Structure refinement and thermal properties of novel cubic borate Lu2Ba3B6O15

Accepted Manuscript Structure refinement and thermal properties of novel cubic borate Lu2Ba3B6O15 Y.P. Biryukov, R.S. Bubnova, M.G. Krzhizhanovskaya, S.K. Filatov PII:

S0254-0584(19)30142-7

DOI:

https://doi.org/10.1016/j.matchemphys.2019.02.047

Reference:

MAC 21390

To appear in:

Materials Chemistry and Physics

Received Date: 19 November 2018 Revised Date:

1 February 2019

Accepted Date: 14 February 2019

Please cite this article as: Y.P. Biryukov, R.S. Bubnova, M.G. Krzhizhanovskaya, S.K. Filatov, Structure refinement and thermal properties of novel cubic borate Lu2Ba3B6O15, Materials Chemistry and Physics (2019), doi: https://doi.org/10.1016/j.matchemphys.2019.02.047. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT Structure refinement and thermal properties of novel cubic borate

Lu2Ba3B6O15 Y.P. Biryukov a, R.S. Bubnova a,b, M.G. Krzhizhanovskaya b, S.K. Filatov b, * a

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Institute of Silicate Chemistry of the Russian Academy of Sciences (ISC RAS), Makarova Emb. 2, Saint Petersburg, 199034, Russia b Institute of Earth Sciences, Department of Crystallography, Saint Petersburg State University, Universitetskaya Emb. 7/9, Saint Petersburg, 199034, Russia * Corresponding author: Institute of Earth Sciences, Department of Crystallography, Saint Petersburg State University, Universitetskaya Emb. 7/9, Saint Petersburg, 199034, Russia E-mail address: [email protected] (Stanislav K. Filatov)

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HIGHLIGHTS

Lu2Ba3B6O15 is prepared using a multi-step solid-state synthesis.

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The Lu2Ba3B6O15 crystal structure is refined by the Rietveld method.

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The Lu2Ba3B6O15 thermal behavior is investigated over a wide range of temperatures.

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The BaO9 thermal deformations contribute the most to the Lu2Ba3B6O15 expansion.

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ABSTRACT

Novel borate Lu2Ba3B6O15 was prepared using a multi-step high-temperature solid-state synthesis. It crystallizes in cubic system, Ia3̅ space group, a = 14.18197(3) Å, V = 2852.396(18) Å3, Z = 8, and it is isostructural with Y2Ba3B6O15. The crystal structure is described as a

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framework composed of the edge-sharing large irregular BaO9 polyhedra. The intersecting tunnels in this framework are filled with the lutetium atoms. Two planar BO3 triangles are connected to each other by the vertices, forming the isolated B2O5 pyroborate groups. The

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Lu2Ba3B6O15 thermal behavior was investigated by thermal analysis and high-temperature X-ray powder diffraction (HTXRD). The Lu2Ba3B6O15 sample starts to melt at 1058 °C. As the

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temperature increases, the coefficient of linear expansion increases (αa = 5.7 at 25 °C and 8.9 × 10–6 C–1 at 800 °C). The Rietveld refinement of the HTXRD data showed that thermal deformations of the non-rigid BaO9 polyhedra have the greatest influence on the Lu2Ba3B6O15

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expansion among those of the other constituent polyhedra.

Keywords: Isotropic thermal expansion; Rietveld refinement; High-temperature X-ray powder

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diffraction (HTXRD); Thermal analysis; Cubic borate

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1. Introduction

Alkaline-earth and rare-earth borates have attracted the attention of researchers due to their non-linear optical [1–4] and luminescent [5–9] properties make them prospective materials for many applications such as lasers hosts, phosphors for light-emitting diodes (LED) and

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plasma display panels (PDP), scintillators for radiation detectors. Novel cubic borate Y2Ba3B6O15 was first obtained in 2011 [10]. It crystallizes in a cubic system, which is very uncommon for borates (about 5% of borates crystallize in a cubic system according to the ICSD-

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2016 database). Later, Duke et al. [11] prepared cerium-substituted Y2Ba3B6O15:Ce3+ and found that this borate exhibits good luminescent properties, that makes it a suitable narrow-emitting

