Mechanical Properties, Quantum Mechanical Calculations, and

May 13, 2016 - The mechanical properties of GaNbO4, Ga(Ta,Nb)O4, and GaTaO4 have been investigated by nanoindentation. Furthermore, the structural dat...
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Mechanical Properties, Quantum Mechanical Calculations, and Crystallographic/Spectroscopic Characterization of GaNbO4, Ga(Ta,Nb)O4, and GaTaO4 Lukas Perfler,*,† Volker Kahlenberg,† Daniel Többens,‡ Andreas Schaur,§ Martina Tribus,† Maria Orlova,† and Reinhard Kaindl⊥ †

Institute of Mineralogy and Petrography, University of Innsbruck, Innrain 52f, 6020 Innsbruck, Austria Helmholtz-Zentrum Berlin für Materialien und Energie GmbH, Department of Crystallography, Hahn-Meitner-Platz 1, 14109 Berlin, Germany § Institute for Structural Engineering and Material Sciences, Material Technology Innsbruck, University of Innsbruck, Technikerstr. 11/19a, 6020 Innsbruck, Austria ⊥ MATERIALS - Institute for Surface Technologies and Photonics, JOANNEUM RESEARCH Forschungsgesellschaft mbH, Leobner Straße 94, 8712 Niklasdorf, Austria ‡

S Supporting Information *

ABSTRACT: Single crystals as well as polycrystalline samples of GaNbO4, Ga(Ta,Nb)O4, and GaTaO4 were grown from the melt and by solid-state reactions, respectively, at various temperatures between 1698 and 1983 K. The chemical composition of the crystals was confirmed by wavelengthdispersive electron microprobe analysis, and the crystal structures were determined by single-crystal X-ray diffraction. In addition, a high-P−T synthesis of GaNbO4 was performed at a pressure of 2 GPa and a temperature of 1273 K. Raman spectroscopy of all compounds as well as Rietveld refinement analysis of the powder X-ray diffraction pattern of GaNbO4 were carried out to complement the structural investigations. Density functional theory (DFT) calculations enabled the assignment of the Raman bands to specific vibrational modes within the structure of GaNbO4. To determine the hardness (H) and elastic moduli (E) of the compounds, nanoindentation experiments have been performed with a Berkovich diamond indenter tip. Analyses of the load−displacement curves resulted in a high hardness of H = 11.9 ± 0.6 GPa and a reduced elastic modulus of Er = 202 ± 9 GPa for GaTaO4. GaNbO4 showed a lower hardness of H = 9.6 ± 0.5 GPa and a reduced elastic modulus of Er = 168 ± 5 GPa. Spectroscopic ellipsometry of the polished GaTa0.5Nb0.5O4 ceramic sample was employed for the determination of the optical constants n and k. GaTa0.5Nb0.5O4 exhibits a high average refractive index of nD = 2.20, at λ = 589 nm. Furthermore, in situ high-temperature powder X-ray diffraction experiments enabled the study of the thermal expansion tensors of GaTaO4 and GaNbO4, as well as the ability to relate them with structural features. This α-PbO2-type structure has been refined to a residual of R = 0.074 for 275 independent reflections (F0 > 6σ(F0)) with the lattice parameter a = 4.612(1), b = 5.588(2), c = 4.974(1), V = 128.19 Å3, Z = 2. As reported in the case of FeNbO4,3 there is the possibility that the structure has been assigned to the wrong crystal system. Due to the β-angle having a value close to 90°, an apparent orthorhombic structure can be pretended instead of the monoclinic wolframite-type structure. Similar to the present study, also in our case, first an orthorhombic structure has been suggested for GaTaO4 by the single-crystal X-ray diffraction software, but on closer inspection of the data, the monoclinic crystal structure could be verified. Compared with the orthorhombic α-PbO2-type structure, the monoclinic

1. INTRODUCTION 3+

Compounds with the general chemical formula ABO4 (A = Al, Ga, In, Fe, Ti, Cr; B5+ = Nb, Ta) have been reported to adopt the following principally different structure types: 1. AlNbO4-type (C2/m), 2. wolframite-type (P2/c), 3. α-PbO2type (Pbcn), and 4. rutile-type (P42/mnm).1−4 In this structuretype sequence, the cation ordering among the crystallographically different metal sites decreases; that is, compounds with rutile-type structure exhibit the highest degree of disorder because of a completely statistical cation distribution. The most important factors which affect the structure type are temperature and cooling rate during the synthesis process. Harneit and Müller-Buschbaum1 prepared single crystals of GaTaO4 by solid-state reactions at 1823 K, followed by slow cooling to room temperature, and assigned the structure to orthorhombic symmetry with space group Pbcn (No. 60; ICSD code: 72570). © XXXX American Chemical Society

