Supporting information
Crystallographic Information File (CIF) https://doi.org/10.1107/S0108270104030525/bc1051sup1.cif | |
Structure factor file (CIF format) https://doi.org/10.1107/S0108270104030525/bc1051I_293_Ksup2.hkl | |
Structure factor file (CIF format) https://doi.org/10.1107/S0108270104030525/bc1051I_150_Ksup3.hkl | |
Structure factor file (CIF format) https://doi.org/10.1107/S0108270104030525/bc1051II_293_Ksup4.hkl | |
Structure factor file (CIF format) https://doi.org/10.1107/S0108270104030525/bc1051II_150_Ksup5.hkl |
Crystals of (I) and (II) originated from the same experiment intended to produce modified rubidium titanyl phosphate, RbTiOPO4 (RTP) (Thomas et al., 1992). They were obtained in a high-temperature solution growth experiment, with a 1:3:2:0.25 molar mixture of TiO2, RbCO3, NH4HPO4 and Yb2O3, for a total of 10 g in the batch. The chemicals were mixed carefully in a 35 ml platinum crucible and heated slowly to 1273 K for about 3 d. The melt was then kept at this temperature for 2 d and thereafter slowly cooled to 1023 K at 1.5 K h−1. The crystals were recovered by dissolving the flux in water.
The langbeinite crystals were easily separated from RTP on the basis of the difference in morphology. Fewer than 1% of the langbeinite crystals had a blue colour, indicating that Ti3+ should be present in these crystals, in agreement with the colour of K2Ti2(PO4)3 (Lunezheva et al., 1989). The reduction of Ti4+ to Ti3+ during growth means that some oxidation must have occurred, possibly of the platinum crucible, which appeared to be affected by the flux. Because of the very small amount of (II) available, it was not possible to verify the amount of Ti3+ present. This amount was calculated from the stoichiometric formula obtained during the crystallographic determination. Energy dispersive X-ray analysis (electro-scan S4–8DV equipped with a Link eX1 EDX system) was used in order to verify the atomic content of the crystals used for the structural work. The measurements indicated a Yb/Ti ratio close to 1:1 and a K/P ratio of 2:3 for (I), and a Yb/Ti ratio of about 1:5 for (II).
The data for (I) and (II) were collected with a laboratory Siemens diffractometer using Mo Kα radiation and at the Max II beamline 711 (Cerenius et al., 2000), respectively. Both data sets were normalized and corrected using SADABS within the SAINT-Plus program (Bruker, 1999). For (II), anomalous scattering factors for neutral atoms were taken from Sasaki (1989) and the linear absorption coefficient µ were calculated using mass attenuation coefficients from Sasaki (1990), both at wavelength 0.872 Å.
The DSC measurements were made on a Perkin–Elmer Pyris with a cooling rate of 10 K min−1 and a sample weight of 23.6 mg. The measurements were made on a mixture of (I) and (II), the latter present in an insignificant amount. An exothermic peak was observed at around 183 K with an approximate enthalpy change of 1.1 kJ mol−1.
The coordinates of (I) were used as starting points for the refinement of (II). The refinements of both (I) and (II) indicated mixed Yb/Ti populations of the two octahedral sites, as shown by M—O bonds longer than the Tiiv—O bond distance of 2.01 Å (Shannon, 1976). This difference was more pronounced for the M1 site. The exisitence of Yb/Ti mixing was also supported by the observation of excess electron density at both sites when 100% Ti occupancies were used. The displacement parameters of the M sites were kept equal to ensure a stable refinement. The rubidium cation occupancies were initially set to refine freely but remained near full occupancy and were fixed at 1.00. For (II), ionic scattering factors for Ti4+, Ti3+ and Yb3+ were tried but did not improve the model. Flack parameters of 0.021 (16) and 0.41 (3) were refined for (I) and (II), respectively, at room temperature. The twin refinement of (II) was performed using the WinGX program suite (Farrugia 1999). The low-temperature refinements were carried out in a similar way.