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blue phosphor for wide-gamut white lighting. These factors lead one to conduct the search of novel isostructural borates in the BaO–REE2O3–B2O3 phase system. The authors of the present paper have previously investigated crystal structures, thermal and luminescent properties of many alkaline-earth and rare-earth borates [4,12–14], in particular, thermal properties of a prospective scintillator LuBa3B9O18 [14]. The ionic radius rion of Lu3+ in octahedral coordination

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(coordination number, C.N. 6) is 0.86 Å, which is approximately equal to the ionic radius of Y3+ for six-fold coordination (0.90 Å) [15]. Thus, it is possible to obtain a novel Lu-containing

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borate isostructural with Y2Ba3B6O15. In the BaO–Lu2O3–B2O3 phase system, there are three barium-lutetium borates known to date: LuBa3B3O9 [16], LuBa3B9O18 [8] and Lu5Ba2B5O17 [9].

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Recently, (Lu2-xCex)Ba3B6O15 (x = 0.005, 0.01, 0.03, 0.05, 0.07) solid solutions have been prepared [17]. However, results of crystal structure refinement and thermal properties determination of the non-doped Lu2Ba3B6O15 are not reported. These borates exhibit luminescence and scintillation, which makes them prospective phosphors [9,11, 17] and scintillators [5–8], respectively. It is rather advantageous for scintillator materials to crystallize in a cubic system [18]. For example, it is well-known that cubic compounds expand isotropically, which allows to grow fine, practically non-defective single- and poly-crystals suitable for such applications. 3

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This paper reports on the synthesis of novel cubic borate Lu2Ba3B6O15, its crystal structure refinement by the Rietveld method, determination of thermal properties of Lu2Ba3B6O15 using thermal analysis (thermogravimetry (TG) and differential scanning calorimetry (DSC)) and high-temperature X-ray powder diffraction (HTXRD). The discussion of

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the nature of thermal deformations of Lu2Ba3B6O15 is given.

2. Experimental details

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2.1. Raw materials

The title compound was prepared by combining polycrystalline BaCO3 (Reahim, 99.99%

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purity), Lu2O3 (Kyrgyz CMC, 99.93% purity) and H3BO3 (Neva Reaktiv, 99.90% purity) in the appropriate stoichiometric ratios. The chemical reaction is 3BaCO3 + Lu2O3 + 6H3BO3 → Lu2Ba3B6O15 + 3CO2 + 9H2O. BaCO3 and Lu2O3 were initially calcined in a LOIP LF 7/13-G1 muffle furnace at 600 °C for 3 hours and at 900 °C for 1 hour, respectively. Excess of H3BO3 (10 wt%) was included to samples. The total weight of the mixture of raw materials was 2.621 g

2.2. Synthesis

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Lu2Ba3B6O15.

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(1.109 g of BaCO3, 0.746 g of Lu2O3 and 0.765 g of H3BO3) in order to produce 2 g of

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The synthesis was performed according to steps described in [11]. The mixture of raw materials was ground with an agate mortar and pestle for 1 hour. Then the powder was pressed into pellets (1 mm) using a hydraulic press (LabTools) at a pressure of 80 bar. After that, the pellets were placed in a platinum crucible and heated in a Nabertherm HTC high-temperature furnace at 500 °C for 25 hours to decompose the metal carbonate and boric acid. The pellets were reground, pressed into pellets and heated to 880 °C for 25 hours. According to the Rietveld refinement of the X-ray powder diffraction pattern, the sample contained in its phase composition Lu2Ba3B6O15 (89.4 wt%), LuBa3B3O9 (9 wt%) and LuBO3 (1.6 wt%) impurities. 4

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The pellets were then reground, pressed into pellets and heated to 900 °C for 25 hours. According to results obtained from the X-ray powder diffraction analysis, the amount of the impurities was decreased. The pellets were reground and heated as pellets for a third time at 910 °C for 25 hours. X-ray phase analysis revealed that the sample contained in its composition

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Lu2Ba3B6O15 and LuBa3B3O9 impurity in an insignificant amount (about 2 wt% according to the Rietveld refinement).

