Thermo-physical properties of nonlinear optical crystal K₃B₆O₁₀Br

The thermo-physical properties of the nonlinear optical (NLO) crystal K₃B₆O₁₀Br (KBB) were experimentally investigated, including specific heat, thermal conductivity, coefficient of thermal expansion and refractive index. The specific heat of KBB is lower than that of LiB₃O₅ and higher than that of other borate NLO crystals, such as β-BaB₂O₄, CsLiB₆O₁₀ and CsB₃O₅, and KBB manifests a high damage threshold because of its lower temperature gradient during laser pulse irradiation. The thermal expansion coefficients were obtained as α_x = 5.09 × 10⁻⁶ K⁻¹ and α_z = 2.39 × 10⁻⁵ K⁻¹, showing weaker anisotropy than those of commonly used NLO crystals. The temperature-dependent Sellmeier dispersion equations of the refractive indices were also obtained, and the phase-matching angles for second harmonic generation (SHG) at temperatures of 313, 343, 373, 403 and 433 K which were calculated from these equations are in good agreement with the experimental values. All results are indicative of the KBB crystal as a novel promising NLO crystal for high power SHG.

Computing details

Program(s) used to solve structure: SHELXS97 (Sheldrick, 1990); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997).

(I)

Crystal data

B6BrK3O10	Dx = 2.670 Mg m^−3
Mr = 422.07	Mo Kα radiation, λ = 0.71073 Å
Trigonal, R3m	Cell parameters from 1535 reflections
a = 10.1252 (14) Å	θ = 3.3–24.9°
c = 8.8687 (18) Å	µ = 5.15 mm^−1
V = 787.4 (2) Å^3	T = 296 K
Z = 3	Block
F(000) = 606	0.1 × 0.08 × 0.07 mm

Data collection

CCD area detector diffractometer	338 reflections with I > 2σ(I)
Radiation source: fine-focus sealed tube	Rint = 0.035
Graphite monochromator	θmax = 25.0°, θmin = 3.3°
phi and ω scans	h = −9→12
1495 measured reflections	k = −12→8
340 independent reflections	l = −10→10

Refinement

Refinement on F^2	Secondary atom site location: difference Fourier map
Least-squares matrix: full	w = 1/[σ^2(Fo^2) + (0.0091P)^2] where P = (Fo^2 + 2Fc^2)/3
R[F^2 > 2σ(F^2)] = 0.019	(Δ/σ)max < 0.001
wR(F^2) = 0.045	Δρmax = 0.34 e Å^−3
S = 1.18	Δρmin = −0.56 e Å^−3
340 reflections	Extinction correction: SHELXL, Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
41 parameters	Extinction coefficient: 0.399 (17)
1 restraint	Absolute structure: Flack H D (1983), Acta Cryst. A39, 876-881
Primary atom site location: structure-invariant direct methods	Absolute structure parameter: −0.030 (12)

Special details

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds 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 > 2sigma(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 (Ų)

	x	y	z	Uiso*/Ueq
Br1	0.0000	0.0000	0.99502 (7)	0.0214 (4)
K1	0.18026 (6)	0.36051 (12)	0.88304 (12)	0.0157 (3)
O1	0.0000	0.0000	0.5512 (7)	0.0057 (11)
O2	0.44484 (16)	0.55516 (16)	1.0558 (4)	0.0108 (7)
O3	0.2327 (2)	0.2336 (2)	0.6246 (3)	0.0115 (6)
B1	0.0871 (2)	0.1741 (5)	0.5452 (6)	0.0072 (10)
B2	0.2997 (5)	0.1499 (2)	0.6611 (6)	0.0073 (11)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Br1	0.0199 (4)	0.0199 (4)	0.0243 (5)	0.0100 (2)	0.000	0.000
K1	0.0136 (5)	0.0188 (6)	0.0165 (6)	0.0094 (3)	−0.0021 (2)	−0.0043 (5)
O1	0.0062 (16)	0.0062 (16)	0.005 (2)	0.0031 (8)	0.000	0.000
O2	0.0135 (11)	0.0135 (11)	0.0092 (14)	0.0095 (14)	0.0012 (6)	−0.0012 (6)
O3	0.0087 (12)	0.0096 (12)	0.0151 (11)	0.0037 (10)	−0.0059 (8)	−0.0021 (8)
B1	0.0050 (16)	0.006 (2)	0.011 (3)	0.0030 (11)	0.0000 (9)	−0.0001 (17)
B2	0.006 (3)	0.0111 (18)	0.003 (2)	0.0031 (13)	0.002 (3)	0.0011 (13)