Data collection: SMART (Siemens, 1995) for I_293_K, I_150_K; SMART-NT (Bruker, 1998) for II_293_K, II_150_K. Cell refinement: SAINT (Siemens, 1995) for I_293_K; SAINT (Siemens, 1995) or SAINT-Plus? (Bruker, 1999) for I_150_K; SAINT-Plus (Bruker, 1999) for II_293_K, II_150_K. Data reduction: SAINT and SADABS (Sheldrick, 2001) for I_293_K; SAINT-Plus (Bruker, 1999) and SADABS (Sheldrick, 2001) for I_150_K; SMART-NT and SADABS (Sheldrick, 2001) for II_293_K; SAINT-Plus and SADABS (Sheldrick, 2001) for II_150_K. Program(s) used to solve structure: SHELXS97 (Sheldrick, 1997) for I_293_K; Coordinates from RA for I_150_K; Coordinates from (I) for II_293_K; Coordinates from (II) at 293K for II_150_K. For all compounds, program(s) used to refine structure: SHELXL97 (Sheldrick, 1997). Molecular graphics: ORTEP-3 for Windows (Farrugia, 1997) and DIAMOND (Brandenburg, 2000) for I_293_K; 'ORTEP-3 for Windows (Farrugia, 1997) and DIAMOND (Brandenburg, 2000)' for I_150_K, II_293_K, II_150_K. For all compounds, software used to prepare material for publication: WinGX (Farrugia, 1999).
Rb2YbTi(PO4)3 | Dx = 4.226 Mg m−3 |
Mr = 676.79 | Mo Kα radiation, λ = 0.71073 Å |
Cubic, P213 | Cell parameters from 7163 reflections |
Hall symbol: P_2ac_2ab_3 | θ = 2.8–33.0° |
a = 10.2083 (2) Å | µ = 19.09 mm−1 |
V = 1063.80 (4) Å3 | T = 293 K |
Z = 4 | Plate, colourless |
F(000) = 1228 | 0.07 × 0.06 × 0.05 mm |
Siemens SMART CCD diffractometer | 1338 independent reflections |
Radiation source: normal-focus sealed tube | 1326 reflections with F2 > 2σ(F2) |
Graphite monochromator | Rint = 0.053 |
ω scans | θmax = 33.1°, θmin = 2.8° |
Absorption correction: multi-scan (SADABS; Sheldrick 2001) | h = −15→15 |
Tmin = 0.257, Tmax = 0.385 | k = −15→15 |
19443 measured reflections | l = −15→15 |
Refinement on F2 | 8 constraints |
Least-squares matrix: full | w = 1/[σ2(Fo2) + (0.01P)2 + 7.1387P] where P = (Fo2 + 2Fc2)/3 |
R[F2 > 2σ(F2)] = 0.024 | (Δ/σ)max = 0.001 |
wR(F2) = 0.056 | Δρmax = 0.63 e Å−3 |
S = 1.24 | Δρmin = −1.35 e Å−3 |
1338 reflections | Absolute structure: Flack (1983) |
60 parameters | Absolute structure parameter: 0.021 (16) |
1 restraint |
Rb2YbTi(PO4)3 | Z = 4 |
Mr = 676.79 | Mo Kα radiation |
Cubic, P213 | µ = 19.09 mm−1 |
a = 10.2083 (2) Å | T = 293 K |
V = 1063.80 (4) Å3 | 0.07 × 0.06 × 0.05 mm |