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2.3. Methods

Powder diffraction data were collected using a Rigaku MiniFlex II diffractometer (CuKα,

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2ϴ = 5–75º, step 0.02º). The sample for the experiment was prepared using hexane. The phase composition was determined using PDXL integrated X-ray powder diffraction software and PDF-2 2016 (ICDD) database.

Powder diffraction data for the Rietveld refinement were collected at 25 °C using a Rigaku Ultima IV diffractometer (CuKα1+2, 40 kV and 35 mA, Bragg-Brentano geometry, PSD

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D/teX Ultra high-speed detector, 2ϴ = 5–125°, step 0.02º, total counting time of about 5 seconds per step). The sample for the experiment was prepared using hexane and placed onto a low-

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background silicon sample holder. The Rietveld full-profile refinement of the X-ray diffraction pattern was performed using a Topas 5 (Bruker AXS 2014). The background was fitted using the

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12-coefficient Chebyshev polynomial. Peak shapes were modeled using a Pearson VII function. The preferred orientation of crystallites was not observed. Structure factors for neutral atoms were used.

Thermal analysis (TG + DSC) was carried out using a STA 429 СD NETZSCH

simultaneous thermal analysis instrument equipped with a platinum-rhodium sample holder (dynamic air atmosphere, air flow 50 cm3/min, temperature range 40–1200 °С, heating rate 20 °С/min). Before the experiment, the calibration of a thermobalance was performed using СаС2О4×2Н2О external standard. The accuracy of determination of the weight was ±0.01 mg. 5

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The temperature (°C) and sensitivity (µV/mW) calibration of the Type S thermocouple was performed using In, Sn, Bi, Zn, Al, Au and Pb external standards. The errors in determinations of the temperature and sensitivity did not exceed ±2 °C and ±2 relative percent, respectively. The pellet for the experiment was weighed with an accuracy of 0.01 mg (the mass was approximately

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20 mg) and placed in an open platinum-rhodium crucible. The temperatures of thermal effects were determined using a NETZSCH Proteus software by the DSC first derivative curve. The HTXRD experiment was conducted using a Rigaku Ultima IV diffractometer with a

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thermal attachment (CoKα, 40 kV and 35 mA, reflection geometry, D/teX Ultra high-speed detector, air atmosphere, 2ϴ = 5–120°, temperature range 20–1000 °C, step 20 °C, heating rate

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0.6 °С/min). A thermocouple was used to control the temperature. Before the HTXRD experiment, Si external standard was measured in the temperature range 20–1000 °C in order to control the thermal expansion coefficients. The temperatures of phase transitions were checked using SiO2 and K2SO4. The error in determination of the temperature did not exceed ±10 °C. Experimental data processing by the Rietveld refinement, approximation of temperature

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dependencies of lattice parameters and drawing α figures were performed using RietToTensor [19].

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Using the coefficients of approximation of temperature dependences of unit cell parameters, the components of the tensor are determined in the Cartesian crystallophysical

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coordinate system as the solution of the system of six equations of the following form:

αd = α11xd2 + α22 yd2 + α33zd2 + 2α12 xd yd + 2α23 yd zd + 2α13xd zd

(1)

where αij are the tensor components, xd, yd, and zd are the directional cosines of the normal

vectors with respect to the xyz crystallophysical axes. Thermal expansion along the normal to the (hkl) plane with the dhkl interplanar distance is calculated as follows: 2 d hkl αd = − 2

 ∂f da ∂f db ∂f dc ∂f dα ∂f dβ ∂f dγ  ⋅  ⋅ + ⋅ + ⋅ + ⋅ + ⋅ + ⋅   ∂a dT ∂b dT ∂c dT ∂α dT ∂β dT ∂γ dT 

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(2)

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where d is a function of hkl indices and of unit cell parameters. Standard orientation of 2

hkl

the crystallographic axes with respect to the crystallophysical axes is used. In the case of cubic crystal system thermal expansion coefficients are equal in all directions, thus they are equal to the eigenvalues of the tensor of thermal expansion α11 = α22 = α33 = αa = αb = αc.

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Based on the calculated eigenvalues of the tensor, the surface of the second-rank symmetric tensor or, in other words, the figure of thermal expansion coefficients can be plotted as a 3D model and its 2D sections images. Each radius vector of this figure represents the value

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of the thermal expansion coefficient in a certain direction.