Received: February 16, 2016

A

DOI: 10.1021/acs.inorgchem.6b00386 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry Table 1. Crystal Data and Structure Refinement of GaNbO4, Ga(Ta,Nb)O4, and GaTaO4 empirical formula molar mass temperature crystal system space group unit cell dimensions

volume Z density (calculated) crystal size (mm) index ranges scan type scan width reflections collected exposure time independent reflections completeness X-ray radiation X-ray power absorption coefficient theta range F(000) refined parameters final R1/wR2 [I > 2σ(I)] R1/wR2 (all data) Goodness-of-fit on F2

GaNbO4

Ga(Ta,Nb)O4

GaTaO4

226.63 g·mol−1 293(2) K monoclinic C12/m1 (No. 12) a = 12.4682(6) Å b = 3.7872(2) Å c = 6.6103(3) Å α = 90° β = 107.835(5)° γ = 90° 297.13(3) Å3 4 5.066 g·cm−3 0.10 × 0.08 × 0.04 −15 ≤ h ≤ 15, −4 ≤ k ≤ 4, −8 ≤ l ≤ 8 ω scans 1° 1966 10 s/frame 354 [R(int) = 0.035] 100.0% (up to θ = 26.3°) Mo Kα, λ = 0.71073 Å 50 kV, 40 mA 12.73 mm−1 3.24 to 26.30° 416 38 0.0265/0.0617 0.0273/0.0627 1.261

270.65 g·mol−1 293(2) K monoclinic P12/c1 (No. 13) a = 4.5846(3) Å b = 5.5529(4) Å c = 4.9452(3) Å α = 90° β = 90.458(6)° γ = 90° 125.890(14) Å3 2 7.140 g·cm−3 0.16 × 0.12 × 0.08 −5 ≤ h ≤ 5, −6 ≤ k ≤ 6, −6 ≤ l ≤ 6 ω scans 1° 1486 5 s/frame 258 [R(int) = 0.056] 100.0% (up to θ = 26.3°) Mo Kα, λ = 0.71073 Å 50 kV, 40 mA 34.47 mm−1 3.67 to 26.32° 240 30 0.0273/0.0712 0.0273/0.0712 1.322

314.64 g·mol−1 293(2) K monoclinic P12/c1 (No. 13) a = 4.5879(5) Å b = 5.5673(6) Å c = 4.9589(5) Å α = 90° β = 90.195(11)° γ = 90° 126.66(2) Å3 2 8.251 g·cm−3 0.04 × 0.04 × 0.02 −5 ≤ h ≤ 5, −7 ≤ k ≤ 7−5 ≤ l ≤ 6 ω scans 1° 753 55 s/frame 288 [R(int) = 0.026] 99.3% (up to θ = 26.3°) Mo Kα, λ = 0.71073 Å 50 kV, 40 mA 53.576 mm−1 3.66° to 28.57° 272 30 0.0320/0.0982 0.0328/0.0984 1.342

application as a promising safer anode material for Li-ion batteries in comparison to the widely used graphite-based anodes. Furthermore, the obtained Raman spectra of all compounds provided additional important information regarding the bond strength and crystal structure. Spectroscopic ellipsometry enabled the determination of the index of refraction (n) and extinction coefficient (k) in the spectral range from 245 to 1000 nm for the gallium tantalum niobium oxide.

