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The title compounds, LiKB4O7 and LiRbB4O7, are newly developed non-linear optical crystals containing two kinds of anionic groups, namely (B3O8)7- and (B5O10)5-. The (B3O8)7- groups form infinite spiral chains parallel to the [100] direction, which are interconnected by sharing O atoms with (B5O10)5- groups.

Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S0108270100013445/br1301sup1.cif
Contains datablocks global, LKB4, LRB4

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S0108270100013445/br1301LKB4sup2.hkl
Contains datablock LKB4

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S0108270100013445/br1301LRB4sup3.hkl
Contains datablock LRB4

Comment top

Since the discovery of β-BaB2O4 (BBO) (Chen et al., 1985), various non-centrosymmetric borate crystals, e.g., LiB3O5 (LBO) (Chen et al., 1989), CsB3O5 (CBO) (Wu et al., 1993), Sr2Be2B2O7 (SBBO) (Chen et al., 1995) and CsLiB6O10 (CLBO) (Sasaki et al., 1995a), have been synthesized and intensively studied because of their excellent nonlinear optical (NLO) properties such as frequency conversion of laser light into the ultraviolet region. Title compounds, LiKB4O7 and LiRbB4O7, are isomorphous and newly developed NLO crystals named as LKB4 and LRB4, respectively. They have sufficient mechanical strength, good chemical stability and wide transparent range down to 190 nm in wavelength. Both single crystals exhibit frequency-doubling for an incident pumping light (λ=720–780 nm) from a Ti:Al2O3 pulsed-laser.

Boron atoms in LKB4 and LRB4 are either trigonally or tetrahedrally coordinated by oxygen atoms. All BO33− trigonal groups are almost perfectly planer with a mean B—O bond length, 1.368 (4) Å, and O—B—O bond angles ranging from 115.2 (4) to 125.2 (5)°. Tetrahedral groups, BO45−, are slightly distorted from the ideal tetrahedron. The B—O distances lie between 1.437 (6) and 1.488 (6) Å, and the O—B—O angles are in the range 105.74 (12)–112.4 (4)°. LBO (Radaev et al., 1992) and CLBO (Sasaki, Mori et al., 1995) also contain both BO33− and BO45− groups with similar bond lengths and angles. Chen et al. (1990) classified the known NLO borate crystals by their coordinated anionic groups and succeeded to predict the second-order NLO susceptibilities. According to their classification, framework structures of LKB4 and LRB4 contain two kinds of anionic groups, (B3O8)7− and (B5O10)5−, in the unit cells. The (B3O8)7− anionic group is a six-membered ring consisting of one BO33− and two BO45− groups, while the (B5O10)5− group is composed from two six-membered rings joined by sharing a tetrahedrally coordinated boron atom, i.e. a double six-membered ring. As an example, the crystal structure of LKB4 is shown in Fig.1. The (B3O8)7− six-membered rings form infinite spiral chains parallel to [100] direction through the O2 bridging atoms. The adjacent (B3O8)7− chains are interconnected by sharing O4, O12, O13 atoms with the (B5O10)5− double six-membered rings. The oxygen atom, O10, is bonded to trigonally coordinated B5 atom in the (B5O10)5− group, but not shared by the other anionic group. The distances between B5 and O10 atoms, 1.318 (2) Å in LKB4 and 1.303 (7) Å in LRB4, respectively, are appreciably short relative to the mean boron-oxygen bond length in the BO33− trigonal groups. Similar non-bridging oxygen atoms with comparable bond lengths have been found in Na2O·2B2O3 (Krogh-Moe, 1974) and LiBa2B5O10 (Huang et al., 1992).

In the present study, the coordination sphere of each cation was limited to the first gap in cation-oxygen bond lengths ranked in increasing order. The coordination sphere of Li1 contains four oxygen atoms, O1, O8, O10 and O14, which form a distorted tetrahedron. There is a good correspondence between Li1—O distances in LKB4 and LRB4. Lithium cations in LBO (Radaev et al., 1992) and CLBO (Sasaki, Mori et al., 1995) also occupy such tetrahedral sites. But, another lithium cation, Li2, is situated in a highly distorted LiO6 octahedron. On the other hand, potassium and rubidium cations do not have a well defined coordination sphere. The cation-oxygen distances are rather widely distributed as reported in other borate compounds (Krogh-Moe, 1972a,b, 1974a,b,c,d). The potassium cations in K2O·2B2O3 (Krogh-Moe, 1972b) and 5K2O.19B2O3 (Krogh-Moe, 1974 d) take the coordination number from six to eight within the limit of 3.20 Å. In this range, K1 and K2 cations in LKB4 are coordinated by seven and eight oxygen atoms, respectively (Fig. 2). The Rb2 cation in LRB4 has eight oxygen neighbours in the range 2.840 (4)–3.423 (4) Å, while, for the Rb1 cation, nine oxygen neighbours are found in the same range.

Experimental top

Single crystals of LiKB4O7 and LiRbB4O7 were grown by Czochralski technique from a congruent melt in air. Starting materials were prepared by a conventional solid state reaction at 953 K. Large single crystals (ca ø15 mm× 20 mm) with high optical quality were obtained.

Refinement top

The absolute structure determination was carried out using Flack's x parameter (Flack, 1983) implemented in the least-squares program. The number of observed Friedel pairs is 911 for LKB4 and 828 for LRB4.