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The crystal structure was visualized using VESTA [20].

3. Results

3.1 Rietveld refinement and description of the Lu2Ba3B6O15 crystal structure The crystal structure of Lu2Ba3B6O15 was refined by the Rietveld method applying the

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model of Y2Ba3B6O15 isostructural borate (cubic symmetry, Ia3̅ space group, a = 14.253(6) Å, V

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= 2895.47(2) Å3, Z = 8) [10] (Fig. 1).

Fig. 1. The Rietveld refinement of the Lu2Ba3B6O15 crystal structure using powder X-ray diffraction data. The measured data is represented by blue cross signs, the refinement fit by a red line and the difference between the data and refinement fit by a gray line.

The details of the refinement and refined crystal structure data are provided in Tables 1– 3. For all the atoms x, y and z values were refined (except for the Lu1, Lu2, Ba1 and O2 atoms 7

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which are on special positions) (Table 2). Isotropic displacement parameter Biso was used for all the atoms, the oxygen atoms were constrained. The refined bond lengths and angles are given in Table 3.

Table 1

Table 2

Lu2Ba3B6O15 25 Cubic, Ia3̅, 8

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14.18197(3) 2852.396(18) 4.97 CuKα1+2 5–125 388 0.0386 0.0405 0.0297 0.0066 1.05 2 (LuBa3B3O9)

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Formula Temperature (°C) Crystal system, Space group, Z Lattice parameter a (Å) Volume (Å3) DX (g/cm3) Radiation type 2ϴ range (deg.) Number of reflections Rp Rwp Rexp RB GOF Impurities, wt%

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Structure refinement details and crystallographic data of Lu2Ba3B6O15

The refined atomic positional and isotropic displacement parameters (Å2) of Lu2Ba3B6O15

x/a

0.0000 0.2500 0.3687(1) 0.1117(1) 0.0308(4) 0.1606(5) 0.1568(5)

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Lu1 Lu2 Ba1 B1 O1 O2 O3

Wyck. Pos. 8a 8b 24d 48e 48e 24d 48e

y/b

z/c

Biso (Å2)

Occ.

0.0000 0.2500 0.0000 0.0667(1) 0.0394(5) 0.0000 0.1482(5)

0.5000 0.2500 0.2500 0.3069(1) 0.3515(5) 0.2500 0.3230(5)

0.51(6) 0.56(6) 0.74(3) 0.37(11) 0.37(11) 0.37(11) 0.37(11)

1 1 1 1 1 1 1

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Atom

Table 3

The refined selected bond lengths (Å) of Lu2Ba3B6O15 and Y2Ba3B6O15 [10], bond valence sums (v.u.) of Lu2Ba3B6O15

Bond

Ba–O3 (×2) Ba–O1 (×2) Ba–O3 (×2)

Lu2Ba3B6O15 [this work] Bond Bond valence length (Å) sum (v.u.) 2.730(7) 0.300 2.769(6) 0.270 2.847(6) 0.218

Y2Ba3B6O15 [10] Bond length (Å) 2.732(3) 2.753(3) 2.862(3) 8

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Ba–O2 2.951(7) 0.165 2.971(4) Ba–O1 (×2) 3.028(6) 0.134 3.018(3) 9 2.85 ∑9 2.013 2.856 REE1–O1 (×6) 2.222(7) ∑6 2.853 2.271(3) REE2–O3 (×6) 2.214(6) ∑6 2.915 2.250(3) B–O3 1.341(18) 1.084 1.356(4) B–O1 1.366(18) 1.013 1.360(4) B–O2 1.424(18) 0.866 1.406(4) 3 1.38 ∑3 2.964 1.37 Two planar BO3 triangles are connected to each other by the vertices (i.e. by the bridging O2 atoms), forming the isolated B2O5 pyroborate groups (Fig. 2a). The B1–O2–B1 angle is equal to 121.7(5)° and the planes are slanted by 80°. The O2–B–O3 angle is 115.9(12)°, O1–B–O2 is

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119.0(12)° and O1–B–O3 is 124.4(13)°. The average bond length equals 1.38 Å. The distance between the B and bridging O2 atom is 1.42 Å. The BO3 triangles are connected to the

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LuO6 octahedra by the vertices and to the BaO9 polyhedra by the vertices and edges. The Lu atoms are surrounded by six oxygen atoms forming the regular Lu1O6 and Lu2O6 octahedra with the Lu1–O and Lu2–O bond lengths equal to 2.22 Å and 2.21 Å, respectively (Fig. 2b). The Ba1–O bond lengths in the BaO9 polyhedra are 2.73–3.02 Å; the next bond is 3.81 Å. The BaO9

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polyhedra are linked to each other through the common O1–O3 edges forming a framework. The

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intersecting tunnels in the framework are filled with the lutetium atoms (Fig. 2c).