wolframite-type structure, exhibits a lower symmetry, enabling an ordered cation distribution. In more detail, ordering occurs among the two octahedrally coordinated different metal sites (2e, 2f) because of the splitting of the statistically occupied metal position (4c). On the other hand, a monoclinic GaNbO4 structure was first described by Morosin and Rosenzweig5 in 1965, but they assigned the gallium niobium oxide to a noncentric space group (C2, No. 5; ICSD code: 18187) instead of the centric space group C2/m (No. 12), with a final R value of 0.08 and the following crystallographic data: a = 12.660(5), b = 3.7921(22), c = 6.6147(28), β = 107.90(2), V = 302.19 Å3, Z = 4. However, an alternative centric interpretation of the data could not be excluded. Because of the expected high hardness (short metal−oxygen bond distances), as well as excellent optical properties (refractive index n > 2.18, low dispersion), combined with good thermal and chemical resistance of gallium niobium and gallium tantalum oxides, we decided to investigate GaNbO4, Ga(Ta,Nb)O4, and GaTaO4 in more detail. The results of the hardness and elastic modulus measurements of the GaNbO4, Ga(Ta,Nb)O4, and GaTaO4 samples by the use of nanoindentation are presented, and the calculated thermal expansion tensors of the gallium niobium and gallium tantalum oxides as a function of temperature are related to structural changes. To complement the crystal structure data, the results of the singlecrystal X-ray diffraction experiments, as well as Rietveld refinements for GaNbO4 are reported. The special structural features combined with the different possible redox couples Nb5+/Nb4+ and Nb4+/Nb3+, could enable GaNbO4 for an

2. EXPERIMENTAL SECTION 2.1. Synthesis. Large single crystals (>500 μm) of GaNbO4, Ga(Ta,Nb)O4, and GaTaO4 were grown directly from melt and by solid-state reactions, respectively, at temperatures between 1698 and 1983 K. Compared to GaNbO4, GaTaO4 exhibits a higher melting point. Stoichiometric amounts of the dried starting materials (Alfa Aesar; Ga2O3, 99.999%; Nb2O5, 99.999%; Ta2O5, 99.993%) were homogenized in a planetary ball mill with ethanol. In the first synthesis experiment, the pressed mixtures were placed on an iridium sheet and fired in a muffle furnace from 1273 to 1873 K (GaNbO4, Ga(Ta,Nb)O4)/1973 K (GaTaO4), respectively, with a heating ramp of 5 K/min. After a dwell time of 10 min, the melt was cooled to 1473 K with a ramp of 1.6 K/min and subsequently quenched in water. In the second synthesis experiment, the homogenized educts were filled in platinum capsules (2 cm long, inner Ø 3 mm) and heated for 70 h at 1633 K (in case of GaNbO4) and at 1863 K (in case of GaTaO4). The samples were first slowly cooled to 1473 K at a rate of 0.8 K/min and finally to 298 K with 1.6 K/min. Polycrystalline GaNbO4, GaTa0.5Nb0.5O4, and GaTaO4 samples were prepared by solid-state reactions in a platinum crucible at temperatures in the range between 1523 and 1698 K. The isostatically pressed (15 kN/30 s) tablets were B

DOI: 10.1021/acs.inorgchem.6b00386 Inorg. Chem. XXXX, XXX, XXX−XXX

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Table 2. Atomic Coordinates, Site Occupancies, and Equivalent Isotropic Displacement Parameters [Å2] for GaNbO4, Ga(Ta,Nb)O4, and GaTaO4 atom Nb Ga O(1) O(2) O(3) O(4) atom

Wyckoff site 4i 4i 4i 4i 4i 4i Wyckoff site

x

y

z

Ueq

0.39671(4) 0.30289(5) 0.3631(3) 0.5540(3) 0.8625(3) 0.2405(3) x

0 0 0 0 0 0

0.26948(6) 0.68626(8) 0.9872(5) 0.3651(7) 0.2987(6) 0.3520(6) z

0.0035(3) 0.0044(3) 0.0112(10) 0.0069(8) 0.0066(8) 0.0051(8) Ueq

occupancy 1 1 1 1 1 1 occupancy

Ga Ta Nb O(1) O(2) atom

2f 2e 2e 4g 4g Wyckoff site

1 0.5 0.5 1 1 occupancy

Ga Ta O(1) O(2)

2f 2e 4g 4g

1 1 1 1

0.5000 0.0000 0.0000 0.2273(13) 0.2694(12) x 0.5000 0.0000 0.228(4) 0.270(4)