Computing details top

Figures top
[Figure 1] Fig. 1. Molecular packing in LiKB4O7 showing the three-dimensional borate framework structure. Thick and thin solid lines represent B—O bonds in BO3 triangles and in BO4 tetrahedra, respectively. Displacement ellipsoids are shown at the 50% probability level.
[Figure 2] Fig. 2. Oxygen coordination around potassium cations in LiKB4O7. Symmetry codes: (ii) 1/2 − x, 1 − y, 1/2 + z; (iii) x − 1, y, z; (vii) 3/2 − x, 1 − y, z − 1/2; (viii) 1 − x, y + 1/2, 1/2 − z; (ix) x − 1/2, 3/2 − y, 1 − z. Displacement ellipsoids are shown at the 50% probability level.
(LKB4) top
Crystal data top
LiKB4O7Dx = 2.233 Mg m3
Dm = 2.19 Mg m3
Dm measured by Archemedes method
Mr = 201.28Mo Kα radiation, λ = 0.71073 Å
Orthorhombic, P212121Cell parameters from 24 reflections
a = 8.4915 (12) Åθ = 12.4–16.5°
b = 11.1454 (13) ŵ = 0.87 mm1
c = 12.6558 (13) ÅT = 293 K
V = 1197.8 (3) Å3Sphere, colourless
Z = 80.16 mm (radius)
F(000) = 784
Data collection top
RIGAKU AFC-5R
diffractometer
θmax = 30.0°
ω–2θ scansh = 1111
13549 measured reflectionsk = 1515
3487 independent reflectionsl = 1717
3342 reflections with F > 4σ(F)3 standard reflections every 150 reflections
Rint = 0.033 intensity decay: 4%
Refinement top
Refinement on F2(Δ/σ)max = 0.001
R[F2 > 2σ(F2)] = 0.024Δρmax = 0.19 e Å3
wR(F2) = 0.055Δρmin = 0.27 e Å3
S = 1.12Extinction correction: SHELXL97 (Sheldrick, 1997), Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4
3342 reflectionsExtinction coefficient: 0.0345 (14)
236 parametersAbsolute structure: Flack (1983)
w = 1/[σ2(Fo2) + (0.0259P)2 + 0.2677P]
where P = (Fo2 + 2Fc2)/3
Absolute structure parameter: 0.01 (3)
Crystal data top
LiKB4O7V = 1197.8 (3) Å3
Mr = 201.28Z = 8
Orthorhombic, P212121Mo Kα radiation
a = 8.4915 (12) ŵ = 0.87 mm1
b = 11.1454 (13) ÅT = 293 K
c = 12.6558 (13) Å0.16 mm (radius)
Data collection top
RIGAKU AFC-5R
diffractometer
Rint = 0.033
13549 measured reflections3 standard reflections every 150 reflections
3487 independent reflections intensity decay: 4%
3342 reflections with F > 4σ(F)
Refinement top
R[F2 > 2σ(F2)] = 0.024Δρmax = 0.19 e Å3
wR(F2) = 0.055Δρmin = 0.27 e Å3
S = 1.12Absolute structure: Flack (1983)
3342 reflectionsAbsolute structure parameter: 0.01 (3)
236 parameters
Special details top

Experimental. The number of chemical formulas in the unit cell was determined to be eight for both crystals from the density measurement and lattice parameters. Weissenberg photographs were taken for space group determination and the non-centrosymmetric space group, P212121, was assigned to both crystals based on the systematic extinction, i.e., h00, 0k0 and 00 l reflections are absent at odd h, k and l,respectively. The crystal structures were solved using the direct method program SIR97 (Altomare, 1994) and the structural parameters were refined by SHELXL97 crystallographic software (Sheldrick, 1997).

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.