Fig. 2. The Lu2Ba3B6O15 crystal structure projection onto the ab and abc planes: B2O5 pyroborate groups (a), LuO6 octahedra (b) and BaO9 polyhedra framework (c).

Lu2Ba3B6O15 is isostructural with Y2Ba3B6O15 [10]. The substitution of the smaller Lu3+ rare-earth cation (rion (C.N. 6) = 0.86 Å) with the larger Y3+ (rion (C.N. 6) = 0.90 Å) leads to the 9

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increase of the unit cell parameters and volume. The unit cell parameter and volume of Lu2Ba3B6O15 are smaller (a = 14.181 Å, V = 2852.39 Å3) (Table 1) than those of Y2Ba3B6O15 (a = 14.253 Å, V = 2895.46 Å3) [10]. The comparison of bond lengths of these borates is given in Table 3.

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The Lu1–O (2.22 Å) and Lu2–O (2.21 Å) bond lengths are shorter than the Y–O ones (Y1–O = 2.27 Å, Y2–O = 2.25 Å). The average bond length is 2.855 Å and the volume of the BaO9 polyhedra is 44.246 Å3 in the Lu2Ba3B6O15 structure. These values are slightly different from those of Y2Ba3B6O15 (2.856 Å and 44.470 Å3). It is expectable that in the case of

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the substitution of the Lu3+ with the Y3+, the volume of the BaO9 polyhedra does not change

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significantly but deformations can occur in these polyhedra. Both Ba–O1 bond lengths in the Lu2Ba3B6O15 crystal structure (2.769 and 3.028 Å) are longer than the Ba–O1 bond lengths in the Y2Ba3B6O15 structure (2.753 Å and 3.018 Å). The values of the short Ba–O3 bond length are comparable to each other (2.730 and 2.732 Å). The other one Ba–O3 bond length and Ba–O2 bond length in the Lu2Ba3B6O15 structure are shorter (2.847 and 2.951 Å) than those in the

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Y2Ba3B6O15 structure (2.862 and 2.971 Å).

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3.2. Thermal analysis (TG, DSC)

As can be seen in Fig. 3 (TG curve), the compound does not undergo a significant mass

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loss in the whole temperature range. The DSC curve (Fig. 3, below) shows three endothermic effects. The first thermal effect is within the range of 800–1000 °С and it is due to the beginning of some solid-state reaction, which is also confirmed by the HTXRD data (see paragraph 3.3). The second effect of low intensity with the starting temperature of 1038 °С and with a maximum at 1052 °С is due to the melting of the eutectic composition Lu2Ba3B6O15 + LuBa3B3O9 + the product of the solid-state reaction. This effect is caused by the presence of the impurity phase. The highest peak is within the range of 1058–1098 °С with a maximum at 1085 °С and it corresponds to the melting of the sample. 10

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Fig. 3. TG and DSC curves of Lu2Ba3B6O15.

3.3. High-temperature X-ray powder diffraction

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From approximately 800 °C the X-ray diffraction patterns begin to change (Fig. 4) – a few peaks of an unidentified phase appear when Lu2Ba3B6O15 is heated to 1000 °C and they

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remain after the subsequent cooling to room temperature.

Fig. 4. The Lu2Ba3B6O15 X-ray diffraction patterns given at different temperatures (peaks of an unidentified phase

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are marked by arrows).

Fig. 5 shows the temperature dependence of the cubic unit cell parameter a.

Fig. 5. Temperature dependence of the cubic unit cell parameter a of Lu2Ba3B6O15.

