Korean J. Crystallography Vol. 16, No. 2, pp.75~80, 2005 LiK 1 x Rb x (x = 0.1, 0.2) ½ ³aÁ½ aá½w bá yc aw» w x, bw» w w, cš w yw Structure Analysis of Mixed Crystals, LiK 1 x Rb x (x = 0.1, 0.2) Jin-Gyu Kim a, Youn Joong Kim a, Hae Jin Kim b and Il-Hwan Suh c a Division of Electron Microscopic Research, Korea Basic Science Institute, 52 Yeoeun-Dong, Yusung-Ku, Daejon 305-333, Korea b Frontier Research Laboratory, Korea Basic Science Institute, 52 Yeoeun-Dong, Yusung-Ku, Daejon 305-333, Korea c Department of Material Chemistry, Korea University, 208 Seochang, Chochiwon, Chung-nam 339-700, Korea LiK 1 Rb SO x x 4 (x = 0.1, 0.2) 313 K g. X- ray z w w œ P6 3 (#173) w. w e ƒ yw ƒƒ 3z z ewš Li w 3 x wš š, 6z z ewš K Rb ƒƒ 12 15 O š. K Rb (0.91 : 0.09), (0.77 : 0.23) y w ƒ k w. Abstract LiK 1 Rb SO x x 4 (x = 0.1, 0.2) crystals were grown by means of aqueous solution growth technique at 313 K. Structure analysis of them was carried out with space group P6 3 (#173) by X-ray diffraction. In these compounds, the Li and ions lying on the three-fold axes formed infinite three-dimensional network and K and Rb atoms located on the six-fold axes are coordinated by twelve and fifteen O atoms respectively. The most suitable stabilization was achieved when the occupancy factors of K and Rb atoms are (0.91 : 0.09), (0.77 : 0.23) respectively. 1. Double sulfate family LiA, A(= Li, Na, K, Rb, Cs), w ƒ y w š. family ü tetrahedral sulfate groups orientation dynamics ùkù š š. 1-3) K ƒ hexagonal axis ew 9 O š, sulfate tetrahedral group w O ƒ p 3 sixfold axis ewš š. 4) Sulfate group w w w wš, Fig. 1 ùkü hexagonal P6 3 trigonal P31c unit cell 75
76 ½ ³Á½ Á½w Á y w wz w single crystal X-ray z» w šwš w. 2. x 2-1. LiK 1 x Rb x w Fig. 1. Crystallographic structure of LiK. (a) Hexagonal structure with the P6 3 phase at room temperature. (b) Trigonal structure with the P31c phase. One of tetrahedral of is rotated about a basal axis (marked r and r') or any equivalent axis. ü wù sulfate group z w. wr 5), w LiK w e y w LiK 1 xrb x (x = 0.1, 0.2, 0.5) w ƒ š ƒ. 6) Raman scattering briefringence d w Rb ƒ LiK wù, ƒ w w. w LiK 0.9 Rb 0.1 w NMR m w 10% Rb ƒ w w LiK trigonal monoclinic ƒ 50 K û šw. w 7) ƒ w Rb ƒƒ e w e š K ey ù. w LiK 1 xrb x (x = 0.1, 0.2) LiK 0.9 Rb 0.1 Li 2 ÁH 2 O, K 2 (90%) Rb 2 (80%) yww w š, rp (ICP- AES) w d w LiK 0.9 Rb 0.1 Rb 9.4 mol% y w. XRD w w š, xk ƒx v xk š. LiK 0.8 Rb 0.2 w. 2-2. X-ray n w x Enraf-Nonius CAD4 diffractometer w š, 8) cell parameters data collection w orientation matrix w. X-ray z graphite-monochromated Mo-Kα radiation(λ = 0.71069 ç) w ω-2θ scan w, 4.5 < θ < 27.4 ü ƒƒ 164 o 316 w. w z ƒ w 3 z kw d w q w. k 3 z 5 d w w, z 1% ü w d. d z Lorentz polarization effects w z, psi-scan 9) ww. SHELXS v w g w w š, SHELXL- 9) 97 v w y w. p, Wycoff letter 2(a) site ew K Rb occupancy factors y w, ƒ ƒƒ 0.91K + 0.09Rb 0.77K + 0.23Rb w w. e y w, R 0.0448 0.0429.» w w
