Structural redetermination, thermal expansion and refractive indices of KLu(WO4)2

Pujol, M.C.; Mateos, X.; Aznar, A.; Solans, X.; Suriñach, S.; Massons, J.; Díaz, F.; Aguiló, M.

doi:10.1107/S0021889806004328

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Structural redetermination, thermal expansion and refractive indices of KLu(WO₄)₂

M. C. Pujol, X. Mateos, A. Aznar, X. Solans, S. Suriñach, J. Massons, F. Díaz and M. Aguiló

The crystal structure of monoclinic KLu(WO₄)₂ (KLuW) crystals was determined at room temperature by using single-crystal X-ray diffraction data. The unit-cell parameters were a = 10.576 (7), b = 10.214 (7), c = 7.487 (2) Å, β = 130.68 (4)°, with Z = 4, in space group C2/c. The unit-cell parameters of KLu_1−xYb_x(WO₄)₂ were determined in relation to Yb concentration. Vickers micro-indentations were used to study the microhardness of KLuW. The linear thermal expansion tensor was determined and the principal axis with maximum thermal expansion ( $\alpha_{33}'$ = 16.72 × 10⁻⁶ K⁻¹),

, was located 13.51° from the c axis. The room-temperature optical tensor was studied in the near-infrared (NIR) and visible range. The principal optical axis with maximum refractive index (n_g = 2.113), N_g, was located 18.5° from the c axis at 632.8 nm. Undoped and ytterbium-doped KLuW crystals were grown by the TSSG (top-seeded-solution growth) slow-cooling method. The crystals show {110}, { $\bar{1}11$ }, {010} and {310} faces that basically constitue the habit of the KLuW crystals.

Keywords: potassium lutetium tungstate; laser material; microhardness; thermal expansion tensor; refractive index.

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Supporting information

	Crystallographic Information File (CIF) https://doi.org/10.1107/S0021889806004328/ks5080sup1.cif Contains datablock I
	Structure factor file (CIF format) https://doi.org/10.1107/S0021889806004328/ks5080Isup2.fcf Contains datablock I

Computing details top

Data collection: CAD-4-PC (Kretschmar, 1996); cell refinement: CAD-4-PC; data reduction: CFEO (Solans, 1978); program(s) used to solve structure: SHELXS97 (Sheldrick, 1997); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: ORTEP-3.2 (Brueggemann & Schmid, 1990); software used to prepare material for publication: PLATON (Spek, 1990).

Figures top

(I) top

Crystal data top

LuO₈W₂·K	F(000) = 1208
M_r = 709.77	D_x = 7.686 Mg m⁻³
Monoclinic, C2/c	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -C 2yc	Cell parameters from 25 reflections
a = 10.576 (7) Å	θ = 9–21°
b = 10.214 (7) Å	µ = 54.07 mm⁻¹
c = 7.487 (2) Å	T = 293 K
β = 130.68 (4)°	Sphere, colourless
V = 613.3 (6) Å³	0.2 × 0.2 × 0.2 mm
Z = 4

Data collection top

Enraf-Nonius CAD4 diffractometer	664 reflections with I > 2σ(I)
Radiation source: fine-focus sealed tube	R_int = 0.034
Graphite monochromator	θ_max = 30.0°, θ_min = 3.2°
ω/2θ scans	h = −14→11
Absorption correction: spherical ?	k = 0→14
T_min = 0.242, T_max = 0.264	l = 0→10
1875 measured reflections	3 standard reflections every 120 min. min
899 independent reflections	intensity decay: none

Refinement top

Refinement on F²	0 restraints
Least-squares matrix: full	Primary atom site location: structure-invariant direct methods
R[F² > 2σ(F²)] = 0.036	Secondary atom site location: difference Fourier map
wR(F²) = 0.083	w = 1/[σ²(F_o²) + (0.0275P)²] where P = (F_o² + 2F_c²)/3
S = 1.21	(Δ/σ)_max = 0.002
899 reflections	Δρ_max = 0.77 e Å⁻³
56 parameters	Δρ_min = −0.67 e Å⁻³