fired using different annealing times (15, 20, 24, 30, 48, and 70 h). All samples were slowly cooled to 1273 K at a rate of 0.8 K/min and finally to room temperature with 1.6 K/min. A high-P−T synthesis of GaNbO4 was performed using a 1000 t press manufactured by Hymag AG (Betzdorf, Germany) equipped with a Boyd and England piston− cylinder module. The polycrystalline GaNbO4 sample contained in a closed platinum capsule was taken to a pressure of 2 GPa and a temperature of 1273 K. After a run duration of 14 days, the sample was quenched to room temperature. 2.2. X-ray Diffraction. Single-crystal diffraction experiments were performed on an Oxford Diffraction Gemini R Ultra diffractometer equipped with a Ruby CCD detector using graphite-monochromatized Mo Kα radiation. Prismatic, colorless single crystals with good optical quality were selected for structural investigations and mounted on the tip of glass fibers using fingernail hardener. Structure solution by direct methods and least-squares refinement calculations were carried out with the programs SIR-20026 and SHELXL-97,7 respectively, embedded in the WinGX program suite (v1.80).8 Data reduction including an absorption correction based on indexed faces has been applied using the data collection and processing software CrysAlisPro (Agilent).9 Details of the data collection and refinement parameters for GaNbO4, Ga(Ta,Nb)O4, and GaTaO4 are given in Table 1. Final full matrix least-squares refinement cycles, including fractional coordinates as well as anisotropic displacement parameters for all atoms, converged to a residual of R1 = 0.0265 for 354 reflections (in the case of GaNbO4) and for Ga(Ta,Nb)O4 as well as GaTaO4 to R1 = 0.0273 for 258 reflections and to R1 = 0.0320 for 288 reflections, respectively, with I > 2σ(I). Refined coordinates, equivalent isotropic displacement parameters, as well as selected interatomic distances for GaNbO4, Ga(Ta,Nb)O4, and GaTaO4 are given in Tables 2 and 3. Anisotropic displacement parameters and selected angles are accessible in the Supporting Information (Tables S1−S2). Figures showing structural details were prepared using the program VESTA 3.1.10 High-resolution powder X-ray diffraction data were recorded under ambient conditions on a Bruker Model AXS D8 Discover powder diffractometer in Bragg−Brentano θ−θ geometry using strictly monochromatic Cu Kα1 radiation (λ = 1.540596 Å; 40 kV, 40 mA) and a one-dimensional LYNXEYE silicon strip detector. The monochromatization of the Cu radiation was accomplished by a primary beam Ge(111) monochromator. Data acquisitions were performed in the 2θ range between 3° and 135°, using a step width of 0.005° and a counting time of 0.5 s per step. A fixed divergence slit (0.3°) and a secondary Soller slit were used. The structural data were refined by the Rietveld method,11 using the TOPAS 4.212 software.

y 0.6653(2) 0.1806(1) 0.1806(1) 0.1143(11) 0.3848(11) y

0.2500 0.2500 0.2500 0.5794(10) 0.0788(10) z

0.0097(4) 0.0087(4) 0.0087(4) 0.0129(12) 0.0137(12) Ueq

0.2500 0.2500 0.578(4) 0.081(4)

0.0022(7) 0.0018(5) 0.020(4) 0.021(4)

0.6634(5) 0.1797(2) 0.113(3) 0.386(3)

Table 3. Selected Bond Lengths [Å] up to 2.35 Å for GaNbO4, Ga(Ta,Nb)O4, and GaTaO4 Nb−O1 Nb−O2 Nb−O3 Nb−O3 Nb−O4 Nb−O2 Ga−O1 Ga−O2 Ga−O4 Ga−O4 Ga−O3 Ga−O4

1.783(3) 1.868(4) 1.964(1) 1.964(1) 2.177(4) 2.303(4) 1.899(3) 1.915(4) 1.964(1) 1.964(1) 2.095(4) 2.106(3)

Ta/Nb−O2 Ta/Nb−O2 Ta/Nb−O1 Ta/Nb−O1 Ta/Nb−O1 Ta/Nb−O1 Ga−O1 Ga−O1 Ga−O2 Ga−O2 Ga−O2 Ga−O2

1.883(6) 1.883(6) 1.961(5) 1.961(5) 2.120(6) 2.120(6) 1.938(6) 1.938(6) 1.966(5) 1.966(5) 2.061(6) 2.061(6)

Ta−O2 Ta−O2 Ta−O1 Ta−O1 Ta−O1 Ta−O1 Ga−O1 Ga−O1 Ga−O2 Ga−O2 Ga−O2 Ga−O2

1.890(17) 1.890(17) 1.966(17) 1.966(17) 2.120(17) 2.120(17) 1.955(17) 1.955(17) 1.972(17) 1.972(17) 2.047(17) 2.047(17)