Refinement. Refinement of F2 against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F2, conventional R-factors R are based on F, with F set to zero for negative F2. The threshold expression of F2 > σ(F2) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F2 are statistically about twice as large as those based on F, and R-factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
K10.80757 (5)0.62347 (3)0.30141 (3)0.02424 (10)
K20.14117 (4)0.54328 (4)0.59747 (3)0.02168 (9)
B10.89264 (18)0.36599 (15)0.48874 (13)0.0090 (3)
B20.7082 (2)0.51670 (15)0.56554 (13)0.0108 (3)
B30.5150 (2)0.63624 (15)0.65814 (13)0.0109 (3)
B40.4948 (2)0.61801 (16)0.46273 (13)0.0127 (3)
B50.4423 (2)0.75218 (15)0.30763 (14)0.0121 (3)
B60.2794 (2)0.57237 (15)0.33415 (14)0.0116 (3)
B70.08840 (19)0.39616 (14)0.34085 (13)0.0090 (3)
B80.1572 (2)0.27084 (14)0.49550 (12)0.0087 (3)
Li10.4319 (3)0.3569 (3)0.3821 (2)0.0163 (6)
Li20.7600 (4)0.3306 (3)0.2998 (2)0.0212 (6)
O10.01048 (13)0.28548 (10)0.53693 (9)0.0118 (2)
O20.76089 (13)0.29504 (10)0.44590 (8)0.0113 (2)
O30.95888 (13)0.43721 (10)0.40457 (9)0.0136 (2)
O40.83425 (12)0.44373 (10)0.57531 (8)0.0122 (2)
O50.64988 (13)0.56550 (10)0.66018 (8)0.0142 (2)
O60.44191 (14)0.66384 (11)0.56678 (9)0.0163 (2)
O70.63568 (14)0.54263 (11)0.47334 (8)0.0161 (2)
O80.36794 (14)0.54105 (10)0.41977 (8)0.0151 (2)
O90.53240 (13)0.71772 (11)0.39267 (9)0.0163 (2)
O100.46795 (14)0.84825 (10)0.24945 (9)0.0134 (2)
O110.30894 (15)0.67984 (11)0.28246 (10)0.0188 (2)
O120.16686 (13)0.50085 (10)0.29274 (9)0.0146 (2)
O130.03543 (15)0.31903 (10)0.25193 (9)0.0174 (2)
O140.20173 (12)0.32249 (10)0.40197 (9)0.0121 (2)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
K10.0295 (2)0.01566 (16)0.02753 (19)0.00171 (15)0.01122 (16)0.00185 (14)
K20.01755 (16)0.02517 (18)0.02230 (17)0.00122 (14)0.00258 (14)0.00714 (15)
B10.0057 (7)0.0116 (7)0.0096 (7)0.0002 (5)0.0000 (5)0.0011 (6)
B20.0092 (7)0.0131 (7)0.0102 (7)0.0003 (6)0.0015 (6)0.0002 (6)
B30.0100 (7)0.0110 (7)0.0118 (7)0.0007 (6)0.0012 (6)0.0006 (6)
B40.0122 (8)0.0156 (8)0.0103 (7)0.0018 (6)0.0032 (6)0.0009 (6)
B50.0102 (7)0.0137 (7)0.0123 (7)0.0006 (6)0.0001 (6)0.0004 (6)
B60.0091 (7)0.0152 (7)0.0104 (7)0.0003 (6)0.0005 (6)0.0021 (6)
B70.0061 (6)0.0110 (7)0.0099 (6)0.0010 (5)0.0005 (5)0.0026 (5)
B80.0085 (7)0.0087 (6)0.0088 (6)0.0005 (5)0.0006 (5)0.0001 (5)
Li10.0169 (13)0.0181 (14)0.0138 (13)0.0022 (11)0.0051 (10)0.0024 (10)
Li20.0213 (15)0.0293 (15)0.0128 (13)0.0051 (12)0.0025 (11)0.0027 (12)
O10.0083 (5)0.0145 (5)0.0128 (5)0.0023 (4)0.0023 (4)0.0055 (4)
O20.0109 (5)0.0135 (5)0.0094 (5)0.0045 (4)0.0006 (4)0.0017 (4)
O30.0109 (5)0.0136 (5)0.0162 (5)0.0038 (4)0.0059 (4)0.0067 (4)
O40.0105 (5)0.0146 (5)0.0114 (5)0.0034 (4)0.0018 (4)0.0019 (4)
O50.0122 (5)0.0213 (6)0.0091 (4)0.0069 (4)0.0005 (4)0.0016 (4)
O60.0148 (5)0.0214 (6)0.0126 (5)0.0076 (5)0.0020 (4)0.0032 (4)
O70.0168 (5)0.0230 (6)0.0086 (4)0.0098 (5)0.0007 (4)0.0001 (4)
O80.0180 (5)0.0145 (5)0.0129 (5)0.0032 (4)0.0054 (4)0.0038 (4)
O90.0150 (5)0.0170 (5)0.0170 (6)0.0025 (4)0.0063 (5)0.0053 (5)
O100.0151 (6)0.0136 (5)0.0116 (5)0.0025 (4)0.0012 (4)0.0009 (4)
O110.0165 (5)0.0200 (6)0.0201 (6)0.0064 (5)0.0084 (5)0.0108 (5)
O120.0123 (5)0.0182 (5)0.0133 (5)0.0059 (4)0.0022 (4)0.0076 (4)
