ISSN 10637745, Crystallography Reports, 2010, Vol. 55, No. 5, pp. 748–752. © Pleiades Publishing, Inc., 2010. Original Russian Text © A.P. Dudka, Yu.V. Pisarevsky, V.I. Simonov, B.V. Mill’, 2010, published in Kristallografiya, 2010, Vol. 55, No. 5, pp. 798–802.

STRUCTURE OF INORGANIC COMPOUNDS

Accurate Crystal Structure Refinement of La3Ta0.25Ga5.25Si0.5O14 A. P. Dudkaa, Yu. V. Pisarevskya, V. I. Simonova, and B. V. Mill’b a

Shubnikov Institute of Crystallography, Russian Academy of Sciences, Leninskií pr. 59, Moscow, 119333 Russia email: [email protected] b

Moscow State University, Moscow, 119992 Russia Received March 3, 2010

Abstract—An accurate Xray diffraction study of an La3Ta0.25Ga5.25Si0.5O14 single crystal has been per formed using two data sets obtained independently for the same sample in different orientations on a diffrac tometer with a 2D CCD detector. This structure was refined with an averaged set of these data (a = 8.1936(15) Å, c = 5.1114(6) Å, sp. gr. P321, Z = 1, R/wR = 0.75/0.71%, 4030 independent reflections). This analysis was aimed at determining the character of the occupancies of the cation position in the structure. The octahedra at the origin of coordinates turned out to be statistically occupied by gallium and tantalum ions of similar sizes, whereas the tetrahedra on the threefold symmetry axes are occupied by gallium and silicon whose ionic radii differ significantly. The latter circumstance caused the splitting of oxygen positions and made it possible to reliably establish the structural position of statistically located [SiO4] and [GaO4] tetrahedra of different sizes. DOI: 10.1134/S1063774510050056

INTRODUCTION La3Ta0.25Ga5.25Si0.5O14 (LTGS) crystals belong to the extensive class of piezoelectric materials of the lan gasite (La3Ga5SiO14 (LGS)) family (structure type Ca3Ga2Ge4O14, sp. gr. Р321, Z = 1 [1]) [2]. LTGS is a 1 : 1 solid solution in the La3Ga5SiO14– La3Ta0.5Ga5.5O14 system, and its properties are inter mediate with respect to the end members of this series. The LTGS acoustic and piezoelectric properties were described in [3], and the Ca3Ga2Ge4O14 structure type was reported in [4, 5]. Systematic accurate structural studies of langasite crystals using highresolution data began in [6]. Their purpose was to determine the structural conditionality of the physical properties of these crystals and estab lish the possibility of controlling them using isomor phic substitutions. In this paper we report the results of an accurate study of the La3Ta0.25Ga5.25Si0.5O14 atomic structure. One important issue was to establish the cat ion distribution over crystallographic positions and determine the fine structural features induced by the corresponding isomorphic substitutions. Our analysis

was performed using special methods for processing CCD diffractometer data [7, 8]. EXPERIMENTAL A transparent 255g LTGS 001 single crystal 27 mm in “diameter” was grown by the Czochralski method in a 43 × 43 mm Pt crucible containing 260 g of stoichiometric melt in an N2–О2 gas mixture with 10% O2 at the beginning of pulling and 3% O2 when the pulling was over. The pulling rate and speed of rotation were 2 mm/h and 40 rpm, respectively [2]. The crystal lateral surface is formed by welldeveloped (110) faces, and the crystallization front is character ized by a welldeveloped (001) face. The sample for diffraction study was optically transparent and shaped into an ellipsoid 0.235–0.250 mm in size by spinning. To increase the reliability and accuracy of the data obtained on an Xcalibur S diffractometer (Oxford Dif fraction) with a 2D CCD detector [9], we indepen dently collected two sets of diffraction data in the full sphere of reciprocal space, which differed in the initial sample orientation. The structural model was refined

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Table 1. Characteristics of two diffraction experiments with an La3Ta0.25Ga5.25Si0.5O14 crystal Experiment

I

II

Chemical formula

La3Ta0.25Ga5.25Si0.5O14

System, sp. gr., Z

Trigonal, P321, 1

a, Å

8.192(1)