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at = 14.185 + 0.077 × 10–3 × t + 0.031 × 10–6 × t2. The calculated thermal expansion coefficients at some temperatures are given in Table 4.

Table 4

25

200

αa = αb = αc

5.7(4)

6.4(2)

αV

17.1(1)

19.1(1)

4. Discussion

Temperature (°C) 400 600

800

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α (10–6 °C–1)

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Thermal expansion coefficients of Lu2Ba3B6O15 at some temperatures

7.2(1)

8.1(2)

8.9(4)

21.7(1)

24.2(1)

26.8(1)

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This cubic borate expands isotropically as it is expected. A number of factors such as thermal vibrations of atoms, bond lengths and angles changes affect the thermal expansion. It is possible to evaluate quantitatively the thermal deformations of the Lu2Ba3B6O15 constituent

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coordination polyhedra and to find out which of them contribute the most to the Lu2Ba3B6O15

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thermal expansion. Visualization of the Lu2Ba3B6O15 crystal structure and of the figures of thermal expansion coefficients (at 25 and 800 °C) is shown in Fig. 6.

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Fig. 6. The Lu2Ba3B6O15 crystal structure and the figures of thermal expansion coefficients (the solid line – 25 °C,

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the dashed line – 800 °C).

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The analysis of the data from the previous investigations of temperature-dependent structural changes in borates by low- and high-temperature single-crystal X-ray diffraction [12,21–23] shows that the В–О bond lengths in the BO3 triangles virtually do not change with an increase in temperature. Thus, it is unlikely that the B–O bond lengths change contributes significantly to thermal expansion of Lu2Ba3B6O15.

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Let us consider cation polyhedra contribution to the Lu2Ba3B6O15 expansion. The Ba2+ atom has the oxidation state of 2+ and it is larger (rion (C.N.9) = 1.46 Å) than the Lu3+ atom (rion

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(C.N.6) = 0.86 Å) [15], therefore the Ba–O bonds are weaker than the Lu–O bonds. Thus, the Ba–O bond lengths must change more intensively with an increase in temperature, and thermal

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deformations of these irregular, large and non-rigid BaO9 polyhedra must have the greatest influence on the Lu2Ba3B6O15 expansion among those of the other constituent polyhedra. Moreover, the similar contribution of non-rigid cation polyhedra to thermal expansion of some oxides and silicates [24–27], borates [12], vanadates [28] is known. Let us try to verify this assumption. The number of refinable structural parameters is small in a cubic compound, which makes it possible to evaluate the Ba–O and Lu–O bond lengths changes with an increase in temperature by the Rietveld refinement of the HTXRD data. Analysis of the bond lengths (Table 13

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5 and Fig. 7) shows that the directions of the maximum elongation of the bonds are virtually equally distributed in the three-dimensional space, which is expectable for a cubic compound and its isotropic lattice expansion. The differences values (∆) between the Lu–O bond lengths given at 800 °C (d800) and 25 °C (d25) are 0.011 Å for the Lu1–O and 0.010 Å for the Lu2–O

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bonds (Table 5). The Ba–O1* and Ba–O3* bond lengths in the BaO9 polyhedra change more intensively among the other Ba–O bond lengths. The difference value between the average Ba–O bond lengths given at 800 °C and 25 °C is equal to 0.02 Å, which is about two times greater than

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those of the Lu–O bond lengths.

Table 5

coefficients αd of the Lu–O and Ba–O bonds

Bond

Bond length (Å) 400 °C 600 °C 2.247(9) 2.250(9) 2.267(9) 2.271(9) 2.726(9) 2.730(9) 2.747(9) 2.751(9) 2.859(9) 2.863(9) 2.964(9) 2.968(9) 3.012(9) 3.016(9) 2.85 2.85

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200 °C 2.245(9) 2.264(9) 2.722(9) 2.743(9) 2.854(9) 2.960(9) 3.008(9) 2.84

800 °C 2.255(9) 2.275(9) 2.736(9) 2.758(9) 2.872(9) 2.972(9) 3.022(9) 2.86

∆(d800– d25) (Å) 0.010 0.011 0.017 0.018 0.018 0.015 0.016 0.02

αd (10–6 °C–1) 5.7 6.2 8 8.7 8.1 6.5 6.8 7.7

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Lu2–O3 (×6) Lu1–O1 (×6) Ba–O3 (×2) Ba–O1* (×2) Ba–O3* (×2) Ba–O2 Ba–O1 (×2) 9

25 °C 2.245(8) 2.264(8) 2.719(8) 2.740(8) 2.854(8) 2.957(8) 3.006(8) 2.84

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Selected bond lengths (Å) of Lu2Ba3B6O15 at different temperatures and the average bond length thermal expansion

Fig. 7. Distribution of the Ba–O bonds in the Lu2Ba3B6O15 crystal structure (Ba–O1* and Ba–O3* bonds are represented by dashed lines).