O130.0272 (7)0.0126 (5)0.0123 (5)0.0035 (5)0.0070 (5)0.0003 (4)
O140.0068 (4)0.0187 (5)0.0108 (5)0.0025 (4)0.0010 (4)0.0066 (4)
Geometric parameters (Å, º) top
B1—O1i1.4759 (19)Li1—O82.176 (3)
B1—O21.4734 (19)Li1—O10xi1.872 (3)
B1—O31.4426 (19)Li1—O142.007 (3)
B1—O41.4822 (19)Li1—Li22.989 (4)
B1—Li22.673 (3)Li1—K2vii3.820 (3)
B1—K2i3.2019 (17)Li1—K1xi4.037 (3)
B2—O41.3497 (19)Li2—O21.891 (3)
B2—O51.4057 (19)Li2—O32.454 (3)
B2—O71.3507 (19)Li2—O5xii2.247 (3)
B2—K1ii3.3720 (17)Li2—O10xi2.043 (3)
B3—O51.391 (2)Li2—O11xi2.062 (3)
B3—O61.348 (2)Li2—B5xi2.358 (4)
B3—O13iii1.357 (2)Li2—O13i2.420 (3)
B3—Li2ii2.646 (4)Li2—B3xii2.646 (4)
B3—K1iv3.2461 (17)K1—O32.7685 (11)
B4—O61.482 (2)K1—O4xii3.1937 (12)
B4—O71.468 (2)K1—O5xii2.7859 (12)
B4—O81.480 (2)K1—O6vi3.1150 (12)
B4—O91.457 (2)K1—O72.7707 (12)
B5—O91.375 (2)K1—O92.8102 (13)
B5—O101.318 (2)K1—O13v2.6427 (13)
B5—O111.426 (2)K1—B3vi3.2462 (17)
B5—Li2v2.358 (4)K1—Li23.289 (3)
B5—K2vi3.0810 (18)K1—O12i3.3449 (13)
B6—O81.3643 (19)K1—B43.3505 (18)
B6—O111.388 (2)K1—B2xii3.3719 (17)
B6—O121.350 (2)K2—O13.1740 (13)
B6—Li12.795 (3)K2—O3viii3.1231 (13)
B6—K2vii3.3299 (18)K2—O4viii2.8464 (12)
B7—O3viii1.4385 (19)K2—O62.9117 (14)
B7—O121.4751 (19)K2—O82.9609 (12)
B7—O131.486 (2)K2—O9iv2.8221 (13)
B7—O141.4828 (19)K2—O10iv2.7162 (12)
B7—K1viii3.5148 (17)K2—O12iii3.0010 (12)
B8—O11.3616 (19)K2—B5iv3.0811 (18)
B8—O2ix1.3653 (19)K2—B1viii3.2018 (17)
B8—O141.3695 (19)K2—B83.3021 (16)
Li1—O1x2.004 (3)K2—B6iii3.3299 (18)
O3—B1—O2108.64 (12)O7—K1—O950.27 (3)
O3—B1—O1i112.04 (12)O5xii—K1—O9130.85 (4)
O2—B1—O1i109.91 (12)O13v—K1—O6vi47.50 (3)
O3—B1—O4110.77 (13)O3—K1—O6vi98.52 (4)
O2—B1—O4109.37 (12)O7—K1—O6vi91.14 (4)
O1i—B1—O4106.07 (12)O5xii—K1—O6vi150.62 (4)
O4—B2—O7124.73 (14)O9—K1—O6vi78.46 (4)
O4—B2—O5115.75 (14)O13v—K1—O4xii98.90 (3)
O7—B2—O5119.50 (14)O3—K1—O4xii114.94 (3)
O6—B3—O13iii121.41 (14)O7—K1—O4xii115.39 (4)
O6—B3—O5121.64 (14)O5xii—K1—O4xii45.31 (3)
O13iii—B3—O5116.88 (14)O9—K1—O4xii98.18 (3)
O9—B4—O7108.27 (13)O6vi—K1—O4xii142.78 (3)
O9—B4—O8112.20 (12)O13v—K1—O12i82.44 (4)
O7—B4—O8107.16 (13)O3—K1—O12i44.42 (3)
O9—B4—O6110.13 (13)O7—K1—O12i111.93 (3)
O7—B4—O6111.27 (12)O5xii—K1—O12i63.37 (3)
O8—B4—O6107.80 (13)O9—K1—O12i157.61 (4)
O10—B5—O9124.88 (15)O6vi—K1—O12i89.68 (3)
O10—B5—O11117.79 (14)O4xii—K1—O12i102.63 (3)
O9—B5—O11117.31 (14)O10iv—K2—O9iv51.04 (3)
O12—B6—O8123.18 (14)O10iv—K2—O4viii75.40 (3)
O12—B6—O11117.04 (14)O9iv—K2—O4viii94.16 (3)
O8—B6—O11119.71 (14)O10iv—K2—O6111.39 (4)
O3viii—B7—O12108.97 (12)O9iv—K2—O681.80 (4)
O3viii—B7—O14112.32 (12)O4viii—K2—O6165.88 (3)
O12—B7—O14111.11 (12)O10iv—K2—O8153.85 (4)
O3viii—B7—O13112.16 (13)O9iv—K2—O8104.73 (3)
O12—B7—O13106.37 (12)O4viii—K2—O8121.15 (3)
O14—B7—O13105.74 (12)O6—K2—O848.10 (3)
O1—B8—O2ix116.45 (13)O10iv—K2—O12iii77.28 (3)
O1—B8—O14122.34 (13)O9iv—K2—O12iii107.22 (3)
O2ix—B8—O14121.17 (14)O4viii—K2—O12iii120.97 (3)
O10xi—Li1—O1x105.22 (14)O6—K2—O12iii73.09 (3)
O10xi—Li1—O14122.96 (16)O8—K2—O12iii105.72 (3)
O1x—Li1—O1496.25 (13)O10iv—K2—O3viii117.23 (4)
O10xi—Li1—O8110.91 (14)O9iv—K2—O3viii103.28 (3)
O1x—Li1—O8135.90 (15)O4viii—K2—O3viii47.28 (3)
O14—Li1—O884.84 (11)O6—K2—O3viii120.34 (3)