8.195(1)

c, Å

5.111(1)

5.112(1)

V, Å3

297.039(6)

297.327(3)

Radiation; λ, Å

MoKα; 0.7107

μ, mm–1

24.50

Т, K

295

Sample size, mm

0.235(5)–0.250(5)

Diffractometer

Xcalibur S ω

Scan mode θmax, deg Ranges of indices h, k, l

71.9

74.1

–20 ≤ h ≤ 21, –21≤ k ≤ 22, –13 ≤ l ≤ 13 –21 ≤ h ≤ 22, –22 ≤ k ≤ 22, –13 ≤ l ≤ 13

Number of reflections: measured/in dependent/Rint with I > 2.0σ(I)

46255/3800/0.020

47413/4026/0.022

0.025

0.017

〈σ(F2)/F2〉 Programs

CrysAlis, ASTRA, JANA

using a cross set (a result of averaging these two sets). 1

The data collection details are listed in Table 1.

In both experiments the available reciprocal space was almost completely covered (at the resolution used). The data were processed like in [8]; i.e., with the application of the ASTRA software package [10, 11]. The data were corrected for thermal diffuse scat tering (TDS) according to [12] using the elastic mod uli c11 = 18.78 × 1010 N m–2, c12 = 10.69 × 1010 N m–2, c13 = 8.573 × 1010 N m–2, c14= 1.165 × 1010 N m–2, c33 = 25.93 × 1010 N m–2, and c44 = 5.202 × 1010 N m–2; the absorption was taken into account according to [13, 14]; the correction for inhomogeneous CCD detector sensitivity [15] was introduced; the extinction effect [16, 17] was refined; and the contribution to the inten sity from the halfwavelength radiation was taken into account [18]. The LTGS structural model was refined using F2 for the data cross set. The atomic scattering curves were taken from [19]. Separately considering 1

The structural data were deposited in the ICSD database (CSD no. 421693). CRYSTALLOGRAPHY REPORTS

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Table 2. Characteristics of the La3Ta0.25Ga5.25Si0.5O14 structure refinement from the crossset reflections a, Å

8.1936(15)

c, Å

5.1114(6)

Number of independent reflec tions in the cross set

4030

sinθ/λ|max, Å–1

1.35

R1ave(|F|), %, R factor for averag ing independent set

0.674

Number of refined coordinate parameters

14

Number of refined parameters of atomic displacements

68

R1(|F|), %, R factor

0.748

wR2(|F|), %, weighting R factor

0.705

Δρmax,

on zero map

0.39

Δρmin, electron/Å3, on zero map

–0.48

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Table 3. Atomic coordinates, position occupancies Q, and equivalent thermal parameters Ueq for La3Ta0.25Ga5.25Si0.5O14 crystal Atom

Q

x/a

y/b

Ueq , Å2

z/c

Symmetry

Multiplicity

La

2

3

1.0

0.422350(9)

0

0

0.012160(6)

Ta

32.

1

0.24(1)

0

0

0

0.01185(3)

Ga1

32.

1

0.76(1)

0

0

0

0.01185(3)

Ga2

2

3

1.0

0.76403(2)

0

1/2

0.01286(4)

Si

3

2

0.24(1)

1/3

2/3

0.53140(2)

0.0092(4)

Ga3

3

2

0.76(1)

1/3

2/3

0.53140(2)

0.01084(5)

O1

3

2

0.25(1)

1/3

2/3

0.2170(6)

0.0134(4)

O1'

3

2

0.75(1)

1/3

2/3

0.1776(2)

0.0135(1)

O2

1

6

0.27(3)

0.4755(6)

0.3230(8)

0.3390(5)

0.0225(8)

O2'

1

6

0.73(3)

0.4561(2)

0.3068(2)

0.3019(2)

0.0159(2)

O3

1

6

1.0

0.2200(1)

0.0785(2)

0.7622(2)

0.0218(1)

Note: O1 and O2 atoms without and with primes belong to Si and Ga tetrahedra, respectively.