Siemens SMART CCD diffractometer | 1338 independent reflections |
Absorption correction: multi-scan (SADABS; Sheldrick 2001) | 1326 reflections with F2 > 2σ(F2) |
Tmin = 0.257, Tmax = 0.385 | Rint = 0.053 |
19443 measured reflections |
R[F2 > 2σ(F2)] = 0.024 | 1 restraint |
wR(F2) = 0.056 | Δρmax = 0.63 e Å−3 |
S = 1.24 | Δρmin = −1.35 e Å−3 |
1338 reflections | Absolute structure: Flack (1983) |
60 parameters | Absolute structure parameter: 0.021 (16) |
Experimental. The data for (I) and (II) were collected with a laboratory Siemens diffractometer using Mo Kα radiation and at the Max II beamline 711 (Cerenius et al., 2000), respectively. Both data sets were normalized and corrected using SADABS within the SAINT-Plus program (Bruker, 1999). For (II), anomalous scattering factors for neutral atoms were taken from Sasaki (1989) and the linear absorption coefficient µ were calculated using mass attenuation coefficients from Sasaki (1990), both at wavelength 0.872 Å. The DSC measurements were made on a Perkin–Elmer Pyris with a cooling rate of 10 K min−1 and a sample weight of 23.6 mg. The measurements were made on a mixture of (I) and (II), the latter present in an insignificant amount. An exothermic peak was observed at around 183 K with an approximate enthalpy change of 1.1 kJ mol−1. |
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. Constraints used during the refinement: Equal Atomic Displacements parameters Ti1 Yb1 Equal Atomic Displacements parameters Ti2 Yb2 Equal Atomic coordinates Ti1 Yb1 Equal Atomic coordinates Ti2 Yb2 Occupancy of Ti1+Yb1 = 1.0 Occupancy of Ti2+Yb2 = 1.0 Restraints used: Occupancy Ti1 + Ti2 = 1.0 |
x | y | z | Uiso*/Ueq | Occ. (<1) | |
Rb1 | 0.42953 (5) | 0.57047 (5) | 1.07047 (5) | 0.02018 (16) | |
Rb2 | 0.20801 (5) | 0.79199 (5) | 1.29199 (5) | 0.02390 (19) | |
Yb1 | 0.08348 (2) | 0.58348 (2) | 0.91652 (2) | 0.00835 (10) | 0.6754 (17) |
Ti1 | 0.08348 (2) | 0.58348 (2) | 0.91652 (2) | 0.00835 (10) | 0.3246 (17) |
Yb2 | 0.35245 (4) | 0.85245 (4) | 0.64755 (4) | 0.00938 (16) | 0.3247 (17) |
Ti2 | 0.35245 (4) | 0.85245 (4) | 0.64755 (4) | 0.00938 (16) | 0.6753 (17) |
P | 0.26495 (13) | 0.87881 (12) | 0.95812 (13) | 0.0159 (2) | |
O1 | 0.4024 (5) | 0.8524 (5) | 1.0058 (4) | 0.0308 (9) | |
O2 | 0.1807 (5) | 0.7568 (5) | 0.9795 (5) | 0.0361 (12) | |