O2—Li2—O10xi108.81 (16)O8—K2—O3viii74.06 (3)
O2—Li2—O11xi108.89 (16)O12iii—K2—O3viii148.31 (3)
O10xi—Li2—O11xi69.84 (11)O10iv—K2—O1112.69 (3)
O2—Li2—O5xii151.12 (18)O9iv—K2—O1138.65 (3)
O10xi—Li2—O5xii91.91 (12)O4viii—K2—O145.83 (3)
O5xii—Li2—B5xi89.18 (12)O6—K2—O1133.81 (3)
O2—Li2—O13i103.27 (14)O8—K2—O192.09 (3)
O10xi—Li2—O13i147.63 (15)O12iii—K2—O1103.91 (3)
O11xi—Li2—O13i95.99 (13)O3viii—K2—O145.20 (3)
B5xi—Li2—O13i122.66 (14)B8—O1—B1viii122.29 (12)
O2—Li2—O364.56 (10)B8x—O2—B1125.34 (12)
O10xi—Li2—O3140.40 (17)B7i—O3—B1122.49 (12)
O11xi—Li2—O3149.63 (17)B2—O4—B1123.34 (12)
B5xi—Li2—O3172.82 (16)B3—O5—B2119.60 (12)
Li1—Li2—K190.87 (10)B3—O6—B4122.95 (12)
O13v—K1—O3120.32 (4)B2—O7—B4124.97 (12)
O13v—K1—O7137.27 (4)B6—O8—B4122.99 (13)
O3—K1—O768.30 (3)B5—O9—B4124.55 (13)
O13v—K1—O5xii113.21 (4)B6—O11—B5121.76 (13)
O3—K1—O5xii71.07 (3)B6—O12—B7128.79 (13)
O7—K1—O5xii109.05 (4)B3vii—O13—B7123.06 (12)
O13v—K1—O9102.48 (4)B8—O14—B7120.30 (12)
O3—K1—O9118.19 (4)
Symmetry codes: (i) x+1, y, z; (ii) x+3/2, y+1, z+1/2; (iii) x+1/2, y+1, z+1/2; (iv) x1/2, y+3/2, z+1; (v) x+1, y+1/2, z+1/2; (vi) x+1/2, y+3/2, z+1; (vii) x+1/2, y+1, z1/2; (viii) x1, y, z; (ix) x1/2, y+1/2, z+1; (x) x+1/2, y+1/2, z+1; (xi) x+1, y1/2, z+1/2; (xii) x+3/2, y+1, z1/2.
(LRB4) top
Crystal data top
LiRbB4O7Dx = 2.637 Mg m3
Dm = 2.63 Mg m3
Dm measured by Archemedes method
Mr = 247.65Mo Kα radiation, λ = 0.71073 Å
Orthorhombic, P212121Cell parameters from 24 reflections
a = 8.6257 (12) Åθ = 12.3–16.3°
b = 11.2576 (13) ŵ = 7.92 mm1
c = 12.8531 (15) ÅT = 293 K
V = 1248.1 (3) Å3Sphere, colourless
Z = 80.16 mm (radius)
F(000) = 928
Data collection top
RIGAKU AFC-5R
diffractometer
Rint = 0.092
ω–2θ scansθmax = 30.0°
Absorption correction: for a sphere
International Tables for X-ray Crystallography Vol.II, Table 5.3.6B
h = 1212
Tmin = 0.184, Tmax = 0.255k = 1515
13091 measured reflectionsl = 1818
3597 independent reflections3 standard reflections every 150 reflections
3090 reflections with F > 4σ(F) intensity decay: 2%
Refinement top
Refinement on F2(Δ/σ)max = 0.001
R[F2 > 2σ(F2)] = 0.050Δρmax = 0.98 e Å3
wR(F2) = 0.075Δρmin = 0.65 e Å3
S = 1.20Extinction correction: SHELXL97 (Sheldrick, 1997), Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4
3090 reflectionsExtinction coefficient: 0.0237 (8)
236 parametersAbsolute structure: Flack (1983)
w = 1/[σ2(Fo2) + (0.014P)2]
where P = (Fo2 + 2Fc2)/3
Absolute structure parameter: 0.002 (11)
Crystal data top
LiRbB4O7V = 1248.1 (3) Å3
Mr = 247.65Z = 8
Orthorhombic, P212121Mo Kα radiation
a = 8.6257 (12) ŵ = 7.92 mm1
b = 11.2576 (13) ÅT = 293 K
c = 12.8531 (15) Å0.16 mm (radius)
Data collection top
RIGAKU AFC-5R
diffractometer
3090 reflections with F > 4σ(F)
Absorption correction: for a sphere
International Tables for X-ray Crystallography Vol.II, Table 5.3.6B
Rint = 0.092
Tmin = 0.184, Tmax = 0.2553 standard reflections every 150 reflections
13091 measured reflections intensity decay: 2%
3597 independent reflections
Refinement top
R[F2 > 2σ(F2)] = 0.050Δρmax = 0.98 e Å3
wR(F2) = 0.075Δρmin = 0.65 e Å3
S = 1.20Absolute structure: Flack (1983)
3090 reflectionsAbsolute structure parameter: 0.002 (11)
236 parameters
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.