Description of the peak shapes was carried out by the fundamental parameters approach.13 To determine the thermal expansion of the gallium tantalum and gallium niobium oxides, in situ high-temperature studies in the range of 298−1373 K (ΔT = 50 K per measurement) were performed with a Siemens D5005 powder X-ray diffractometer equipped with an Anton Paar HTK1200 high-temperature stage. Data were collected in the 2θ range between 5° and 90° with a step size of 0.02° and an acquisition time of 6 s per step. In order to achieve thermal equilibrium inside the chamber, the polycrystalline samples were kept at the target temperature for 5 min before the next measurement was started. The determination of the thermal expansion tensor αij from the powder diffraction data of GaNbO4 and GaTaO4 was carried out with the TEV (v0.9.4) program.14 2.3. Raman Spectroscopy. Confocal Raman spectra of the samples in the range of 50−4000 cm−1 were recorded with a Horiba Jobin Yvon Labram-HR 800 Raman microspectrometer. The samples were excited using the 532 nm emission line of a frequency-doubled 100 mW Nd:YAG laser and the 633 nm emission line of a 17 mW He−Ne laser under an Olympus 100× objective lens (numerical aperture of 0.9). The size of the laser spot on the surface was ∼1 μm in diameter. The scattered light was dispersed by an optical grating with 1800 lines mm−1 and collected by a 1024 × 256 open-electrode CCD detector. The spectral resolution, determined by measuring the Rayleigh line, was 1600 K) for more than 20 h, showed a strong preferred orientation along (001). To reduce this preferred orientations the polycrystalline samples were synthesized at 1613 K for a short time (2 × 15 h), including an intermediate grinding. This enabled an improved Rietveld refinement of the powder diffraction data of GaNbO4. The structure refinement of GaNbO4 converged at Rp = 8.53, Rwp = 11.23, Rexp = 6.31 with a goodness of fit (GOF) of 1.78 and R-Bragg value of 5.15. The values for the lattice parameters resulting from the Rietveld refinement are a = 12.47476(3), b = 3.78879(1), c = 6.61367(1), β = 107.8641(2)°, V = 297.519(1) Å3. Structural data as well as Miller indices, d values and 2θ values (up to 57°) of the Rietveld refinement of GaNbO4 are given in Table S3 and Table S4. A Rietveld analysis of the diffraction pattern of monoclinic GaTaO4 has been reported only recently by Pan et al. in 2014.30 Transmitted light microscope images of transparent and colorless GaNbO4 single crystals with a length up to ∼1500 μm are given in Figure S1. The prismatic and elongated crystals show well-formed crystal morphologies. Backscattered electron shadow (BES) images of a polished GaNbO4 sample, which was fired at 1633 K for 70 h in a platinum capsule, revealed the presence of chemically homogeneous crystals (Figure S2). Results of the wavelength-dispersive X-ray spectroscopy analyses for all compounds are given in Table S3. Electron microprobe elemental (Ga and Nb) maps of single crystals, which were grown directly from melt at 1873 K (using a homogenized mixture of Ga2O3:Nb2O5 = 1:1) show in addition to GaNbO4 the presence of Ga2O3 and Nb2O5 (Figure S3). 3.2. Analysis of the Thermal Expansion. In situ hightemperature powder X-ray diffraction experiments enabled the study of the thermal expansion of GaTaO4 and GaNbO4. Patterns were recorded from 323 to 1373 K, in steps of 50 K. Whole powder pattern fitting of the diffractograms based on the LeBail method31 was applied to determine the lattice

Figure 6. Evolution of the a-, b-, and c-lattice parameters for GaTaO4 with increasing temperature.

(Figure 7). This last observation may indicate a potential phase transition of the monoclinic wolframite-type crystal structure to the orthorhombic α-PbO2-type structure at high temperatures. Within the structure of GaNbO4, on the other hand, only the values of the crystallographic a- and c-axes show a significant variation depending on the temperature (Figure 8), while the values of the lattice parameter b are almost constant. To calculate the components αij of the thermal expansion tensor the temperature dependence of the lattice parameters P over the temperature range 298−1323 K have been fitted with polynomials of first degree: P(T ) = p0 + p1 T F

(1) DOI: 10.1021/acs.inorgchem.6b00386 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

Figure 7. Evolution of the lattice parameter β and of the unit cell volume for GaTaO4.

where T is the temperature (given in Kelvin). The quality of the fitting can be described numerically by the coefficient of determination R2: n

