 2 mm h⁻¹ downward feeding rod shift. When the feeding rod was shifted 2 mm h⁻¹ upward, more nucleation sites appeared. These results support the argument above.

Experimental methods

The structure of the samples was characterized by using a Rigaku RU-200b X-ray diffractometer (XRD) with Cu Kα radiation. A Bruker AXS D8 Discover with GADDS X-ray diffractometer (XRD²) was used to probe the orientation of the as-grown crystal, in which a part of the Debye–Scherrer ring is two-dimensionally detected. As a result, orientation can be characterized easily. The macroscopic defects were checked with an Olympus Model BX-51 micropolariscopy in cross transmission arrangement. The Raman spectra of the samples were obtained using a Jobin-Yvon LABRAM-HR 800 spectrometer equipped with a Peltier-cooled CCD detector and a confocal 50× objective Olympus microscope. The spectral resolution and the lateral resolution used were approximately 1 cm⁻¹ and 2 μm, respectively. Measurements were conducted in backscattering geometry configuration by using the 514.5 nm line from an Ar ions laser with 40 mW power (Spectra Physics Stabilite 2017) as the excitation source. Edge filter for stray light rejection was also used. In-site temperature-dependent Raman spectra from 84 to 834 K were performed in a Linkam THMSE 600 cooling/heating stage equipped to the Raman spectrometer.

3. Results and discussion

Fig. 1b shows a crystal wafer that was cut perpendicular to the natural cleavage plane and parallel to the growth direction from the larger domain, then fine polished for further testing. The bubbles and low-angle grain boundary microscopic defects in the wafer (Fig. 1b) were characterized via micropolariscopy in a cross-transmission configuration. Fig. 1c is a photograph of the wafer (Fig. 1b) under polarized light, showing where the wafer did not contain any bubbles or low-angle grain boundaries.

Mg₄Ta₂O₉ crystals were crushed to powder form to obtain thorough structural information for the crystal as-grown. Fig. 2 shows the XRD pattern of the crushed crystal powder. All peaks can be indexed to the diffraction peaks of corundum Mg₄Ta₂O₉ (JCPDS 38-1458).

Fig. 2 Powder XRD pattern of crushed Mg₄Ta₂O₉ crystals.

To determine the growth direction and natural cleavage plane parallel to the growth direction of a single Mg₄Ta₂O₉ crystal, XRD² analyses were conducted on a slice cut perpendicular to the growth direction of the wafer. The obtained XRD² patterns were plotted as shown in Fig. 3a and b, where both exhibit only one peak at 62.3° and 12.5°, which can be indexed to the (3 0 0) and (0 0 2) planes, respectively. The XRD² results suggest that the Mg₄Ta₂O₉ crystal was cleaved parallel to the c-plane and grew along the a-axis.

Fig. 3 XRD² pattern of (a) measured along growth direction and (b) the as-grown Mg₄Ta₂O₉ wafer.

In-site temperature-dependent Raman measurements were performed on a microcrystalline sample with crystallite size of 1 μm³, taken from the crushed Mg₄Ta₂O₉ crystal, to obtain rapid temperature response. A total of 16 temperature-measurement points were observed, from 84 K to 834 K every 50 K. Raman spectra obtained at selected temperatures are shown in Fig. 4.

Fig. 4 In-site temperature-dependent Raman spectra of the as-grown Mg₄Ta₂O₉ crystal.

At 84 K, a total of 16 Raman peaks were identified. As temperature increased, all Raman modes showed blue shift with decreasing intensity, continuously broadening line width, and overlapping. When the temperature reached 834 K, only 12 Raman peaks were left due to overlapping. No new Raman modes were observable after the process began. At 84 K, the strongest mode at 823 cm⁻¹ was identified as the terminal Ta–O stretching mode.³³ Three bands between 550 and 700 cm⁻¹ were also attributed to stretching vibration modes of Ta–O bonds: the lower band at 581 cm⁻¹ had lower energy, which can be attributed to the bridged Ta–O bond stretching mode; and the bands at 671 and 640 cm⁻¹ can be attributed to the two chain Ta–O bonds, because the two chain bonds had similar bonding lengths and energies so their wavenumbers were close. The two bands overlapped and degenerated as temperature increased, and the thermal effect force between the two chains became greater.

Similarly, three weaker modes at 202, 254, and 262 cm⁻¹ were attributed to bending vibration in the O–Ta–O bond. The fuzzy modes between 300 and 500 cm⁻¹ originated from MgO₆ octahedrons. The lowest wavenumber and second strongest mode at 122 cm⁻¹ was attributed to an external mode, where the Ta–Ta stretching mode between face-shared TaO₆ octahedrons made it stronger than the other tantalate. Four representative bands at 823, 581, 254, and 122 cm⁻¹ were selected to further investigate temperature-dependent Raman scattering.

Anharmonic interactions plus thermal expansion were the primary cause of temperature-induced Raman changes in Mg₄Ta₂O₉. Researchers typically discuss relevant phenomena according to the theoretical thermodynamics of crystals.³⁴ Cubic and quartic anharmonic terms must be accounted for in the potential energy, while total energy must be calculated in second-order perturbation in order to correctly identify harmonic energies as anharmonic self-energies. Anharmonic self-energy is rather complex, as discussed below. It can be expressed as follows:^34–36

ℏΔω(λ) = ℏΔ(λ) − iℏΓ(λ) (2)

where λ is a mode with polarization and a specific wavevector. The quantity Δ(λ) corresponds to the wavenumber of the phonon. Γ(λ) is the full width at half maximum (FWHM) of the Raman modes. Both cubic and quartic anharmonic terms contribute to Δ(λ) in second-order perturbation, whereas only the cubic term contributes to Γ(λ).