Refinement. Refinement of F2 against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F2, conventional R-factors R are based on F, with F set to zero for negative F2. The threshold expression of F2 > σ(F2) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F2 are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Rb10.79945 (6)0.62459 (5)0.29148 (4)0.02087 (14)
Rb20.13857 (6)0.53825 (5)0.59969 (4)0.02138 (14)
B10.8781 (6)0.3600 (5)0.4836 (4)0.0087 (10)
B20.7012 (7)0.5166 (5)0.5571 (4)0.0109 (10)
B30.5118 (6)0.6323 (6)0.6510 (5)0.0144 (11)
B40.4866 (7)0.6143 (6)0.4590 (4)0.0146 (11)
B50.4353 (6)0.7491 (5)0.3059 (5)0.0129 (12)
B60.2669 (7)0.5742 (5)0.3374 (4)0.0136 (11)
B70.0757 (6)0.3984 (4)0.3379 (4)0.0086 (10)
B80.1432 (7)0.2738 (4)0.4912 (4)0.0096 (10)
Li10.4272 (11)0.3554 (8)0.3814 (7)0.019 (2)
Li20.7574 (11)0.3287 (9)0.3043 (8)0.021 (2)
O10.0033 (4)0.2839 (3)0.5311 (3)0.0114 (7)
O20.7468 (4)0.2872 (3)0.4487 (3)0.0117 (7)
O30.9356 (4)0.4233 (3)0.3942 (3)0.0170 (8)
O40.8252 (4)0.4422 (3)0.5666 (3)0.0135 (8)
O50.6496 (4)0.5681 (3)0.6501 (3)0.0154 (8)
O60.4376 (4)0.6583 (3)0.5614 (3)0.0164 (8)
O70.6255 (4)0.5381 (3)0.4677 (2)0.0163 (7)
O80.3620 (4)0.5393 (3)0.4167 (3)0.0172 (7)
O90.5231 (4)0.7143 (3)0.3902 (3)0.0156 (8)
O100.4660 (4)0.8392 (3)0.2457 (3)0.0132 (7)
O110.2990 (4)0.6803 (3)0.2852 (3)0.0178 (8)
O120.1462 (5)0.5096 (3)0.3030 (3)0.0245 (9)
O130.0426 (6)0.3292 (4)0.2426 (3)0.0312 (11)
O140.1867 (4)0.3259 (3)0.3997 (3)0.0124 (7)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Rb10.0269 (3)0.0148 (2)0.0210 (3)0.0021 (2)0.0082 (2)0.0016 (2)
Rb20.0172 (2)0.0245 (3)0.0225 (3)0.0030 (2)0.0037 (2)0.0082 (2)
B10.007 (2)0.007 (2)0.012 (2)0.0025 (19)0.0018 (19)0.000 (2)
B20.009 (2)0.010 (3)0.013 (2)0.000 (2)0.001 (2)0.003 (2)
B30.010 (3)0.017 (3)0.016 (3)0.003 (2)0.004 (2)0.001 (3)
B40.014 (3)0.020 (3)0.010 (3)0.002 (2)0.003 (2)0.003 (2)
B50.006 (2)0.018 (3)0.015 (3)0.003 (2)0.001 (2)0.004 (2)
B60.010 (3)0.019 (3)0.012 (3)0.001 (2)0.002 (2)0.004 (2)
B70.006 (2)0.007 (3)0.012 (3)0.0001 (19)0.000 (2)0.002 (2)
B80.012 (2)0.007 (2)0.009 (2)0.002 (2)0.001 (2)0.001 (2)
Li10.025 (5)0.025 (5)0.006 (4)0.005 (4)0.003 (4)0.002 (4)
Li20.022 (5)0.022 (5)0.020 (5)0.003 (4)0.003 (4)0.002 (4)
O10.0087 (16)0.0169 (19)0.0085 (17)0.0017 (14)0.0021 (14)0.0033 (14)
O20.0098 (16)0.0177 (18)0.0077 (16)0.0046 (13)0.0004 (13)0.0026 (14)
O30.0103 (16)0.0200 (18)0.0208 (18)0.0077 (14)0.0085 (17)0.0120 (16)
O40.0122 (18)0.0147 (18)0.0134 (16)0.0047 (14)0.0019 (13)0.0015 (14)
O50.0179 (18)0.0190 (18)0.0094 (16)0.0069 (16)0.0011 (15)0.0026 (14)
O60.0164 (18)0.021 (2)0.0121 (17)0.0052 (16)0.0009 (15)0.0025 (15)
O70.0175 (17)0.0224 (19)0.0090 (16)0.0096 (17)0.0018 (15)0.0007 (16)
O80.0232 (16)0.0125 (16)0.0160 (18)0.0004 (17)0.0101 (16)0.0044 (15)
O90.0108 (16)0.0203 (19)0.0156 (18)0.0023 (14)0.0073 (15)0.0042 (16)
O100.0151 (17)0.0172 (19)0.0073 (16)0.0032 (14)0.0044 (14)0.0036 (14)
O110.0147 (16)0.0191 (18)0.0196 (18)0.0082 (16)0.0057 (17)0.0124 (16)
O120.0228 (19)0.024 (2)0.027 (2)0.0109 (17)0.0069 (19)0.0182 (17)
O130.057 (3)0.021 (2)0.016 (2)0.018 (2)0.017 (2)0.0062 (17)
O140.0086 (15)0.0190 (17)0.0098 (15)0.0031 (13)0.0009 (15)0.0061 (14)
Geometric parameters (Å, º) top
B1—O1i1.468 (6)Li1—O82.193 (10)
B1—O21.468 (6)Li1—O10ix1.885 (9)
B1—O31.440 (6)Li1—O142.114 (10)
B1—O41.484 (6)Li1—Li23.031 (13)
B1—Li22.553 (11)Li1—Rb2vii3.856 (9)
B1—Rb2i3.362 (5)Li1—Rb1ix3.938 (10)
B2—O41.364 (6)Li2—O21.915 (10)
B2—O51.402 (6)Li2—O32.198 (10)
B2—O71.343 (6)Li2—O5xii2.433 (10)
B2—Rb1ii3.407 (5)Li2—O10ix2.035 (10)
B3—O51.391 (7)Li2—O11ix2.086 (10)
B3—O61.349 (7)Li2—B5ix2.360 (11)
B3—O13iii1.340 (7)Li2—O13i2.585 (11)
B3—Li2ii2.836 (11)Li2—B3xii2.836 (11)
B3—Rb1iv3.375 (6)Li2—Rb2xi4.431 (10)
B3—Rb1ii3.778 (6)Rb1—O32.874 (3)