16«2y, 2005 LiK 1 xrb x (x = 0.1, 0.2) 77 Table 1. Summary of crystal data and structure refinement for LiK 1 xrb x (x = 0.1, 0.2) LiK 0.91 (x = 0.1) (x = 0.2) Crystal data Formular weight 146.27 152.23 Temperature 293(2) K 293(2) K Wavelength Mo Kα radiation, 0.71069 ç Mo Kα radiation, 0.71069 ç Crystal system Hexagonal Hexagonal Space group P6 3 P6 3 Unit cell dimensions a = 5.1463(5) ç, α =90 o a = 5.1656(5) ç, α =90 o b = 5.1463(5) ç, β =90 o c = 8.655(5) ç, γ = 120 o b = 5.1656(5) ç, β =90 o c = 8.6689(15) ç, γ = 120 o Volume 198.51(5) ç 3 200.33(4) ç 3 Z, Calculated density 2, 2.447 Mg/m 3 2, 2.529 Mg/m 3 Absorption coefficient 2.729 mm 1 4.194 mm 1 Crystal size 0.463 0.396 0.363 mm 0.33 0.297 0.297 mm Data Collection Diffractometer Enraf-Nonius CAD4 Enraf-Nonius CAD4 θ range for data collection 4.57~27.43 o 4.56~27.44 o Index ranges 1 <= h <= 5 0 <= h <= 6 0 <= k <= 6 6 <= k <= 5 0 <= l <= 11 11 <= l <= 11 Reflections collected/unique 164/158 (R int = 0.0311) 316/285 (R int = 0.0714) Completeness to θ = 100% 100% Absorption correction Psi-scan Psi-scan Max. and min. transmission 0.3794 and 0.5332 0.5335 and 0.6000 Used standard reflections 3 3 Intensity decay 1% 1% Refinement Refinement method Full-matrix least-squares on F 2 Full-matrix least-squares on F 2 Final R indices [I > 2σ(I)] R1 a = 0.0458, wr2 b = 0.1230 R1 a = 0.0429, wr2 b = 0.0791 R indices (all data) R1 a = 0.0465, wr2 b = 0.1240 R1 a = 0.0458, wr2 b = 0.0818 Weight w = 1/[σ 2 (F o2 ) + (0.0176P) 2 + 0.0000P], w = 1/[σ 2 (F o2 ) + (0.0176P) 2 + 0.0000P], where P = (F o2 + 2F c2 )/3 where P = (F o2 + 2F c2 )/3 Data/restraints/parameters 164/1/35 316/1/36 Goodness-of-fit on F 2 1.253 1.342 Extinction coefficient none none Largest diff. peak and hole 0.574 and 0.912 eç 3 1.407 and 0.815 eç 3 Atomic scattering factors from International Tables for Crystallography 10) a R1 = Σ F o F c /Σ F o, b wr 2 = [Σ[w(F o 2 F c2 ) 2 /Σ[w(F o2 ) 2 ] 1/2 Table 2. Atomic coordinates ( 10 4 ) and equivalent isotropic displacement parameters (Å 2 10 3 ) LiK 0.91 x y z S.O.F U(eq) x y z S.O.F U(eq) K 0 0 254(7) 0.91 20(2) 0 0 20(20) 0.77 21(3) Rb 0 0 270(140) 0.09 70(30) 0 0 60(20) 0.23 25(4) Li 3333 6667 2990(40) 1.0 30(7) 3333 6667 3160(20) 1.0 25(3) S 6667 3333 1809(3) 1.0 14(1) 6667 3333 2051(0) 1.0 13(1) O1 6667 3333 135(18) 1.0 46(4) 6667 3333 362(8) 1.0 44(2) O2 3960(20) 3440(20) 2370(20) 0.620 41(3) 4077(14) 3493(14) 2599(8) 0.525 36(2) O2' 4080(30) 640(30) 2400(30) 0.380 32(4) 4043(15) 573(13) 2613(8) 0.475 26(2) U(eq) is defined as one-third of the trace of the orthogonalized U ij tensor.