The FWHM and wavenumber of all the modes in the entire Raman spectra were obtained by fitting the bands with Lorentzian line shape. The temperature-dependent FWHM and wavenumbers of the four selected vibration modes are shown in Fig. 5 and 6. Generally speaking, the FWHM gradually broadened and the Raman wavenumber steadily decreased as temperature increased.

Fig. 5 Temperature-dependent Raman shift for the selected Raman bonds.

Fig. 6 Temperature-dependent FWHM for the selected Raman bonds.

The temperature-dependent Raman wavenumber is expressed by the following equation:

where d(λ) and d(λ, λ′) are temperature-independent factors that relate to the strengths of the cubic and quartic anharmonic interactions and crystal configuration. n(λ′) is the Bose–Einstein occupation number, which can be expressed as follows:

n(λ') = {exp[ℏΔ_o(λ′)/kT] − 1}⁻¹ (4)

where Δ_o(λ′) refers to the harmonic frequency, ℏ is Planck's constant, T is absolute temperature, and k is Boltzmann's constant. Combining eqn (3) and (4) yields the following equation:

Δ(λ) = A + B{exp[ℏΔ_o(λ′)/kT] − 1}⁻¹ (5)

All four data points shown in Fig. 5 were well-fitted (marked by solid purple lines) using eqn (5). Table 1 provides the best fit parameters for all four modes. The four characteristic frequencies Δ_o(λ′) for specific Raman modes were close to certain Raman modes of Mg₄Ta₂O₉; therefore, the shift in the four modes against temperature are assumed to be phonon–phonon anharmonic interactions.

Table 1 Best values of the parameters A, B, and Δ_o(λ′) obtained by fitting eqn (5) for the temperature-dependent Raman wavenumber

	A (cm^−1)	B (cm^−1)	Δo(λ′) (cm^−1)
1	122	−4.7	448
2	254	−8.8	411
3	581	−13.8	364
4	823	−19.5	701

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Based on the theory described above, phonon damping can be attributed to crystal field-phonon, spin-phonon, disordered, or phonon–phonon interactions. Disorder effects do not change with temperature. Crystal-field-phonon contribution can be eliminated because no crystal field levels for the material fell below 1000 cm⁻¹. Spin-phonon interactions should also be neglected, because they are nonmagnetic. Thus, phonon damping with temperature can be attributed to phonon–phonon anharmonic contributions. According to second-order perturbation, temperature-dependent FWHM only arises via cubic anharmonic interactions related to combination and decay processes. Best fit for the four internal modes was acquired after assuming only phonon–phonon combination among phonons of wavenumber ω′, creating a third excitation wavenumber ω′′, where ω′′ = ω + ω′. FWHM for the four Raman bands was fitted by the following equation:

Γ(λ) = C + D[n(ω′) − n(ω + ω′)] (6)

where C refers to the FWHM at 84 K and D reflects the strength of cubic anharmonic interaction, which is not dependent on temperature. The best fit for the four modes is represented by the green solid line in Fig. 6, and Table 2 lists all four modes' parameters.

Table 2 Best fitting values of the parameters ω′ and ω′′ obtained from eqn (6) for the temperature-dependent FWHM

	ω (cm^−1) at 83 K	ω′ (cm^−1) (observed mode)	ω′′ (cm^−1) (observed mode)
1	122	390 (399)	512 (491)
2	254	564 (581)	818 (823)
3	581	261 (253)	842 (823)
4	823	350 (362)	1175 (no)

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To summarize, all the ω′ were close to Raman bands of Mg₄Ta₂O₉. Except for Raman modes at 823 cm⁻¹, the fitted values for ω′′ identify known vibrations of Mg₄Ta₂O₉. The modes at 254 and 581 cm⁻¹ all related to the mode at 823 cm⁻¹, indicating that the terminal Ta–O stretching mode had strong interaction with the two modes (254 and 581 cm⁻¹) under temperature effects. The temperature-dependent FWHM of the four modes can thus be considered characterized by phonon–phonon anharmonic interactions. Theories regarding temperature-dependent Raman wavenumber and FWHM were discussed previously by Wallace;³⁴ in our experiment, we identified only phonon–phonon anharmonic interactions without any anomalous changes. Therefore, the optical phonon behavior of corundum Mg₄Ta₂O₉ is demonstrably stable in the entire temperature range.

4. Conclusions

A large multigrained crystalline boule of Mg₄Ta₂O₉ was prepared via the optical floating zone method. The as-grown sample has dimensions of Φ 5–8 mm × L 65 mm, with the largest crystal grain being Φ 4 mm × L 12 mm. The boule cleaved parallel to the c plane and grew along the a-axis. The obtained Mg₄Ta₂O₉ crystal wafer was free of low angle grain boundaries and bubbles. The temperature-dependent Raman spectra of Mg₄Ta₂O₉ were also discussed thoroughly.

Acknowledgements

The financial support from the National Foundation for Fostering Talents of basic Science (Grant No. J1103202), the National Basic Research Program of China (No. 2011CB808200), the Program for Changjiang Scholars and Innovative Research Team in University (No. IRT1132), the National Natural Science Foundation of China (Grant No. 11274137, 11074090, 11304113) is greatly appreciated.

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