O3 | 0.2645 (5) | 0.9171 (5) | 0.8125 (5) | 0.0334 (10) | |
O4 | 0.2031 (5) | 0.9908 (5) | 1.0365 (6) | 0.0397 (13) |
U11 | U22 | U33 | U12 | U13 | U23 | |
Rb1 | 0.02018 (16) | 0.02018 (16) | 0.02018 (16) | 0.00167 (17) | 0.00167 (17) | −0.00167 (17) |
Rb2 | 0.02390 (19) | 0.02390 (19) | 0.02390 (19) | 0.00101 (19) | 0.00101 (19) | −0.00101 (19) |
Yb1 | 0.00835 (10) | 0.00835 (10) | 0.00835 (10) | −0.00094 (8) | 0.00094 (8) | 0.00094 (8) |
Ti1 | 0.00835 (10) | 0.00835 (10) | 0.00835 (10) | −0.00094 (8) | 0.00094 (8) | 0.00094 (8) |
Yb2 | 0.00938 (16) | 0.00938 (16) | 0.00938 (16) | 0.00015 (12) | −0.00015 (12) | −0.00015 (12) |
Ti2 | 0.00938 (16) | 0.00938 (16) | 0.00938 (16) | 0.00015 (12) | −0.00015 (12) | −0.00015 (12) |
P | 0.0181 (5) | 0.0124 (5) | 0.0173 (5) | −0.0003 (4) | −0.0007 (4) | −0.0012 (4) |
O1 | 0.030 (2) | 0.031 (2) | 0.031 (2) | 0.0086 (18) | −0.0062 (18) | −0.0006 (18) |
O2 | 0.043 (3) | 0.027 (2) | 0.039 (3) | −0.015 (2) | 0.005 (2) | −0.005 (2) |
O3 | 0.042 (3) | 0.030 (2) | 0.028 (2) | −0.002 (2) | −0.0082 (19) | 0.0151 (19) |
O4 | 0.031 (2) | 0.026 (2) | 0.062 (4) | 0.0076 (19) | −0.008 (2) | −0.021 (2) |
Rb1—O1 | 2.966 (5) | Yb1—Pii | 3.5155 (14) |
Rb1—O1i | 2.966 (5) | Yb1—Px | 3.5155 (14) |
Rb1—O1ii | 2.966 (5) | Yb1—Rb1xii | 3.8687 (3) |
Rb1—O4iii | 3.064 (5) | Yb2—O3 | 2.019 (6) |
Rb1—O4iv | 3.064 (5) | Yb2—O3xi | 2.019 (6) |
Rb1—O4v | 3.064 (5) | Yb2—O3iii | 2.019 (6) |
Rb1—O2iii | 3.153 (6) | Yb2—O4xiii | 2.041 (5) |
Rb1—O2iv | 3.153 (6) | Yb2—O4xiv | 2.041 (5) |
Rb1—O2v | 3.153 (6) | Yb2—O4xv | 2.041 (5) |
Rb1—O2i | 3.306 (6) | Yb2—P | 3.3048 (14) |
Rb1—O2 | 3.306 (6) | Yb2—Pxi | 3.3048 (14) |
Rb1—O2ii | 3.306 (6) | Yb2—Piii | 3.3048 (14) |
Rb2—O3vi | 2.990 (5) | Yb2—Rb1xvi | 3.8549 (11) |
Rb2—O3vii | 2.990 (5) | Yb2—Rb2xvii | 3.9660 (4) |
Rb2—O3viii | 2.990 (5) | P—O1 | 1.510 (5) |
Rb2—O2i | 3.222 (5) | P—O2 | 1.529 (5) |
Rb2—O2ii | 3.222 (5) | P—O4 | 1.532 (5) |
Rb2—O2 | 3.222 (5) | P—O3 | 1.537 (5) |
Rb2—O4i | 3.305 (6) | P—Rb1x | 3.4753 (15) |
Rb2—O4ii | 3.305 (6) | P—Yb1iv | 3.5155 (14) |
Rb2—O4 | 3.305 (6) | P—Rb2xiv | 3.7743 (15) |
Rb2—O4vi | 3.460 (6) | O1—Ti1iv | 2.115 (5) |
Rb2—O4vii | 3.460 (6) | O1—Yb1iv | 2.115 (5) |
Rb2—O4viii | 3.460 (6) | O2—Rb1x | 3.153 (6) |
Yb1—O1ix | 2.115 (5) | O3—Rb2xiv | 2.990 (5) |