Table 4. Parameters of anisotropic atomic displacements Uij (in Å2) for La3Ta0.25Ga5.25Si0.5O14 crystal Atom

U11

U22

U33

U12

U13

U23

La

0.013873(8)

0.011430(9)

0.010364(6)

0.005715(4)

0.000223(3)

0.000445(6)

Ta

0.01408(6)

0.01408(6)

0.00739(6)

0.00704(3)

0.0

0.0

Ga1

0.01408(6)

0.01408(6)

0.00739(6)

0.00704(3)

0.0

0.0

Ga2

0.01199(4)

0.01360(8)

0.01353(4)

0.00680(4)

Si

0.0105(9)

0.0105(9)

0.0066(4)

0.0052(5)

0.0

0.0

Ga3

0.0116(1)

0.0116(1)

0.00926(5)

0.00581(5)

0.0

0.0

O1

0.0155(5)

0.0155(5)

0.0091(9)

0.0078(3)

0.0

0.0

O1'

0.0156(2)

0.0156(2)

0.0093(3)

0.0078(3)

0.0

0.0

O2

0.0146(9)

0.034(1)

0.0132(7)

0.0077(9)

0.0019(5)

0.0052(7)

O2'

0.0122(2)

0.0208(2)

0.0135(2)

0.0075(2)

0.0013(2)

0.0043(2)

O3

0.0207(1)

0.0311(2)

0.0191(1)

0.0170(2)

0.0077(1)

0.0147(1)

Friedel pairs in a set of reflections made it possible to establish the enantiomorphic modification of the crys tal studied, which was found to be righthanded according to the terminology of [20]. The Flack parameter [21] is close to zero; i.e., the crystal is sin gledomain. The significance of anharmonic parame ters was verified by constructing the probability density function for atomic displacements from the equilib rium position and plotting Fourier difference maps using the JANA program [22].

–0.00254(3)

–0.00508(6)

RESULTS AND DISCUSSION We had to reveal the following details of the struc tural model of the crystal: the occupancies of mixed positions and the possible splitting of the structural position of some atoms. It is known that, since the Xray collection time is fairly long, the static disorder ing of an atom over similar positions and the anhar monic character of its thermal motion correlate and are difficult to distinguish based on diffraction data. Obviously, lowtemperature measurements signifi

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O1' O1

Si

Ga

O2 O2

O2' La atoms

[(Ta, Ga)O6] octahedra

[SiO4] and [GaO'4] tetrahedra

O2' Fig. 2. Schematic comparison of statistically located [SiO4] and [GaO'4] tetrahedra. The designations corre sponding to the silicon tetrahedron are brighter. The oxy gen atoms entering the gallium tetrahedron are primed.

[GaO'4] tetrahedra

Fig. 1. Structural model of La3Ta0.25Ga5.25Si0.5O14 crystal.

cantly reduce thermal vibrations and thus simplify this problem. From the computational point of view, it is simpler to take into account anharmonicity because it always results in good fitting. However, in this case additional parameters must be introduced and refined; their physical meaning manifests itself only when cal culating the probability density function for atomic displacements. The real anharmonicity is caused by the differ ence in the chemical bond forces acting on an atom in a crystal in opposite directions (nonspherical effective potential around the atom). If there are no significant differences in the character of atomic chemical bonds but the refinement indicates a high significance of anharmonicity, it is desirable to check the corresponding atomic position for possi ble splitting. Most often the absence of splitting is reliably indicated by the atom thermal vibrations having a very large size a peculiar orientation in each position. The problem of determining the occupancies of mixed cation positions was initially solved without considering possible position splitting, taking into account only the anharmonicity of thermal vibrations of all atoms in the structure. This analysis revealed that La and O displacements are characterized by a signif icant thirdrank anharmonicity, while the displace ments of three other cations exhibit significant anhar monicity up to the fourth rank. It was also established that the positions of La atoms on the twofold symme CRYSTALLOGRAPHY REPORTS