Crystal data top

LuO₈W₂·K	V = 613.3 (6) Å³
M_r = 709.77	Z = 4
Monoclinic, C2/c	Mo Kα radiation
a = 10.576 (7) Å	µ = 54.07 mm⁻¹
b = 10.214 (7) Å	T = 293 K
c = 7.487 (2) Å	0.2 × 0.2 × 0.2 mm
β = 130.68 (4)°

Data collection top

Enraf-Nonius CAD4 diffractometer	664 reflections with I > 2σ(I)
Absorption correction: spherical ?	R_int = 0.034
T_min = 0.242, T_max = 0.264	3 standard reflections every 120 min. min
1875 measured reflections	intensity decay: none
899 independent reflections

Refinement top

R[F² > 2σ(F²)] = 0.036	56 parameters
wR(F²) = 0.083	0 restraints
S = 1.21	Δρ_max = 0.77 e Å⁻³
899 reflections	Δρ_min = −0.67 e Å⁻³

Special details top

Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell e.s.d.'s are taken into account individually in the estimation of e.s.d.'s in distances, angles and torsion angles; correlations between e.s.d.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell e.s.d.'s is used for estimating e.s.d.'s involving l.s. planes.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq
W1	0.19691 (3)	0.00005 (2)	0.73532 (5)	0.01801 (16)
Lu	0.0000	0.72841 (3)	0.2500	0.01989 (19)
K	0.5000	0.2027 (3)	0.7500	0.0249 (6)
O1	0.3768 (7)	−0.0828 (7)	0.8121 (13)	0.0462 (16)
O2	0.0239 (7)	−0.1070 (6)	0.4722 (11)	0.0334 (12)
O3	0.2835 (7)	0.1522 (6)	0.8784 (13)	0.0418 (16)
O4	0.2003 (6)	−0.0749 (8)	0.9536 (12)	0.0402 (14)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
W1	0.01930 (19)	0.0183 (2)	0.0168 (3)	−0.00007 (7)	0.0119 (2)	−0.00015 (10)
Lu	0.0213 (2)	0.0194 (2)	0.0196 (3)	0.000	0.0136 (2)	0.000
K	0.0237 (8)	0.0325 (8)	0.0218 (15)	0.000	0.0162 (9)	0.000
O1	0.040 (2)	0.049 (3)	0.053 (4)	−0.004 (3)	0.032 (3)	0.003 (4)
O2	0.041 (2)	0.031 (2)	0.032 (3)	−0.004 (2)	0.026 (2)	−0.002 (3)
O3	0.042 (2)	0.040 (3)	0.039 (4)	0.002 (3)	0.025 (2)	0.005 (4)
O4	0.043 (2)	0.041 (3)	0.033 (3)	0.003 (3)	0.023 (3)	0.000 (4)