Geometric parameters (Å, º)

Br1—K1^i	3.3135 (12)	O1—B1	1.528 (4)
Br1—K1	3.3135 (12)	O1—B1^i	1.528 (4)
Br1—K1^ii	3.3135 (12)	O1—B1^ii	1.528 (4)
Br1—K1^iii	3.3258 (13)	O2—B2^iii	1.374 (6)
Br1—K1^iv	3.3258 (13)	O2—B1^xi	1.449 (6)
Br1—K1^v	3.3258 (13)	O2—K1^xii	2.851 (2)
K1—O3^iii	2.793 (2)	O3—B2	1.364 (3)
K1—O3^vi	2.793 (2)	O3—B1	1.465 (3)
K1—O3^vii	2.806 (3)	O3—K1^xiii	2.793 (2)
K1—O3	2.806 (3)	B1—O2^xiv	1.449 (6)
K1—O2	2.851 (2)	B1—O3^vii	1.465 (3)
K1—O2^viii	2.851 (2)	B2—O3^xv	1.364 (3)
K1—B2^iii	3.146 (3)	B2—O2^xiii	1.374 (6)
K1—B2^ix	3.146 (3)	B2—K1^xiii	3.146 (3)
K1—Br1^x	3.3258 (13)	B2—K1^xvi	3.146 (3)
K1—B1	3.413 (5)	B2—K1^ii	3.531 (3)
K1—B2^i	3.531 (3)
K1^i—Br1—K1	111.42 (2)	O2—K1—B1	139.33 (7)
K1^i—Br1—K1^ii	111.42 (2)	O2^viii—K1—B1	139.33 (7)
K1—Br1—K1^ii	111.42 (2)	B2^iii—K1—B1	116.07 (9)
K1^i—Br1—K1^iii	161.26 (4)	B2^ix—K1—B1	116.07 (9)
K1—Br1—K1^iii	77.987 (9)	Br1—K1—B1	78.83 (8)
K1^ii—Br1—K1^iii	77.988 (9)	Br1^x—K1—B1	82.44 (8)
K1^i—Br1—K1^iv	77.987 (9)	O3^iii—K1—B2^i	135.24 (8)
K1—Br1—K1^iv	161.26 (4)	O3^vi—K1—B2^i	57.51 (10)
K1^ii—Br1—K1^iv	77.988 (9)	O3^vii—K1—B2^i	21.14 (9)
K1^iii—Br1—K1^iv	88.70 (3)	O3—K1—B2^i	66.84 (8)
K1^i—Br1—K1^v	77.987 (9)	O2—K1—B2^i	174.66 (9)
K1—Br1—K1^v	77.987 (9)	O2^viii—K1—B2^i	103.29 (10)
K1^ii—Br1—K1^v	161.26 (4)	B2^iii—K1—B2^i	157.66 (16)
K1^iii—Br1—K1^v	88.70 (3)	B2^ix—K1—B2^i	77.47 (3)
K1^iv—Br1—K1^v	88.70 (3)	Br1—K1—B2^i	70.61 (7)
O3^iii—K1—O3^vi	150.64 (11)	Br1^x—K1—B2^i	95.35 (6)
O3^iii—K1—O3^vii	124.33 (9)	B1—K1—B2^i	42.28 (8)
O3^vi—K1—O3^vii	75.79 (3)	B1—O1—B1^i	119.88 (4)
O3^iii—K1—O3	75.79 (3)	B1—O1—B1^ii	119.88 (4)
O3^vi—K1—O3	124.33 (9)	B1^i—O1—B1^ii	119.88 (4)
O3^vii—K1—O3	49.46 (9)	B2^iii—O2—B1^xi	130.6 (4)
O3^iii—K1—O2	49.49 (7)	B2^iii—O2—K1	89.11 (18)
O3^vi—K1—O2	119.97 (8)	B1^xi—O2—K1	116.73 (11)
O3^vii—K1—O2	157.68 (8)	B2^iii—O2—K1^xii	89.11 (18)
O3—K1—O2	115.35 (7)	B1^xi—O2—K1^xii	116.73 (11)