78 ½ ³Á½ Á½w Á y w wz Table 1 š, t Table 2 ùkü. 3. š» Li(1), K(1), Rb(1), S(1), O(2) 6 e» wš. Li, S, O1 3-z z ewš, K Rb 6-z z ewš. w O2 t w, O2' disordering w y ùkü (Table 2). Table 1 Table 2 ùkù, w LiK 11),12) LiK 1 xrb x w w, LiK Rb Fig. 2. View along the c-axis of LiK 0.91 using ORTEP diagram. Thermal ellipsoids are drawn at 30% probability. Table 3. Selected bond distances (Å) and angles ( o ) for LiK 1 xrb x LiK 0.91 K-O1 2.990(2) Rb-O1 2.991(15) K-O1 2.997(2) Rb-O1 3.004(3) K-O1 a 2.990(2) Rb-O1 a 2.991(15) K-O1 a 2.997(2) Rb-O1 a 3.004(3) K-O1 b 2.9903(17) Rb-O1 b 2.991(15) K-O1 b 2.997(2) Rb-O1 b 3.004(3) K-O2 c 2.816(17) Rb-O2 c 2.808(86) K-O2 c 2.877(15) Rb-O2 c 2.833(22) K-O2 d 2.816(17) Rb-O2 d 2.808(86) K-O2 d 2.877(15) Rb-O2 d 2.833(22) K-O2 e 2.816(17) Rb-O2 e 2.808(86) K-O2 e 2.877(15) Rb-O2 e 2.833(22) K-O2 2.971(19) Rb-O2 2.979(89) K-O2 2.985(16) Rb-O2 3.031(24) K-O2 f 2.971(19) Rb-O2 f 2.979(89) K-O2 f 2.985(16) Rb-O2 f 3.031(24) K-O2 g 2.971(19) Rb-O2 g 2.979(89) K-O2 g 2.985(16) Rb-O2 g 3.031(24) K-O2' c 2.821(22) Rb-O2' c 2.814(87) K-O2' c 2.858(16) Rb-O2' c 2.814(22) K-O2' d 2.821(22) Rb-O2' d 2.814(87) K-O2' d 2.858(16) Rb-O2' d 2.814(22) K-O2' e 2.821(22) Rb-O2' e 2.814(87) K-O2' e 2.858(16) Rb-O2' e 2.814(22) K-O2' 3.014(24) Rb-O2' 3.021(91) K-O2' 2.983(16) Rb-O2' 3.030(24) K-O2' f 3.014(24) Rb-O2' f 3.021(91) K-O2' f 2.983(16) Rb-O2' f 3.030(24) K-O2' g 3.014(24) Rb-O2' g 3.021(91) K-O2' g 2.983(16) Rb-O2' g 3.030(24) S-O1 1.449(16) Li-O1 j 1.859(33) S-O1 1.464(7) Li-O1 j 1.911(13) S-O2 1.499(12) Li-O2 1.921(15) S-O2 1.460(6) Li-O2 1.923(7) S-O2 h 1.499(12) Li-O2 k 1.921(15) S-O2 h 1.460(6) Li-O2 k 1.923(7) S-O2 i 1.499(12) Li-O2 l 1.921(15) S-O2 i 1.460(6) Li-O2 l 1.923(7) S-O2' 1.451(15) Li-O2' f 1.952(17) S-O2' 1.475(6) Li-O2' f 1.921(7) S-O2' h 1.451(15) Li-O2' i 1.952(17) S-O2' h 1.475(6) Li-O2' i 1.921(7) S-O2' i 1.451(15) Li-O2' m 1.952(17) S-O2' i 1.475(6) Li-O2' m 1.921(7) O1-S-O2 108.7(8) O1 j -Li-O2 106.3(2) O1-S-O2 109.0(3) O1 j -Li-O2 104.6(6) O2-S-O2 h 110.2(8) O2-Li-O2 k 112.5(10) O2-S-O2 h 109.9(3) O2-Li-O2 k 113.9(4) O2 h -S-O2 i 110.2(8) O2 k -Li-O2 l 112.5(10) O2 h -S-O2 i 109.9(3) O2 k -Li-O2 l 113.9(4) O1-S-O2' 110.5(11) O1 j -Li-O2' f 105.2(13) O1-S-O2' 109.3(3) O1 j -Li-O2' f 105.2(13) O2'-S-O2' h 108.4(11) O2' f -Li-O2' h 113.4(11) O2'-S-O2' h 109.6(3) O2' f -Li-O2' h 104.2(5) O2' h -S-O2' i 108.4(11) O2' h -Li-O2' i 113.4(11) O2' h -S-O2' i 109.6(3) O2' h -Li-O2' i 104.2(5) Symmetry codes: (a) x 1, y 1, z; (b) x 1, y, z; (c) x, y, z 1/2; (d) y, x+y, z 1/2; (e) x y, x, z 1/ 2; (f) y, x y, z; (g) x+y, x, z; (h) y + 1, x y, z; (i) x+y+1, x + 1, z; (j) x + 1, y + 1, z + 1/2; (k) y + 1, x y + 1, z; (l) x+y, x + 1, z; (m) x, y + 1, z.