Geometric parameters (Å, º) top

W1—O3	1.767 (7)	K—O4ⁱⁱ	2.739 (6)
W1—O4	1.784 (8)	K—O4^iv	2.739 (6)
W1—O1	1.801 (6)	K—O4^xiv	2.786 (8)
W1—O2	1.930 (6)	K—O4^xi	2.786 (8)
W1—O2ⁱ	2.081 (6)	K—O1ⁱⁱ	2.894 (8)
W1—O4ⁱⁱ	2.265 (8)	K—O1^iv	2.894 (8)
W1—Luⁱⁱⁱ	3.5128 (18)	K—O2^xi	2.976 (7)
W1—K^iv	3.648 (3)	K—O2^xiv	2.976 (7)
W1—K^v	3.725 (3)	K—O3^xv	3.050 (8)
W1—K	3.756 (2)	K—O3	3.050 (8)
W1—K^vi	4.110 (3)	K—O1	3.348 (7)
Lu—O1^vii	2.217 (7)	K—O1^xv	3.348 (7)
Lu—O1^vi	2.217 (7)	O1—Lu^vi	2.217 (7)
Lu—O2^viii	2.260 (7)	O1—K^iv	2.894 (8)
Lu—O2^ix	2.260 (7)	O2—W1ⁱ	2.081 (6)
Lu—O3^x	2.299 (7)	O2—Lu^xvi	2.260 (7)
Lu—O3^xi	2.299 (7)	O2—K^v	2.976 (7)
Lu—O3^xii	2.765 (6)	O3—Lu^xvii	2.299 (7)
Lu—O3ⁱⁱⁱ	2.765 (6)	O3—Luⁱⁱⁱ	2.765 (6)
Lu—W1^xii	3.5128 (18)	O4—W1^xviii	2.265 (8)
Lu—W1ⁱⁱⁱ	3.5128 (18)	O4—K^iv	2.739 (6)
Lu—K^x	3.7527 (10)	O4—K^v	2.786 (8)
Lu—K^xiii	3.7527 (10)