O3^iii—K1—O2^viii	119.97 (8)	K1—O2—K1^xii	109.25 (12)
O3^vi—K1—O2^viii	49.49 (7)	B2—O3—B1	124.8 (3)
O3^vii—K1—O2^viii	115.35 (7)	B2—O3—K1^xiii	91.8 (2)
O3—K1—O2^viii	157.68 (8)	B1—O3—K1^xiii	128.1 (2)
O2—K1—O2^viii	72.88 (12)	B2—O3—K1	111.0 (3)
O3^iii—K1—B2^iii	25.67 (8)	B1—O3—K1	101.46 (19)
O3^vi—K1—B2^iii	144.32 (10)	K1^xiii—O3—K1	96.52 (6)
O3^vii—K1—B2^iii	139.71 (10)	O2^xiv—B1—O3	110.7 (2)
O3—K1—B2^iii	91.25 (11)	O2^xiv—B1—O3^vii	110.7 (2)
O2—K1—B2^iii	25.90 (11)	O3—B1—O3^vii	106.5 (3)
O2^viii—K1—B2^iii	98.78 (10)	O2^xiv—B1—O1	109.2 (4)
O3^iii—K1—B2^ix	144.32 (10)	O3—B1—O1	109.8 (3)
O3^vi—K1—B2^ix	25.67 (8)	O3^vii—B1—O1	109.8 (3)
O3^vii—K1—B2^ix	91.24 (11)	O2^xiv—B1—K1	134.2 (3)
O3—K1—B2^ix	139.71 (10)	O3—B1—K1	53.67 (18)
O2—K1—B2^ix	98.78 (10)	O3^vii—B1—K1	53.67 (18)
O2^viii—K1—B2^ix	25.90 (11)	O1—B1—K1	116.6 (4)
B2^iii—K1—B2^ix	124.67 (17)	O3^xv—B2—O3	121.0 (4)
O3^iii—K1—Br1	81.07 (5)	O3^xv—B2—O2^xiii	119.3 (2)
O3^vi—K1—Br1	81.07 (5)	O3—B2—O2^xiii	119.3 (2)
O3^vii—K1—Br1	82.32 (5)	O3^xv—B2—K1^xiii	145.6 (3)
O3—K1—Br1	82.32 (5)	O3—B2—K1^xiii	62.55 (16)
O2—K1—Br1	114.20 (6)	O2^xiii—B2—K1^xiii	64.99 (15)
O2^viii—K1—Br1	114.20 (6)	O3^xv—B2—K1^xvi	62.55 (16)
B2^iii—K1—Br1	103.42 (6)	O3—B2—K1^xvi	145.6 (3)
B2^ix—K1—Br1	103.42 (6)	O2^xiii—B2—K1^xvi	64.99 (15)
O3^iii—K1—Br1^x	102.20 (5)	K1^xiii—B2—K1^xvi	95.29 (13)
O3^vi—K1—Br1^x	102.20 (5)	O3^xv—B2—K1^ii	47.9 (2)
O3^vii—K1—Br1^x	80.67 (5)	O3—B2—K1^ii	132.8 (3)
O3—K1—Br1^x	80.67 (5)	O2^xiii—B2—K1^ii	93.0 (2)
O2—K1—Br1^x	80.45 (6)	K1^xiii—B2—K1^ii	157.65 (16)
O2^viii—K1—Br1^x	80.45 (6)	K1^xvi—B2—K1^ii	77.23 (3)
B2^iii—K1—Br1^x	84.80 (8)	O3^xv—B2—K1	132.8 (3)
B2^ix—K1—Br1^x	84.80 (8)	O3—B2—K1	47.9 (2)
Br1—K1—Br1^x	161.26 (4)	O2^xiii—B2—K1	93.0 (2)
O3^iii—K1—B1	99.58 (6)	K1^xiii—B2—K1	77.23 (3)
O3^vi—K1—B1	99.58 (6)	K1^xvi—B2—K1	157.66 (16)
O3^vii—K1—B1	24.87 (4)	K1^ii—B2—K1	101.67 (13)
O3—K1—B1	24.87 (4)

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