16«2y, 2005 LiK 1 xrb x (x = 0.1, 0.2) 79 e w, cell parameters w š, K e ey œ. K Rb t R w EXYZ constraint j š y ww» š. w w» w Fig. 2 13) ORTEP v w LiK 0.91 c- unit cell ùkü.» sulfate groups K r, Fig. 1 w P6 3 w e, K Rb 6 LiO 4 groups w. K 2.816(17) ç ~ 2.990(2) ç ü 12 O w š, Rb 2.808(86) ç ~ 3.021(91) ç ü 15 O w. w K 2.858(15) ç ~ 2.997(2) ç ü 15 w š, Rb w 2.833(22) ç ~ 3.031(24) ç ü 15 w š. w K O w sulfate tetrahedral group. ü w ¼ ƒ Table 3 ùkü. Fig. 3 tetrahedral LiO4 group ù kü. LiK 1 xrb x LiK ü O2 ƒ disordering. Rb ƒ unit cell y œ w w O2 anisotropic displacementƒ w. w tetrahedral ( wƒ 109.28 ) o w. LiK 0.91 ü w¼ wƒ r, S-O1 = 1.449(16) ç, S-O2 = 1.499(12) o ç š, O1-S-O2 = 108.7(8) o, O2-S-O2 = 110.2(8) p tetrahedral ƒ š. ƒ LiO 4 ü w¼ wƒ r Li- O1 = 1.859(33) ç, Li-O2 = 1.921 ç š o, O1-Li- O2 = 106.3(2) o, O2-Li-O2 = 112.5(10) p tetrahedral x wš. w ü w¼ wƒ r, S-O1 = 1.464(7) ç, S-O2 = 1.460(6) ç š o, O1-S-O2 = 109.0(3) o, O2-S-O2 = 109.9(3) tetrahederal x wš w¼ wƒ w tetrahedral x wš Fig. 3. ORTEP diagram of the tetrahedral group and LiO 4 group. Fig. 4. View of network of tetrahedral chain in the crystal. The O2' atoms are omitted for simplicity of the structure. The thermal ellipsoids are drawn to a scale of 50% probability.
80 ½ ³Á½ Á½w Á y w wz š, Li groups p tetrahedral x wš. sulfate groups K Rb coordination š w š. š Rb ƒ y k e wš š w. w yw ƒ þƒ x mw v w., Fig. 4 ü LiO 4 groups tetrahedral chain network [100] w ùkü. Tetrahedral chain š O w š. p, O1 [001] w S Li w tetrahedral group chain x w w wš, O2 O2' 3-z z e w [210], [110], [120] w tetrahedral groups w 3 network x wš. 4. LiK 1 xrb x (x = 0.1, 0.2) XRD» w ww,. 1) w LiK e w, Rb ƒ w cell parametersƒ y š. w Rb unit cell j wš K e ey w. 3) ƒ Rb ƒ O coordination y w tetrahedral sulfate groups» wš. 4) O1, O2 w LiO 4 tetrahedral groupsƒ chain 3 network x wš. š x 1) Cummins, H. Z., Phys. Rep., 185, 211 (1990). 2) Desért, A., Gibaud, A., Righi, A., Leitão, U. A. and Moreira, R. L., J. Phys.: Condens. Matter, 7, 8445 (1995). 3) Willis, F., Leisure, R. G. and Kanashiro, T., Phys. Rev. B, 54, 9077 (1996). 4) Tomaszewski, P. E. and Lukaszewicz, K., Phase Transit., 4, 37 (1983). 5) Bansal, M. L. and Roy, A. P., Phys. Rev. B, 30, 7307 (1984). 6) Moreira, R. L., Bourson, P., Leitao, U. A., Righi, A., Belo, L. C. M. and Pimenta, M. A., Phys. Rev. B, 52, 12591 (1995). 7) Kim, H. J., Jeong. D. Y., Zalar. B., Blinc, R. and Choh, S. H., Phys. Rev. B, 61, 9307 (2000). 8) Enraf-Nonius CAD4 Express software. Structure Determination Package, Enraf-Nonius, Delft The Netherlans (1994). 9) Sheldrick, G. M., SHELXS and SHELX-97, Program for the Refinement of Crystal Structures, University of Gottingen, Germany (1997). 10) International Tables for Crystallography, Vol. C, by Wilson, A. J. C., Kluwer Academic Publisher, Dordrecht, Netherlands (1995). 11) Karppinen, M., Lundgren, J. O. and Liminga, R., Acta Cryst., C39, 34 (1983). 12) Sandhya, B. T., Sequeira, A. and Chidambram, R., Acta Cryst., Sect., C40, 1648 (1984). 13) Burnett, M. N. and Johnson, C. K., ORTEP III, Oak Ridge National Lab. Tennessess, U.S.A. (1996).