O3—W1—O4	97.4 (3)	O3^xii—Lu—K^x	70.88 (17)
O3—W1—O1	101.4 (3)	O3ⁱⁱⁱ—Lu—K^x	112.91 (17)
O4—W1—O1	96.9 (3)	W1^xii—Lu—K^x	68.82 (4)
O3—W1—O2	152.7 (2)	W1ⁱⁱⁱ—Lu—K^x	118.16 (4)
O4—W1—O2	97.6 (3)	O1^vii—Lu—K^xiii	50.3 (2)
O1—W1—O2	99.3 (3)	O1^vi—Lu—K^xiii	123.0 (2)
O3—W1—O2ⁱ	82.9 (2)	O2^viii—Lu—K^xiii	52.46 (18)
O4—W1—O2ⁱ	104.6 (2)	O2^ix—Lu—K^xiii	135.52 (17)
O1—W1—O2ⁱ	157.4 (3)	O3^x—Lu—K^xiii	122.41 (19)
O2—W1—O2ⁱ	71.3 (3)	O3^xi—Lu—K^xiii	54.30 (19)
O3—W1—O4ⁱⁱ	87.2 (4)	O3^xii—Lu—K^xiii	112.91 (17)
O4—W1—O4ⁱⁱ	174.1 (2)	O3ⁱⁱⁱ—Lu—K^xiii	70.88 (17)
O1—W1—O4ⁱⁱ	78.5 (3)	W1^xii—Lu—K^xiii	118.16 (4)
O2—W1—O4ⁱⁱ	79.7 (3)	W1ⁱⁱⁱ—Lu—K^xiii	68.82 (4)
O2ⁱ—W1—O4ⁱⁱ	79.6 (3)	K^x—Lu—K^xiii	171.96 (8)
O3—W1—Luⁱⁱⁱ	51.0 (2)	O4ⁱⁱ—K—O4^iv	123.1 (3)
O4—W1—Luⁱⁱⁱ	88.2 (2)	O4ⁱⁱ—K—O4^xiv	153.79 (16)
O1—W1—Luⁱⁱⁱ	152.4 (2)	O4^iv—K—O4^xiv	83.1 (2)
O2—W1—Luⁱⁱⁱ	107.00 (19)	O4ⁱⁱ—K—O4^xi	83.1 (2)
O2ⁱ—W1—Luⁱⁱⁱ	37.74 (18)	O4^iv—K—O4^xi	153.79 (16)
O4ⁱⁱ—W1—Luⁱⁱⁱ	97.58 (19)	O4^xiv—K—O4^xi	70.7 (3)
O3—W1—K^iv	96.2 (2)	O4ⁱⁱ—K—O1ⁱⁱ	56.8 (2)
O4—W1—K^iv	46.34 (19)	O4^iv—K—O1ⁱⁱ	98.3 (2)
O1—W1—K^iv	51.5 (3)	O4^xiv—K—O1ⁱⁱ	125.8 (2)
O2—W1—K^iv	110.63 (19)	O4^xi—K—O1ⁱⁱ	96.0 (2)
O2ⁱ—W1—K^iv	150.7 (2)	O4ⁱⁱ—K—O1^iv	98.3 (2)
O4ⁱⁱ—W1—K^iv	129.70 (16)	O4^iv—K—O1^iv	56.8 (2)
Luⁱⁱⁱ—W1—K^iv	123.07 (4)	O4^xiv—K—O1^iv	96.0 (2)
O3—W1—K^v	141.1 (3)	O4^xi—K—O1^iv	125.8 (2)
O4—W1—K^v	45.6 (2)	O1ⁱⁱ—K—O1^iv	130.0 (3)
O1—W1—K^v	95.9 (2)	O4ⁱⁱ—K—O2^xi	107.26 (19)
O2—W1—K^v	52.6 (2)	O4^iv—K—O2^xi	109.0 (2)
O2ⁱ—W1—K^v	94.20 (17)	O4^xiv—K—O2^xi	57.7 (2)
O4ⁱⁱ—W1—K^v	130.63 (18)	O4^xi—K—O2^xi	57.94 (19)
Luⁱⁱⁱ—W1—K^v	106.78 (6)	O1ⁱⁱ—K—O2^xi	152.57 (17)
K^iv—W1—K^v	68.24 (5)	O1^iv—K—O2^xi	70.4 (2)
O3—W1—K	53.3 (2)	O4ⁱⁱ—K—O2^xiv	109.0 (2)
O4—W1—K	134.64 (19)	O4^iv—K—O2^xiv	107.26 (19)
O1—W1—K	63.0 (2)	O4^xiv—K—O2^xiv	57.94 (19)
O2—W1—K	124.4 (2)	O4^xi—K—O2^xiv	57.7 (2)
O2ⁱ—W1—K	104.69 (18)	O1ⁱⁱ—K—O2^xiv	70.4 (2)
O4ⁱⁱ—W1—K	46.39 (15)	O1^iv—K—O2^xiv	152.57 (17)
Luⁱⁱⁱ—W1—K	94.36 (6)	O2^xi—K—O2^xiv	98.4 (3)
K^iv—W1—K	97.83 (7)	O4ⁱⁱ—K—O3^xv	112.0 (2)
K^v—W1—K	158.64 (6)	O4^iv—K—O3^xv	57.6 (2)
O3—W1—K^vi	69.5 (2)	O4^xiv—K—O3^xv	81.4 (2)
O4—W1—K^vi	145.4 (2)	O4^xi—K—O3^xv	115.1 (2)
O1—W1—K^vi	116.8 (2)	O1ⁱⁱ—K—O3^xv	56.46 (15)
O2—W1—K^vi	85.36 (19)	O1^iv—K—O3^xv	114.18 (19)
O2ⁱ—W1—K^vi	43.69 (19)	O2^xi—K—O3^xv	138.94 (17)
O4ⁱⁱ—W1—K^vi	40.00 (18)	O2^xiv—K—O3^xv	57.77 (17)
Luⁱⁱⁱ—W1—K^vi	58.35 (4)	O4ⁱⁱ—K—O3	57.6 (2)
K^iv—W1—K^vi	160.58 (4)	O4^iv—K—O3	112.0 (2)
K^v—W1—K^vi	131.12 (5)	O4^xiv—K—O3	115.1 (2)