B4—O61.468 (7)Rb1—O4xii3.175 (3)
B4—O71.478 (7)Rb1—O5xii2.864 (3)
B4—O81.472 (7)Rb1—O6vi3.312 (4)
B4—O91.466 (7)Rb1—O72.886 (3)
B5—O91.379 (7)Rb1—O92.883 (4)
B5—O101.303 (7)Rb1—O12i3.262 (4)
B5—O111.433 (6)Rb1—O13v2.712 (4)
B5—Li2v2.360 (11)Rb1—O14v3.345 (4)
B5—Rb2vi3.206 (6)Rb1—Li23.355 (10)
B6—O81.367 (6)Rb1—B3vi3.375 (6)
B6—O111.398 (6)Rb1—B2xii3.407 (5)
B6—O121.345 (7)Rb2—O13.236 (4)
B6—Rb2vii3.406 (6)Rb2—O3viii3.423 (4)
B7—O3viii1.437 (6)Rb2—O4viii2.942 (3)
B7—O121.462 (6)Rb2—O62.953 (4)
B7—O131.478 (7)Rb2—O83.041 (4)
B7—O141.488 (6)Rb2—O9iv2.961 (4)
B7—Rb1viii3.538 (5)Rb2—O10iv2.840 (4)
B7—Rb1ix3.664 (5)Rb2—B5iv3.206 (6)
B8—O11.369 (7)Rb2—O12iii3.251 (4)
B8—O2x1.367 (6)Rb2—B83.288 (5)
B8—O141.366 (6)Rb2—B1viii3.362 (5)
Li1—O1xi2.021 (10)Rb2—B6iii3.406 (6)
O3—B1—O2107.3 (4)O9—Rb1—O4xii101.75 (9)
O3—B1—O1i112.4 (4)O7—Rb1—O4xii117.30 (10)
O2—B1—O1i109.8 (4)O13v—Rb1—O12i83.33 (12)
O3—B1—O4111.8 (4)O5xii—Rb1—O12i65.64 (10)
O2—B1—O4109.3 (4)O3—Rb1—O12i44.90 (9)
O1i—B1—O4106.2 (4)O9—Rb1—O12i151.29 (10)
O7—B2—O4124.6 (5)O7—Rb1—O12i107.88 (10)
O7—B2—O5120.1 (4)O4xii—Rb1—O12i104.94 (9)
O4—B2—O5115.2 (4)O13v—Rb1—O6vi44.33 (11)
O13iii—B3—O6120.9 (5)O5xii—Rb1—O6vi150.01 (10)
O13iii—B3—O5118.3 (5)O3—Rb1—O6vi99.94 (10)
O6—B3—O5120.8 (5)O9—Rb1—O6vi77.75 (10)
O9—B4—O6110.1 (5)O7—Rb1—O6vi89.31 (10)
O9—B4—O8112.0 (4)O4xii—Rb1—O6vi144.73 (9)
O6—B4—O8108.3 (4)O12i—Rb1—O6vi86.39 (10)
O9—B4—O7108.5 (4)O13v—Rb1—O14v44.58 (10)
O6—B4—O7111.2 (4)O5xii—Rb1—O14v92.39 (9)
O8—B4—O7106.7 (4)O3—Rb1—O14v149.01 (9)
O10—B5—O9125.2 (5)O9—Rb1—O14v96.64 (9)
O10—B5—O11118.6 (5)O7—Rb1—O14v145.46 (9)
O9—B5—O11116.3 (5)O4xii—Rb1—O14v60.24 (9)
O12—B6—O8123.6 (5)O12i—Rb1—O14v105.62 (8)
O12—B6—O11117.3 (5)O6vi—Rb1—O14v84.64 (9)
O8—B6—O11119.0 (5)O10iv—Rb2—O4viii78.37 (10)
O3viii—B7—O12109.7 (4)O10iv—Rb2—O6110.61 (10)
O3viii—B7—O13110.9 (4)O4viii—Rb2—O6161.17 (10)
O12—B7—O13106.1 (4)O10iv—Rb2—O9iv48.40 (10)
O3viii—B7—O14112.2 (4)O4viii—Rb2—O9iv92.48 (10)
O12—B7—O14111.5 (4)O6—Rb2—O9iv82.56 (10)
O13—B7—O14106.1 (4)O10iv—Rb2—O8150.63 (10)
O2x—B8—O14121.5 (5)O4viii—Rb2—O8118.15 (9)
O2x—B8—O1115.7 (4)O6—Rb2—O846.83 (10)
O14—B8—O1122.7 (5)O8—Rb2—B5iv129.55 (13)
O10ix—Li1—O1xi105.2 (4)O10iv—Rb2—O1114.97 (10)
O10ix—Li1—O14124.1 (5)O4viii—Rb2—O144.60 (9)
O1xi—Li1—O1496.2 (4)O6—Rb2—O1133.61 (9)
O10ix—Li1—O8113.3 (5)O9iv—Rb2—O1135.82 (10)
O1xi—Li1—O8133.9 (5)B5iv—Rb2—O1123.85 (11)
O14—Li1—O882.7 (4)O10iv—Rb2—O12iii79.47 (10)
O2—Li2—O10ix106.0 (5)O4viii—Rb2—O12iii125.47 (10)
O2—Li2—O11ix109.1 (5)O6—Rb2—O12iii73.19 (10)
O10ix—Li2—O11ix69.6 (3)O9iv—Rb2—O12iii108.21 (10)
O2—Li2—O369.0 (3)B5iv—Rb2—O12iii97.57 (13)
O10ix—Li2—O3143.1 (5)B1viii—Rb2—B6iii109.65 (13)
O2—Li2—O5xii157.1 (5)O10iv—Rb2—O3viii117.09 (9)
O10ix—Li2—O5xii91.5 (4)O4viii—Rb2—O3viii43.89 (9)
O11ix—Li2—O5xii90.6 (4)O6—Rb2—O3viii119.43 (9)
O2—Li2—O13i110.1 (4)O9iv—Rb2—O3viii102.57 (10)
O10ix—Li2—O13i143.5 (5)O1—Rb2—O3viii42.42 (8)
O11ix—Li2—O13i93.1 (4)O12iii—Rb2—O3viii148.19 (9)
O13v—Rb1—O5xii117.64 (13)B8—O1—B1viii122.5 (4)
O13v—Rb1—O3122.61 (12)B8xi—O2—B1127.7 (4)
O5xii—Rb1—O368.37 (10)B7i—O3—B1126.6 (4)
O13v—Rb1—O9100.89 (13)B2—O4—B1124.0 (4)
O5xii—Rb1—O9132.17 (11)B3—O5—B2119.5 (4)
O3—Rb1—O9114.32 (10)B3—O6—B4123.7 (4)
O13v—Rb1—O7132.42 (12)B2—O7—B4124.2 (4)
O5xii—Rb1—O7108.78 (11)B6—O8—B4123.3 (4)
O3—Rb1—O765.52 (10)B5—O9—B4125.1 (4)
O9—Rb1—O748.93 (10)B6—O11—B5122.4 (4)
O13v—Rb1—O4xii102.95 (10)B6—O12—B7133.2 (4)
O5xii—Rb1—O4xii45.16 (9)B3vii—O13—B7128.7 (4)
O3—Rb1—O4xii111.72 (10)B8—O14—B7121.3 (4)
Symmetry codes: (i) x+1, y, z; (ii) x+3/2, y+1, z+1/2; (iii) x+1/2, y+1, z+1/2; (iv) x1/2, y+3/2, z+1; (v) x+1, y+1/2, z+1/2; (vi) x+1/2, y+3/2, z+1; (vii) x+1/2, y+1, z1/2; (viii) x1, y, z; (ix) x+1, y1/2, z+1/2; (x) x1/2, y+1/2, z+1; (xi) x+1/2, y+1/2, z+1; (xii) x+3/2, y+1, z1/2.