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The average bond length thermal expansion coefficients αd (Table 6) were calculated using the equation of the following form:

αd =

1 d t2 − d t1 d t 2 − t1

(3)

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where d is the average bond length over the given temperature interval, dt2 − dt1 is the difference between the values of the bond lengths given at 800 °C and 25 °C, t 2 − t1 is the difference between the values of the highest (800 °C) and room (25 °C) temperatures.

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It can be seen that the calculated thermal expansion coefficients αd of the Ba–O and Lu– O bond lengths (Table 5) are comparable with the average linear thermal expansion coefficient of

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Lu2Ba3B6O15 (αa = 7 × 10–6 °C–1), although αd of the average Ba–O bond length is slightly greater than those of the Lu–O bond lengths.

It is also possible to calculate the average polyhedral thermal expansion coefficients αV for the BaO9, Lu1O6 and Lu2O6 (Table 6):

1 Vt2 − Vt1 V t 2 − t1

(4)

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αV =

where V is the average polyhedra volume over the given temperature interval, Vt2 −Vt1 is

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the difference between the values of the polyhedra volumes given at 800 °C and 25 °C, t 2 − t1 is

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the difference between the values of the highest (800 °C) and room (25 °C) temperatures.

Table 6

The average polyhedral thermal expansion coefficients αV of the Lu1O6, Lu2O6 and BaO9 polyhedra

Polyhedron Lu2O6 Lu1O6 BaO9

25 °C 14.151 15.122 43.952

Polyhedral volume (Å3) 200 °C 400 °C 600 °C 800 °C 14.125 14.177 14.233 14.356 15.122 15.182 15.252 15.351 44.041 44.224 44.422 44.721

∆(d800– d25) (Å3) 0.205 0.229 0.769

αV (10–6 °C–1) 18 19 22

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, it can be seen from Tables 5 and 6 that the maximum linear and volume thermal expansion is in the BaO9 polyhedra. Therefore, one can assume that the highest contribution to the Lu2Ba3B6O15

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thermal expansion is made by the thermal deformations of these irregular, large and non-rigid BaO9 polyhedra.

Conclusion

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Novel cubic borate Lu2Ba3B6O15 has been prepared using a multi-step solid-state synthesis. The crystal structure is composed of the BaO9 polyhedra, LuO6 octahedra and isolated B2O5 pyroborate groups. The Lu2Ba3B6O15 sample starts to melt at 1058 °C. It has been shown

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that thermal deformations of the irregular, large and non-rigid BaO9 polyhedra have the greatest influence on the isotropic thermal expansion of Lu2Ba3B6O15 among those of the other

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constituent polyhedra.

Acknowledgments

This work was supported by the Russian Foundation for Basic Research [grant number 18-03-00679]. The X-ray diffraction experiments were performed at The Centre for X-ray

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Diffraction Studies (Saint Petersburg State University). The authors are grateful to V.L. Ugolkov, Ph.D. (Institute of Silicate Chemistry, Russian Academy of Sciences) for conducting

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the thermal analysis experiment and L.B. Alekseeva, Ph.D. (The Institute of Foreign Languages, Department of Modern European Languages, Herzen State Pedagogical University of Russia) for

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English language consultations.

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HIGHLIGHTS

Lu2Ba3B6O15 is prepared using a multi-step solid-state synthesis.

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The Lu2Ba3B6O15 crystal structure is refined by the Rietveld method.

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The Lu2Ba3B6O15 thermal behavior is investigated over a wide range of temperatures.

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The BaO9 thermal deformations contribute the most to the Lu2Ba3B6O15 expansion.

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