R2 =

n

∑i = 1 (ai − a ̅ )2 − ∑i = 1 (ai − aî )2 n ∑i = 1 (ai − a ̅ )2

(2)

where ai is the observed value for component i; â the calculated value for component i; ai̅ the mean, and n the number of different temperatures.14 The thermal expansion of a monoclinic crystal can be expressed by a second rank tensor of the form: ⎡ α11 0 α13 ⎤ ⎥ ⎢ ⎢ 0 α22 0 ⎥ ⎥ ⎢ ⎣ α31 0 α33 ⎦

Figure 8. Evolution of the unit cell volume and of the a- and c-lattice parameters for GaNbO4.

increasing temperature and exhibit low tensor component values with a maximum of 6.7276 × 10−6 K−1 (α11) at 298 K for GaTaO4 and 8.3860 × 10−6 K−1 (α33) for GaNbO4. It is obvious from Figure 9 that in the case of GaNbO4, at 298 K the largest thermal expansion occurs parallel to [001] and the lowest parallel to [010]. Along the crystallographic b-axis, even negative thermal expansion values can be observed. At higher temperatures, the thermal expansion decreases parallel to the aand c-axis. By relating the thermal expansion data with the crystal structure of GaNbO4, it becomes obvious that maximum thermal expansion occurs perpendicular to the endless linear columns and zigzag chains of the corner and edge-sharing octahedra, respectively. This correlation could be observed previously while studying the thermal expansion behavior of monoclinic TiTa2O7 and TiNb2O7.33 On the other hand, GaTaO4 shows a different thermal expansion behavior because of the crystal structure. The largest thermal expansion, at 298 K, occurs parallel to [100] and the lowest parallel to [001]. At higher temperatures, the thermal

(3)

where α13 = α31. This tensor refers to an orthogonalized coordinate system {e1, e2, e3}. Within the TEV program,14 e3 is chosen parallel to the crystallographic basis vector c, e2 is parallel to b* and e1 = e2 × e3. The determination of the components αij of the thermal expansion tensor in the infinitesimal temperature limit was first described by Paufler and Weber.32 By using the TEV program,14 the tensor components in the temperature range 298−1323 K were calculated for GaTaO4 and GaNbO4 (Table 4, Table 5), and the three-dimensional (3-D) representation surface for the second rank tensor at 323 K (Figure 9), as well as twodimensional (2-D) sections at 323, 532, 773, 1023, and 1273 K were plotted for the gallium tantalum (Figure 10) and gallium niobium oxide (Figure 11). The compounds show very low variations of the thermal expansion values as a function of G

DOI: 10.1021/acs.inorgchem.6b00386 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry Table 4. Coefficients of the Thermal Expansion Tensors [× 10−6 K−1] for GaTaO4 T [K]

α11

α22

α33

α13

298 323 373 423 473 523 573 623 673 723 773 823 873 923 973 1023 1073 1123 1173 1223 1273 1323 1373

6.7276 6.7263 6.7237 6.7210 6.7184 6.7158 6.7131 6.7105 6.7079 6.7052 6.7026 6.7000 6.6974 6.6947 6.6921 6.6895 6.6869 6.6842 6.6816 6.6790 6.6764 6.6738 6.6712

5.5415 5.5407 5.5392 5.5377 5.5361 5.5346 5.5331 5.5315 5.5300 5.5285 5.5269 5.5254 5.5239 5.5224 5.5208 5.5193 5.5178 5.5163 5.5147 5.5132 5.5117 5.5102 5.5087

4.8691 4.8685 4.8673 4.8662 4.8650 4.8638 4.8626 4.8614 4.8602 4.8591 4.8579 4.8567 4.8555 4.8543 4.8532 4.8520 4.8508 4.8496 4.8485 4.8473 4.8461 4.8449 4.8438

1.3930 1.3931 1.3932 1.3933 1.3935 1.3936 1.3937 1.3939 1.3940 1.3941 1.3943 1.3944 1.3945 1.3946 1.3948 1.3949 1.3950 1.3952 1.3953 1.3954 1.3956 1.3957 1.3958

Table 5. Coefficients of the Thermal Expansion Tensors [× 10−6 K−1] for GaNbO4 T [K]

α11

α22

α33

α13

298 323 373 423 473 523 573 623 673 723 773 823 873 923 973 1023 1073 1123 1173 1223 1273 1323 1373

7.1873 7.1860 7.1834 7.1808 7.1782 7.1756 7.1730 7.1704 7.1678 7.1652 7.1626 7.1601 7.1575 7.1549 7.1523 7.1497 7.1472 7.1446 7.1420 7.1395 7.1369 7.1343 7.1318