Yb1—O1ii | 2.115 (5) | O3—Rb1x | 3.624 (5) |
Yb1—O1x | 2.115 (5) | O4—Ti2vi | 2.041 (5) |
Yb1—O2 | 2.128 (5) | O4—Yb2vi | 2.041 (5) |
Yb1—O2xi | 2.128 (5) | O4—Rb1x | 3.064 (5) |
Yb1—O2iii | 2.128 (5) | O4—Rb2xiv | 3.460 (6) |
Yb1—Pix | 3.5155 (14) | ||
O1—Rb1—O1i | 98.41 (12) | O1x—Yb1—Px | 11.86 (13) |
O1—Rb1—O1ii | 98.41 (12) | O2—Yb1—Px | 103.32 (15) |
O1i—Rb1—O1ii | 98.41 (12) | O2xi—Yb1—Px | 88.41 (14) |
O1—Rb1—O4iii | 99.34 (15) | O2iii—Yb1—Px | 166.37 (15) |
O1i—Rb1—O4iii | 150.75 (13) | Pix—Yb1—Px | 78.72 (3) |
O1ii—Rb1—O4iii | 101.77 (14) | Pii—Yb1—Px | 78.72 (3) |
O1—Rb1—O4iv | 101.77 (14) | O1ix—Yb1—Rb1 | 115.98 (13) |
O1i—Rb1—O4iv | 99.33 (15) | O1ii—Yb1—Rb1 | 49.42 (13) |
O1ii—Rb1—O4iv | 150.75 (13) | O1x—Yb1—Rb1 | 131.02 (13) |
O4iii—Rb1—O4iv | 54.26 (14) | O2—Yb1—Rb1 | 58.67 (16) |
O1—Rb1—O4v | 150.75 (13) | O2xi—Yb1—Rb1 | 129.02 (14) |
O1i—Rb1—O4v | 101.77 (13) | O2iii—Yb1—Rb1 | 54.54 (16) |
O1ii—Rb1—O4v | 99.34 (15) | Pix—Yb1—Rb1 | 110.19 (2) |
O4iii—Rb1—O4v | 54.26 (14) | Pii—Yb1—Rb1 | 60.78 (2) |
O4iv—Rb1—O4v | 54.26 (14) | Px—Yb1—Rb1 | 134.46 (2) |
O1—Rb1—O2iii | 85.63 (13) | O1ix—Yb1—Rb1xii | 49.42 (13) |
O1i—Rb1—O2iii | 158.23 (12) | O1ii—Yb1—Rb1xii | 131.02 (13) |
O1ii—Rb1—O2iii | 59.82 (12) | O1x—Yb1—Rb1xii | 115.98 (13) |
O4iii—Rb1—O2iii | 46.78 (12) | O2—Yb1—Rb1xii | 129.02 (14) |
O4iv—Rb1—O2iii | 100.76 (14) | O2xi—Yb1—Rb1xii | 54.54 (16) |
O4v—Rb1—O2iii | 83.44 (15) | O2iii—Yb1—Rb1xii | 58.67 (16) |
O1—Rb1—O2iv | 59.82 (12) | Pix—Yb1—Rb1xii | 60.78 (2) |
O1i—Rb1—O2iv | 85.63 (13) | Pii—Yb1—Rb1xii | 134.46 (2) |
O1ii—Rb1—O2iv | 158.23 (12) | Px—Yb1—Rb1xii | 110.19 (2) |
O4iii—Rb1—O2iv | 83.44 (15) | Rb1—Yb1—Rb1xii | 112.851 (6) |
O4iv—Rb1—O2iv | 46.78 (12) | O3—Yb2—O3xi | 92.69 (19) |
O4v—Rb1—O2iv | 100.76 (14) | O3—Yb2—O3iii | 92.69 (19) |
O2iii—Rb1—O2iv | 114.43 (7) | O3xi—Yb2—O3iii | 92.69 (19) |
O1—Rb1—O2v | 158.23 (12) | O3—Yb2—O4xiii | 86.3 (2) |
O1i—Rb1—O2v | 59.82 (12) | O3xi—Yb2—O4xiii | 172.5 (2) |
O1ii—Rb1—O2v | 85.63 (13) | O3iii—Yb2—O4xiii | 94.8 (2) |
O4iii—Rb1—O2v | 100.76 (14) | O3—Yb2—O4xiv | 94.8 (2) |
O4iv—Rb1—O2v | 83.44 (15) | O3xi—Yb2—O4xiv | 86.3 (2) |
O4v—Rb1—O2v | 46.78 (12) | O3iii—Yb2—O4xiv | 172.5 (2) |
O2iii—Rb1—O2v | 114.43 (7) | O4xiii—Yb2—O4xiv | 86.4 (2) |
O2iv—Rb1—O2v | 114.43 (7) | O3—Yb2—O4xv | 172.5 (2) |