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O2' O2

try axis, Ga atoms on the threefold symmetry axis, and all oxygen atoms are characterized by full occupancy. It was found that the position at the origin of coordi nates is statistically occupied with tantalum and gal lium by 24% and 76%, respectively, and the position on the threefold axis is statistically occupied with sili con and gallium by 24% and 76%, respectively; these occupancies correspond to the formula La3Ta0.24Ga5.28Si0.48O14. The calculated deviation from electroneutrality is within the errors of diffraction analysis. The ionic radii of Ga3+ (0.62 Å) and Та5+ (0.64 Å) cations in the octahedral environment are similar, whereas the ionic radii of Ga3+ (0.47 Å) and Si4+ (0.26 Å) in tetrahedra differ significantly [23]. Thus, it is reasonable to suggest that the crystal contains statis tically distributed [SiO4] and [GaO4] tetrahedra. Fur ther structure refinement showed that the positions of oxygen atoms in [(Si,Ga)O4] tetrahedra are split, although silicon and gallium cations have identical coordinates with a high accuracy. We restored the har monic displacement model for the split oxygen (O1, O2) and cation (Si + Ga3) positions and retained anharmonic tensors of the above mentioned ranks for La, (Ta + Ga1), Ga2, and O3. The results of the final structure refinement are listed in Table 2. The atomic coordinates, parameters of anisotropic atomic dis placements, and interatomic distances are given in Tables 3, 4, and 5, respectively. The structural model is shown in Fig. 1. Gallium and silicon tetrahedra with their nearest oxygen environment are presented in Fig. 2.

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Table 5. Interatomic distance in the La3Ta0.25Ga5.25Si0.5O14 structure [LaO8] polyhedron#

(Ta,Ga) octahedron

La–O1 × 2 La–O'1 × 2 La–O2(1) × 2 La–O2'(1) × 2

2.689(2) 2.612(1) 2.512(6) 2.468(3)

(Ta+Ga)–O3(1) × 6 O3(1)–O3(1) × 3* O3(1)–O3(2) × 6 O3(1)–O3(3) × 3

La–O2(2) × 2

3.007(6)

La–O'2(2) × 2 La–O3 × 2 O1–O2 × 4 O'1–O'2 × 4

2.843(2) Si–O1 2.389(2) Si–O2(1) × 3 3.225(7) O1–O2(1) × 3 2.942(5) O2(1)–O2(2) × 3*

O1–O2 × 2

3.600(7)

[SiO4] tetrahedron 1.607(5) 1.663(6) 2.735(7) 2.642(8)

[GaO4' ] tetrahedron

O'1–O2' × 2

3.616(2) Ga–O'1 O1–O3(1) × 2 3.182(2) Ga–O'2(1) × 3 O'1–O3(1) × 2 3.195(2) O'1–O'2(1) × 3 O2(1)–O2(2) × 2* 2.642(8) O'2(1)–O'2(2) × 3* O'2(1)–O'2(2) × 2* 2.818(2)

1.995(2) 2.675(5) 2.741(2) 3.153(5)

1.808(4) 1.837(2) 3.018(5) 2.818(2)

Ga2 tetrahedron

4.086(9) Ga–O2 × 2 O'2(1)–O'2(1) 3.743(6) Ga–O'2 × 2 O2(1)–O3(1) × 2 3.847(6) Ga–O3(1) × 2 O'2(1)–O3(1) × 2 3.948(2) O2(1)–O2(1) O2(2)–O3(1) × 2 3.094(5) O'2(1)–O'2(1) O'2(2)–O3(1) × 2 2.929(2) O2(1)–O3(1) × 2 O2(2)–O3(2) × 2 3.591(6) O2(1)–O3(1) × 2 O'2(2)–O3(2) × 2 3.352(5) O2(1)–O3(2) × 2 O3(1)–O3(1)* 2.675(5) O2(1)–O3(2) × 2 O3(1)–O3(1)

O2(1)–O2(1)

O1–O'1 O2–O'2

1.908(8) 1.889(2) 1.819(2) 2.720(8) 2.931(4) 2.969(5) 2.826(2) 3.847(6) 3.026(4) 3.349(5) 0.201(3) 0.240(3)

# With allowance for the split positions of oxygen atoms.

*Shared edges of polyhedra. O and O' atoms have different coordi nates and belong to [SiO4] and [GaO4' ] tetrahedra, respectively.