−1.0729 −1.0730 −1.0730 −1.0731 −1.0731 −1.0732 −1.0732 −1.0733 −1.0734 −1.0734 −1.0735 −1.0735 −1.0736 −1.0737 −1.0737 −1.0738 −1.0738 −1.0739 −1.0739 −1.0740 −1.0741 −1.0741 −1.0742

8.3860 8.3843 8.3808 8.3773 8.3738 8.3703 8.3668 8.3633 8.3598 8.3563 8.3528 8.3493 8.3458 8.3423 8.3388 8.3354 8.3319 8.3284 8.3250 8.3215 8.3180 8.3146 8.3111

0.1519 0.1518 0.1517 0.1515 0.1514 0.1512 0.1511 0.1509 0.1508 0.1507 0.1505 0.1504 0.1502 0.1501 0.1499 0.1498 0.1497 0.1495 0.1494 0.1492 0.1491 0.1489 0.1488

Figure 9. Three-dimensional representation surface of the thermal expansion tensor for GaTaO4 and GaNbO4 at 298 K, respectively. In the case of GaNbO4, red parts of the surface indicate directions with negative values of thermal expansion.

3.3. Raman Spectroscopy and Density-Functional Theory Calculations (DFT). From the selection rules of factor group C2h (2/m) (space group P2/c) a total number of 36 vibrational modes are predicted for wolframite-type GaTaO4 and GaTa0.5Nb0.5O4 with the irreducible representations: Γvib = 8Ag + 8Au + 10Bg + 10Bu. 18 modes (8Ag + 10Bg) are Ramanactive while 15 modes (7Au + 8Bu) are IR-active. In addition, 1Au and 2Bu modes are acoustic. For monoclinic GaNbO4 with space group C2/m (factor group C2h (2/m)), also a total number of 36 modes should exist. The irreducible representations in case of GaNbO4 are as follows: Γvib = 12Ag + 6Au + 6Bg + 12Bu. Again, 3 modes are acoustic (1Au and 2Bu), 18 optical modes are Raman-active (12Ag + 6Bg), and 15 modes (5Au + 10Bu) are IR-active. As a result, only nondegenerated modes are expected in the Raman spectrum. A comparison of the Raman spectrum of monoclinic GaNbO4 (C2/m), the high-pressure modification of GaNbO4 (P2/c) as well as the wolframite-type Ga(Ta,Nb)O4 and GaTaO4 is given in Figure 12. The Raman spectrum of GaNbO4 (C2/m) shows strong Raman bands at 917, 266, 140, 110 cm−1, medium bands at 539, 435, 345, 273, 244, 188, 155 cm−1, and weak bands at 773, 704, 488, 467, 406, 297, 176 cm−1. Calculations of the Raman shifts of monoclinic GaNbO4 (C2/m) were performed with the program CRYSTAL 0616 from first-principles using 3Dperiodic density functional theory with Gaussian basis sets on an all-electron model. Vibrational frequencies were calculated at Γ-point from numerically computed second derivatives of the energy at a stationary point on the potential energy surface.17 The assignment of the experimental modes to the corresponding theoretical ones is unambiguous because all of the 18

expansion decreases parallel to the a-, b-, and c-axis. By relating the thermal expansion data with the crystal structure of GaTaO4, it is also visible that minimum thermal expansion occurs parallel to the endless zigzag chains and of the edgesharing GaO6 and TaO6 octahedra, respectively. In contrast to the crystal structure of GaNbO4, only chemically equivalent octahedra are connected by edges and form zigzag chains along the c-axes. H

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Figure 10. Sections through the 3-D representation surface for GaTaO4 at 323, 523, 773, 1023, and 1273 K correlated with projections of the crystal structure.

Figure 11. Sections through the 3-D representation surface for GaNbO4 at 323, 523, 773, 1023, and 1273 K correlated with projections of the crystal structure.