O1—Rb1—O2i | 53.76 (12) | O3xi—Yb2—O4xv | 94.8 (2) |
O1i—Rb1—O2i | 46.17 (12) | O3iii—Yb2—O4xv | 86.3 (2) |
O1ii—Rb1—O2i | 112.95 (13) | O4xiii—Yb2—O4xv | 86.4 (2) |
O4iii—Rb1—O2i | 137.82 (15) | O4xiv—Yb2—O4xv | 86.4 (2) |
O4iv—Rb1—O2i | 96.09 (13) | O3—Yb2—P | 18.77 (13) |
O4v—Rb1—O2i | 135.86 (15) | O3xi—Yb2—P | 97.14 (13) |
O2iii—Rb1—O2i | 138.52 (9) | O3iii—Yb2—P | 74.31 (14) |
O2iv—Rb1—O2i | 55.61 (18) | O4xiii—Yb2—P | 84.26 (15) |
O2v—Rb1—O2i | 104.925 (14) | O4xiv—Yb2—P | 113.18 (16) |
O1—Rb1—O2 | 46.17 (12) | O4xv—Yb2—P | 157.62 (18) |
O1i—Rb1—O2 | 112.95 (13) | O3—Yb2—Pxi | 74.31 (14) |
O1ii—Rb1—O2 | 53.76 (12) | O3xi—Yb2—Pxi | 18.77 (13) |
O4iii—Rb1—O2 | 96.09 (13) | O3iii—Yb2—Pxi | 97.14 (13) |
O4iv—Rb1—O2 | 135.86 (15) | O4xiii—Yb2—Pxi | 157.62 (18) |
O4v—Rb1—O2 | 137.82 (15) | O4xiv—Yb2—Pxi | 84.26 (15) |
O2iii—Rb1—O2 | 55.61 (18) | O4xv—Yb2—Pxi | 113.18 (16) |
O2iv—Rb1—O2 | 104.925 (14) | P—Yb2—Pxi | 80.84 (4) |
O2v—Rb1—O2 | 138.52 (9) | O3—Yb2—Piii | 97.14 (13) |
O2i—Rb1—O2 | 86.30 (13) | O3xi—Yb2—Piii | 74.31 (14) |
O1—Rb1—O2ii | 112.95 (13) | O3iii—Yb2—Piii | 18.77 (13) |
O1i—Rb1—O2ii | 53.76 (12) | O4xiii—Yb2—Piii | 113.18 (16) |
O1ii—Rb1—O2ii | 46.17 (12) | O4xiv—Yb2—Piii | 157.62 (18) |
O4iii—Rb1—O2ii | 135.86 (15) | O4xv—Yb2—Piii | 84.26 (15) |
O4iv—Rb1—O2ii | 137.82 (15) | P—Yb2—Piii | 80.84 (4) |
O4v—Rb1—O2ii | 96.09 (13) | Pxi—Yb2—Piii | 80.84 (4) |
O2iii—Rb1—O2ii | 104.925 (14) | O3—Yb2—Rb1xvi | 123.34 (14) |
O2iv—Rb1—O2ii | 138.52 (9) | O3xi—Yb2—Rb1xvi | 123.34 (14) |
O2v—Rb1—O2ii | 55.61 (18) | O3iii—Yb2—Rb1xvi | 123.34 (14) |
O2i—Rb1—O2ii | 86.30 (13) | O4xiii—Yb2—Rb1xvi | 52.22 (14) |
O2—Rb1—O2ii | 86.30 (13) | O4xiv—Yb2—Rb1xvi | 52.22 (14) |
O3vi—Rb2—O3vii | 91.73 (13) | O4xv—Yb2—Rb1xvi | 52.22 (14) |
O3vi—Rb2—O3viii | 91.73 (13) | P—Yb2—Rb1xvi | 131.52 (2) |
O3vii—Rb2—O3viii | 91.73 (13) | Pxi—Yb2—Rb1xvi | 131.52 (2) |
O3vi—Rb2—O2i | 80.16 (14) | Piii—Yb2—Rb1xvi | 131.52 (2) |
O3vii—Rb2—O2i | 100.84 (13) | O3—Yb2—Rb2xvii | 130.45 (13) |
O3viii—Rb2—O2i | 165.17 (13) | O3xi—Yb2—Rb2xvii | 47.29 (13) |
O3vi—Rb2—O2ii | 165.17 (13) | O3iii—Yb2—Rb2xvii | 113.49 (13) |
O3vii—Rb2—O2ii | 80.16 (14) | O4xiii—Yb2—Rb2xvii | 129.22 (14) |
O3viii—Rb2—O2ii | 100.84 (13) | O4xiv—Yb2—Rb2xvii | 60.69 (18) |