Experimental details

(LKB4)(LRB4)
Crystal data
Chemical formulaLiKB4O7LiRbB4O7
Mr201.28247.65
Crystal system, space groupOrthorhombic, P212121Orthorhombic, P212121
Temperature (K)293293
a, b, c (Å)8.4915 (12), 11.1454 (13), 12.6558 (13)8.6257 (12), 11.2576 (13), 12.8531 (15)
V3)1197.8 (3)1248.1 (3)
Z88
Radiation typeMo KαMo Kα
µ (mm1)0.877.92
Crystal size (mm)0.16 (radius)0.16 (radius)
Data collection
DiffractometerRIGAKU AFC-5R
diffractometer
RIGAKU AFC-5R
diffractometer
Absorption correctionFor a sphere
International Tables for X-ray Crystallography Vol.II, Table 5.3.6B
Tmin, Tmax0.184, 0.255
No. of measured, independent and
observed [F > 4σ(F)] reflections
13549, 3487, 3342 13091, 3597, 3090
Rint0.0330.092
(sin θ/λ)max1)0.7030.703
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.024, 0.055, 1.12 0.050, 0.075, 1.20
No. of reflections33423090
No. of parameters236236
No. of restraints??
Δρmax, Δρmin (e Å3)0.19, 0.270.98, 0.65
Absolute structureFlack (1983)Flack (1983)
Absolute structure parameter0.01 (3)0.002 (11)

Selected bond lengths (Å) for (LKB4) top
B1—O1i1.4759 (19)B8—O141.3695 (19)
B1—O21.4734 (19)Li1—O1v2.004 (3)
B1—O31.4426 (19)Li1—O82.176 (3)
B1—O41.4822 (19)Li1—O10vi1.872 (3)
B2—O41.3497 (19)Li1—O142.007 (3)
B2—O51.4057 (19)Li2—O21.891 (3)
B2—O71.3507 (19)Li2—O32.454 (3)
B3—O51.391 (2)Li2—O5vii2.247 (3)
B3—O61.348 (2)Li2—O10vi2.043 (3)
B3—O13ii1.357 (2)Li2—O11vi2.062 (3)
B4—O61.482 (2)Li2—O13i2.420 (3)
B4—O71.468 (2)K1—O32.7685 (11)
B4—O81.480 (2)K1—O4vii3.1937 (12)
B4—O91.457 (2)K1—O5vii2.7859 (12)
B5—O91.375 (2)K1—O6viii3.1150 (12)
B5—O101.318 (2)K1—O72.7707 (12)
B5—O111.426 (2)K1—O92.8102 (13)
B6—O81.3643 (19)K1—O13ix2.6427 (13)
B6—O111.388 (2)K2—O13.1740 (13)
B6—O121.350 (2)K2—O3iii3.1231 (13)
B7—O3iii1.4385 (19)K2—O4iii2.8464 (12)
B7—O121.4751 (19)K2—O62.9117 (14)
B7—O131.486 (2)K2—O82.9609 (12)
B7—O141.4828 (19)K2—O9x2.8221 (13)
B8—O11.3616 (19)K2—O10x2.7162 (12)
B8—O2iv1.3653 (19)K2—O12ii3.0010 (12)
Symmetry codes: (i) x+1, y, z; (ii) x+1/2, y+1, z+1/2; (iii) x1, y, z; (iv) x1/2, y+1/2, z+1; (v) x+1/2, y+1/2, z+1; (vi) x+1, y1/2, z+1/2; (vii) x+3/2, y+1, z1/2; (viii) x+1/2, y+3/2, z+1; (ix) x+1, y+1/2, z+1/2; (x) x1/2, y+3/2, z+1.
Selected bond lengths (Å) for (LRB4) top
B1—O1i1.468 (6)B8—O141.366 (6)
B1—O21.468 (6)Li1—O1v2.021 (10)
B1—O31.440 (6)Li1—O82.193 (10)
B1—O41.484 (6)Li1—O10vi1.885 (9)
B2—O41.364 (6)Li1—O142.114 (10)
B2—O51.402 (6)Li2—O21.915 (10)
B2—O71.343 (6)Li2—O32.198 (10)
B3—O51.391 (7)Li2—O5vii2.433 (10)
B3—O61.349 (7)Li2—O10vi2.035 (10)
B3—O13ii1.340 (7)Li2—O11vi2.086 (10)
B4—O61.468 (7)Li2—O13i2.585 (11)
B4—O71.478 (7)Rb1—O32.874 (3)
B4—O81.472 (7)Rb1—O4vii3.175 (3)
B4—O91.466 (7)Rb1—O5vii2.864 (3)
B5—O91.379 (7)Rb1—O6viii3.312 (4)
B5—O101.303 (7)Rb1—O72.886 (3)
B5—O111.433 (6)Rb1—O92.883 (4)
B6—O81.367 (6)Rb1—O13ix2.712 (4)
B6—O111.398 (6)Rb2—O13.236 (4)
B6—O121.345 (7)Rb2—O3iii3.423 (4)
B7—O3iii1.437 (6)Rb2—O4iii2.942 (3)
B7—O121.462 (6)Rb2—O62.953 (4)
B7—O131.478 (7)Rb2—O83.041 (4)
B7—O141.488 (6)Rb2—O9x2.961 (4)
B8—O11.369 (7)Rb2—O10x2.840 (4)
B8—O2iv1.367 (6)Rb2—O12ii3.251 (4)
Symmetry codes: (i) x+1, y, z; (ii) x+1/2, y+1, z+1/2; (iii) x1, y, z; (iv) x1/2, y+1/2, z+1; (v) x+1/2, y+1/2, z+1; (vi) x+1, y1/2, z+1/2; (vii) x+3/2, y+1, z1/2; (viii) x+1/2, y+3/2, z+1; (ix) x+1, y+1/2, z+1/2; (x) x1/2, y+3/2, z+1.
 

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