predicted modes could be observed in the Raman spectrum of GaNbO4 (Figure 13). Wavenumbers of the experimentally determined Raman bands and the calculated modes and their deviations, as well as the symmetry and assignment of the modes are listed in Table 6. The deviations between the observed and calculated Raman modes are reasonably small, with a standard deviation of 6 cm−1 and a maximum deviation of 15 cm−1. The lattice parameters of the fully relaxed structure are in very good agreement with the experimental values, with the calculated values ≤1.0% too large and the monoclinic angle correct within 0.02°. According to the DFT calculations, the Raman modes at 917 and 773 cm−1 can be assigned to symmetric Nb−O and Ga−O stretching vibrations. In the highwavenumber region, only the oxygen atoms are moving, and the metal atoms are almost stagnant. In more detail, the intense Raman band at 917 cm−1 is predominantly caused by vibrations of the corner-sharing oxygen atoms perpendicular to the b-axis, while the band at 773 cm−1 can be related to vibrations of the edge-sharing oxygen atoms. Raman modes at 704 and 539 cm−1 can be assigned to antisymmetric vibrations of the edge-sharing oxygen atoms along the endless zigzag chains of the GaO6/ NbO6 octahedra ([010] direction). O−Nb−O and O−Ga−O bending vibrations lead to Raman bands in the wavenumber region between 300 and 500 cm−1, whereby the edge-sharing oxygen atoms are moving perpendicular to the crystallographic b-axis and the endless GaO6/NbO6 zigzag chains, respectively.

Figure 12. Raman spectra of GaNbO4 (top), HP-GaNbO4 synthesized at 2 GPa, GaTa0.5Nb0.5O4, and GaTaO4 (bottom) in the region between 100 and 1100 cm−1, excited with the 532 nm emission line.

Metal atoms and corner-sharing oxygen atoms have no noticeable share on the vibrational modes in this region. Nb−O−Ga and O−Ga−O bending vibrations are responsible for the Raman band at 435 cm−1. On the other hand, Raman modes in the low-wavenumber region ( 2.15) and high Vickers hardness values (Hv > 8 GPa). As we could prove in this study, GaNbO4, Ga(Ta,Nb)O4, and GaTaO4 are fulfilling these premises with indentation hardness values ranging from H = 9.6 ± 0.5 GPa (GaNbO4) up to H = 11.9 ± 0.6 GPa (GaTaO4) and an average refractive index ranging from n̅ = 2.19 (GaTaO4) up to n̅ = 2.23 (GaNbO4). In addition, GaNbO4 and GaTaO4 show very low variations of the thermal expansion values as a function of increasing temperature and exhibit low tensor component values with a maximum of 6.7276 × 10−6 K−1 (α11) for GaTaO4 and 8.3860 × 10−6 K−1 (α33) for GaNbO4 at 298 K. In the case of GaNbO4, even negative thermal expansion values can be observed along the crystallographic b-axis. By relating the thermal expansion data with the crystal structure, it becomes obvious that maximum thermal expansion occurs perpendicular to the endless linear columns and zigzag chains of the corner- and edge-sharing octahedra, respectively. Another peculiarity of the GaNbO4 crystal structure are the infinite channels along the b-axis, permitting a theoretical incorporation of ion/atoms with a calculated radius up to 1.3 Å. Because of the high hardness and high average refractive index, the special structural features and temperature behavior of the gallium niobium and gallium tantalum oxides, these materials could be of interest for further applications, e.g., optical coatings, synthetic gemstones, low-thermal-expansion materials, or as new supporting materials for Li-ion batteries.

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ACKNOWLEDGMENTS Financial support for this project has been obtained from the Austrian Research Promotion Agency (FFG): 829673, B2. We acknowledge the use of the High-Performance-ComputingCluster dirac at the HZB. Special thanks go to Roman Lackner and Andreas Saxer for providing the nanoindenter as well as Florian Pfuner for the ellipsometric measurements and Jürgen Konzett for the high-pressure synthesis.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.6b00386. Anisotropic displacement parameters (Table S1), selected bond angles (Table S2), structural data of the Rietveld refinement for GaNbO4 (Table S3/S4), results of the wavelength-dispersive X-ray spectroscopy analyses (Table S5) for the chemical compounds, microscope images (Figure S1/S2) of GaNbO4, an electron microprobe elemental map (Figure S3), the refined unit cell parameters of GaNbO4 and GaTaO4 in the temperature range from 298 to 1373 K (Table S6), and the deconvolution of the Raman spectra (Figures S4−S7) of GaNbO4, Ga(Ta,Nb)O4, and GaTaO4 (PDF) Crystallographic information file 1 (CIF) Crystallographic information file 2 (CIF) Crystallographic information file 3 (CIF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: Lukas.Perfl[email protected]. Notes

The authors declare no competing financial interest. M

DOI: 10.1021/acs.inorgchem.6b00386 Inorg. Chem. XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.inorgchem.6b00386 Inorg. Chem. XXXX, XXX, XXX−XXX