O2i—Rb2—O2ii | 89.14 (15) | O4xv—Yb2—Rb2xvii | 56.34 (18) |
O3vi—Rb2—O2 | 100.84 (13) | P—Yb2—Rb2xvii | 142.20 (3) |
O3vii—Rb2—O2 | 165.17 (14) | Pxi—Yb2—Rb2xvii | 61.75 (2) |
O3viii—Rb2—O2 | 80.16 (14) | Piii—Yb2—Rb2xvii | 97.37 (2) |
O2i—Rb2—O2 | 89.14 (15) | Rb1xvi—Yb2—Rb2xvii | 77.062 (10) |
O2ii—Rb2—O2 | 89.14 (15) | O1—P—O2 | 109.3 (3) |
O3vi—Rb2—O4i | 82.41 (14) | O1—P—O4 | 110.3 (3) |
O3vii—Rb2—O4i | 56.41 (13) | O2—P—O4 | 107.6 (3) |
O3viii—Rb2—O4i | 147.16 (13) | O1—P—O3 | 111.1 (3) |
O2i—Rb2—O4i | 44.44 (12) | O2—P—O3 | 110.1 (3) |
O2ii—Rb2—O4i | 82.76 (12) | O4—P—O3 | 108.3 (3) |
O2—Rb2—O4i | 132.68 (13) | O1—P—Yb2 | 92.50 (19) |
O3vi—Rb2—O4ii | 147.16 (13) | O2—P—Yb2 | 102.9 (2) |
O3vii—Rb2—O4ii | 82.41 (14) | O4—P—Yb2 | 132.3 (2) |
O3viii—Rb2—O4ii | 56.41 (13) | O1—P—Rb1x | 165.8 (2) |
O2i—Rb2—O4ii | 132.68 (13) | O2—P—Rb1x | 65.1 (2) |
O2ii—Rb2—O4ii | 44.44 (12) | O4—P—Rb1x | 61.76 (19) |
O2—Rb2—O4ii | 82.76 (13) | O3—P—Rb1x | 83.0 (2) |
O4i—Rb2—O4ii | 119.16 (3) | Yb2—P—Rb1x | 101.41 (4) |
O3vi—Rb2—O4 | 56.41 (12) | O2—P—Yb1iv | 123.9 (2) |
O3vii—Rb2—O4 | 147.16 (13) | O4—P—Yb1iv | 96.26 (19) |
O3viii—Rb2—O4 | 82.41 (14) | O3—P—Yb1iv | 109.1 (2) |
O2i—Rb2—O4 | 82.76 (12) | Yb2—P—Yb1iv | 96.21 (3) |
O2ii—Rb2—O4 | 132.68 (13) | Rb1x—P—Yb1iv | 157.75 (4) |
O2—Rb2—O4 | 44.44 (12) | O1—P—Rb2 | 78.41 (19) |
O4i—Rb2—O4 | 119.16 (3) | O2—P—Rb2 | 64.5 (2) |
O4ii—Rb2—O4 | 119.16 (3) | O4—P—Rb2 | 67.6 (2) |
O3vi—Rb2—O4vi | 44.64 (13) | O3—P—Rb2 | 170.5 (2) |
O3vii—Rb2—O4vi | 50.35 (13) | Yb2—P—Rb2 | 160.03 (4) |
O3viii—Rb2—O4vi | 106.45 (12) | Rb1x—P—Rb2 | 87.52 (3) |
O2i—Rb2—O4vi | 76.43 (13) | Yb1iv—P—Rb2 | 80.22 (3) |
O2ii—Rb2—O4vi | 122.87 (12) | O1—P—Rb1 | 48.29 (19) |
O2—Rb2—O4vi | 143.94 (12) | O2—P—Rb1 | 61.6 (2) |
O4i—Rb2—O4vi | 48.72 (16) | O4—P—Rb1 | 130.7 (2) |
O4ii—Rb2—O4vi | 130.98 (10) | O3—P—Rb1 | 120.7 (2) |
O4—Rb2—O4vi | 100.35 (3) | Yb2—P—Rb1 | 95.97 (3) |
O3vi—Rb2—O4vii | 106.45 (12) | Rb1x—P—Rb1 | 126.33 (4) |
O3vii—Rb2—O4vii | 44.64 (13) | Yb1iv—P—Rb1 | 64.27 (2) |
O3viii—Rb2—O4vii | 50.35 (13) | Rb2—P—Rb1 | 64.67 (3) |
O2i—Rb2—O4vii | 143.94 (12) | O1—P—Rb2xiv | 103.6 (2) |
O2ii—Rb2—O4vii | 76.43 (13) | O2—P—Rb2xiv | 146.1 (2) |
O2—Rb2—O4vii | 122.87 (12) | O4—P—Rb2xiv | 66.4 (2) |
O4i—Rb2—O4vii | 100.35 (3) | O3—P—Rb2xiv | 48.7 (2) |
O4ii—Rb2—O4vii | 48.72 (17) | Yb2—P—Rb2xiv | 67.77 (2) |