CONCLUSIONS The LTGS structure was subjected to highpreci sion Xray diffraction analysis characterized by the following accuracy parameters: R1(F)/wR2(F) = 0.75/0.71%, Δρmax/Δρmin= +0.39/–0.48 e/Å3 for 4030 independent reflections and 87 model parame ters. The study was performed using highresolution experimental data (sinθ/λ|max ≈ 1.35 Å–1) with the cor rection of systematic errors in two independent exper iments. One structural feature of the crystal studied is the presence of two statistically located tetrahedra, [SiO4] and [GaO'4], with significantly different sizes.

ACKNOWLEDGMENTS This study was supported by the Russian Founda tion for Basic Research, project nos. 080291302 IND_a and 090200444a, and grant NSh 4034.2010.5 for the Support of Leading Scientific Schools. REFERENCES 1. E. L. Belokoneva and N. V. Belov, Dokl. Akad. Nauk SSSR 260 (6), 1363 (1981). 2. B. V. Mill and Yu. V. Pisarevsky, in Proc. 2000 IEEE/EIA Intern. Frequency Control Symp., Kansas City, Missouru, USA, p. 133. 3. Yu. V. Pisarevsky, B. V. Mill, A. Belokopitov, and P. A. Senushenkov, in Abstr. 2002 IEEE Intern. Fre quency Control Symp., New Orleans, USA, p. 50. 4. E. L. Belokoneva, S. Yu. Stefanovich, Yu. V. Pisarevsky, et al., Zh. Neorg. Khim. 45 (11), 1786 (2000). 5. B. V. Mill’, A. A. Klimenkova, B. A. Maksimov, et al., Kristallografiya 52 (5), 841 (2007). [Crystallogr. Rep. 52 (5), 785 (2007)]. 6. A. P. Dudka, B. V. Mill’, and Yu. V. Pisarevsky, Kristal lografiya 54 (4), 599 (2009). 7. A. P. Dudka, Kristallografiya 47 (1), 156 (2002) [Crys tallogr. Rep. 47 (1), 152 (2002)]. 8. A. P. Dudka and B. V. Mill’, Kristallografiya 55, 6 (2010) (in press). 9. Oxford Diffraction. CrysAlisPro. 2009. Version 171.33.52 (Oxford Diffraction Ltd., Abingdon, 2009). 10. A. P. Dudka, Kristallografiya 47 (1), 163 (2002) [Crys tallogr. Rep. 47 (1), 152 (2002)]. 11. A. Dudka, J. Appl. Crystallogr. 40, 602 (2007). 12. A. P. Dudka, M. Kh. Rabadanov, and A. A. Loshmanov, Kristallografiya 34 (4), 818 (1989) [Sov. Phys. Crystal logr. 34 (4), 490 (1989)]. 13. A. P. Dudka, Kristallografiya 50 (6), 1148 (2005) [Crys tallogr. Rep. 50 (6), 1068 (2005)]. 14. A. P. Dudka, Kristallografiya 51 (1), 165 (2006) [Crys tallogr. Rep. 51 (1), 157 (2006)]. 15. A. P. Dudka, in Proc. VII Nat. Conf. on Application of X Rays, Synchrotron Radiation, Neutrons, and Elec trons. RNSÉNBIK2009, Moscow, 2009, p. 486. 16. P. J. Becker and P. Coppens, Acta Crystallogr. A 30, 129 (1974). 17. Page. Y. Le and E. J. Gabe, J. Appl. Crystallogr. 11, 254 (1978). 18. A. Dudka, J. Appl. Crystallogr. 43, 27 (2010). 19. Z. Su and P. Coppens, Acta Crystallogr. A 54, 646 (1998). 20. V. N. Molchanov, B. A. Maksimov, D. F. Kondakov, et al., Pis’ma Zh. Eksp. Teor. Fiz. 74 (4), 244 (2001). 21. H. D. Flack, Acta Crystallogr. A 39, 76 (1983). 22. V. Petricek, M. Dusek, and L. Palatinus, JANA2006. The Crystallographic Computing System. 2006 (Insti tute of Physics, Prague, 2006). 23. R. D. Shannon, Acta Crystallogr. A 32, 751 (1976).

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