K—W1—K^vi	63.25 (5)	O4^xi—K—O3	81.4 (2)
O1^vii—Lu—O1^vi	95.7 (4)	O1ⁱⁱ—K—O3	114.2 (2)
O1^vii—Lu—O2^viii	98.3 (3)	O1^iv—K—O3	56.46 (15)
O1^vi—Lu—O2^viii	148.7 (2)	O2^xi—K—O3	57.77 (17)
O1^vii—Lu—O2^ix	148.7 (2)	O2^xiv—K—O3	138.94 (17)
O1^vi—Lu—O2^ix	98.3 (3)	O3^xv—K—O3	160.6 (3)
O2^viii—Lu—O2^ix	83.9 (3)	O4ⁱⁱ—K—O1	49.3 (2)
O1^vii—Lu—O3^x	76.6 (3)	O4^iv—K—O1	79.8 (2)
O1^vi—Lu—O3^x	77.1 (2)	O4^xiv—K—O1	149.3 (2)
O2^viii—Lu—O3^x	133.5 (2)	O4^xi—K—O1	124.09 (17)
O2^ix—Lu—O3^x	79.4 (2)	O1ⁱⁱ—K—O1	81.97 (14)
O1^vii—Lu—O3^xi	77.1 (2)	O1^iv—K—O1	53.3 (2)
O1^vi—Lu—O3^xi	76.6 (3)	O2^xi—K—O1	104.71 (19)
O2^viii—Lu—O3^xi	79.4 (2)	O2^xiv—K—O1	152.15 (18)
O2^ix—Lu—O3^xi	133.5 (2)	O3^xv—K—O1	109.67 (18)
O3^x—Lu—O3^xi	140.4 (3)	O3—K—O1	50.88 (19)
O1^vii—Lu—O3^xii	151.1 (2)	O4ⁱⁱ—K—O1^xv	79.8 (2)
O1^vi—Lu—O3^xii	73.5 (2)	O4^iv—K—O1^xv	49.3 (2)
O2^viii—Lu—O3^xii	80.8 (2)	O4^xiv—K—O1^xv	124.09 (17)
O2^ix—Lu—O3^xii	60.24 (19)	O4^xi—K—O1^xv	149.3 (2)
O3^x—Lu—O3^xii	124.7 (3)	O1ⁱⁱ—K—O1^xv	53.3 (2)
O3^xi—Lu—O3^xii	74.3 (3)	O1^iv—K—O1^xv	81.97 (14)
O1^vii—Lu—O3ⁱⁱⁱ	73.5 (2)	O2^xi—K—O1^xv	152.15 (18)
O1^vi—Lu—O3ⁱⁱⁱ	151.1 (2)	O2^xiv—K—O1^xv	104.71 (19)
O2^viii—Lu—O3ⁱⁱⁱ	60.24 (19)	O3^xv—K—O1^xv	50.88 (19)
O2^ix—Lu—O3ⁱⁱⁱ	80.8 (2)	O3—K—O1^xv	109.67 (18)
O3^x—Lu—O3ⁱⁱⁱ	74.3 (3)	O1—K—O1^xv	58.8 (3)
O3^xi—Lu—O3ⁱⁱⁱ	124.7 (3)	W1—O1—Lu^vi	153.1 (4)
O3^xii—Lu—O3ⁱⁱⁱ	127.7 (3)	W1—O1—K^iv	99.3 (3)
O1^vii—Lu—W1^xii	167.9 (2)	Lu^vi—O1—K^iv	93.5 (3)
O1^vi—Lu—W1^xii	94.68 (18)	W1—O1—K	88.4 (3)
O2^viii—Lu—W1^xii	69.61 (17)	Lu^vi—O1—K	102.7 (2)
O2^ix—Lu—W1^xii	34.30 (14)	K^iv—O1—K	126.7 (2)
O3^x—Lu—W1^xii	111.87 (18)	W1—O2—W1ⁱ	108.7 (3)
O3^xi—Lu—W1^xii	99.33 (17)	W1—O2—Lu^xvi	138.5 (3)
O3^xii—Lu—W1^xii	29.77 (14)	W1ⁱ—O2—Lu^xvi	108.0 (3)
O3ⁱⁱⁱ—Lu—W1^xii	99.89 (15)	W1—O2—K^v	96.5 (3)
O1^vii—Lu—W1ⁱⁱⁱ	94.68 (18)	W1ⁱ—O2—K^v	107.4 (2)
O1^vi—Lu—W1ⁱⁱⁱ	167.9 (2)	Lu^xvi—O2—K^v	90.5 (2)
O2^viii—Lu—W1ⁱⁱⁱ	34.30 (14)	W1—O3—Lu^xvii	138.2 (3)
O2^ix—Lu—W1ⁱⁱⁱ	69.61 (17)	W1—O3—Luⁱⁱⁱ	99.3 (2)
O3^x—Lu—W1ⁱⁱⁱ	99.33 (17)	Lu^xvii—O3—Luⁱⁱⁱ	105.7 (3)
O3^xi—Lu—W1ⁱⁱⁱ	111.87 (18)	W1—O3—K	99.0 (3)
O3^xii—Lu—W1ⁱⁱⁱ	99.89 (15)	Lu^xvii—O3—K	87.95 (19)
O3ⁱⁱⁱ—Lu—W1ⁱⁱⁱ	29.77 (14)	Luⁱⁱⁱ—O3—K	133.1 (2)
W1^xii—Lu—W1ⁱⁱⁱ	75.71 (5)	W1—O4—W1^xviii	134.8 (4)
O1^vii—Lu—K^x	123.0 (2)	W1—O4—K^iv	105.5 (3)
O1^vi—Lu—K^x	50.3 (2)	W1^xviii—O4—K^iv	96.8 (2)
O2^viii—Lu—K^x	135.52 (17)	W1—O4—K^v	107.1 (3)
O2^ix—Lu—K^x	52.46 (18)	W1^xviii—O4—K^v	108.5 (3)
O3^x—Lu—K^x	54.30 (19)	K^iv—O4—K^v	96.9 (2)
O3^xi—Lu—K^x	122.41 (19)

Symmetry codes: (i) −x, −y, −z+1; (ii) x, −y, z−1/2; (iii) −x, −y+1, −z+1; (iv) −x+1, −y, −z+2; (v) x−1/2, y−1/2, z; (vi) −x+1/2, −y+1/2, −z+1; (vii) x−1/2, −y+1/2, z−1/2; (viii) x, y+1, z; (ix) −x, y+1, −z+1/2; (x) x−1/2, y+1/2, z−1; (xi) −x+1/2, y+1/2, −z+3/2; (xii) x, −y+1, z−1/2; (xiii) x−1/2, y+1/2, z; (xiv) x+1/2, y+1/2, z; (xv) −x+1, y, −z+3/2; (xvi) x, y−1, z; (xvii) x+1/2, y−1/2, z+1; (xviii) x, −y, z+1/2.

Experimental details

Crystal data
Chemical formula	LuO₈W₂·K
M_r	709.77
Crystal system, space group	Monoclinic, C2/c
Temperature (K)	293
a, b, c (Å)	10.576 (7), 10.214 (7), 7.487 (2)
β (°)	130.68 (4)
V (Å³)	613.3 (6)
Z	4
Radiation type	Mo Kα
µ (mm⁻¹)	54.07
Crystal size (mm)	0.2 × 0.2 × 0.2

Data collection
Diffractometer	Enraf-Nonius CAD4 diffractometer
Absorption correction	Spherical
T_min, T_max	0.242, 0.264
No. of measured, independent and observed [I > 2σ(I)] reflections	1875, 899, 664
R_int	0.034
(sin θ/λ)_max (Å⁻¹)	0.703

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.036, 0.083, 1.21
No. of reflections	899
No. of parameters	56
Δρ_max, Δρ_min (e Å⁻³)	0.77, −0.67

Computer programs: CAD-4-PC (Kretschmar, 1996), CAD-4-PC, CFEO (Solans, 1978), SHELXS97 (Sheldrick, 1997), SHELXL97 (Sheldrick, 1997), ORTEP-3.2 (Brueggemann & Schmid, 1990), PLATON (Spek, 1990).

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