O4—Rb2—O4vii | 130.98 (10) | Rb1x—P—Rb2xiv | 84.36 (3) |
O4vi—Rb2—O4vii | 83.96 (12) | Yb1iv—P—Rb2xiv | 89.91 (3) |
O3vi—Rb2—O4viii | 50.35 (13) | Rb2—P—Rb2xiv | 131.46 (4) |
O3vii—Rb2—O4viii | 106.45 (12) | Rb1—P—Rb2xiv | 148.49 (4) |
O3viii—Rb2—O4viii | 44.64 (13) | P—O1—Ti1iv | 151.4 (3) |
O2i—Rb2—O4viii | 122.87 (12) | P—O1—Yb1iv | 151.4 (3) |
O2ii—Rb2—O4viii | 143.94 (12) | P—O1—Rb1 | 109.4 (2) |
O2—Rb2—O4viii | 76.43 (13) | Ti1iv—O1—Rb1 | 97.78 (16) |
O4i—Rb2—O4viii | 130.98 (10) | Yb1iv—O1—Rb1 | 97.78 (16) |
O4ii—Rb2—O4viii | 100.35 (3) | P—O1—Rb2 | 77.2 (2) |
O4—Rb2—O4viii | 48.72 (16) | Ti1iv—O1—Rb2 | 103.39 (16) |
O4vi—Rb2—O4viii | 83.96 (12) | Yb1iv—O1—Rb2 | 103.39 (16) |
O4vii—Rb2—O4viii | 83.96 (12) | Rb1—O1—Rb2 | 72.74 (11) |
O1ix—Yb1—O1ii | 93.38 (18) | P—O2—Yb1 | 153.7 (3) |
O1ix—Yb1—O1x | 93.38 (18) | P—O2—Rb1x | 88.8 (2) |
O1ii—Yb1—O1x | 93.38 (18) | Yb1—O2—Rb1x | 92.10 (19) |
O1ix—Yb1—O2 | 174.2 (2) | P—O2—Rb2 | 90.1 (2) |
O1ii—Yb1—O2 | 84.5 (2) | Yb1—O2—Rb2 | 115.59 (19) |
O1x—Yb1—O2 | 92.1 (2) | Rb1x—O2—Rb2 | 99.68 (15) |
O1ix—Yb1—O2xi | 92.1 (2) | P—O2—Rb1 | 94.4 (2) |
O1ii—Yb1—O2xi | 174.2 (2) | Yb1—O2—Rb1 | 87.98 (17) |
O1x—Yb1—O2xi | 84.46 (19) | Rb1x—O2—Rb1 | 172.64 (18) |
O2—Yb1—O2xi | 90.24 (19) | Rb2—O2—Rb1 | 73.72 (12) |
O1ix—Yb1—O2iii | 84.46 (19) | P—O3—Yb2 | 136.2 (3) |
O1ii—Yb1—O2iii | 92.1 (2) | P—O3—Rb2xiv | 108.7 (3) |
O1x—Yb1—O2iii | 174.2 (2) | Yb2—O3—Rb2xiv | 102.97 (17) |
O2—Yb1—O2iii | 90.24 (19) | P—O3—Rb1x | 72.12 (19) |
O2xi—Yb1—O2iii | 90.24 (19) | Yb2—O3—Rb1x | 134.9 (2) |
O1ix—Yb1—Pix | 11.86 (13) | Rb2xiv—O3—Rb1x | 94.41 (14) |
O1ii—Yb1—Pix | 82.05 (13) | P—O4—Ti2vi | 171.8 (3) |
O1x—Yb1—Pix | 90.53 (13) | P—O4—Yb2vi | 171.8 (3) |
O2—Yb1—Pix | 166.37 (15) | P—O4—Rb1x | 92.1 (2) |
O2xi—Yb1—Pix | 103.32 (15) | Ti2vi—O4—Rb1x | 96.01 (17) |
O2iii—Yb1—Pix | 88.41 (14) | Yb2vi—O4—Rb1x | 96.01 (17) |
O1ix—Yb1—Pii | 90.53 (13) | P—O4—Rb2 | 87.0 (2) |
O1ii—Yb1—Pii | 11.86 (13) | Ti2vi—O4—Rb2 | 92.7 (2) |
O1x—Yb1—Pii | 82.05 (13) | Yb2vi—O4—Rb2 | 92.7 (2) |
O2—Yb1—Pii | 88.41 (14) | Rb1x—O4—Rb2 | 99.76 (16) |
O2xi—Yb1—Pii | 166.37 (15) | P—O4—Rb2xiv | 89.6 (3) |
O2iii—Yb1—Pii | 103.32 (15) | Ti2vi—O4—Rb2xiv | 88.35 (18) |
Pix—Yb1—Pii | 78.72 (3) | Yb2vi—O4—Rb2xiv | 88.35 (18) |
O1ix—Yb1—Px | 82.05 (13) | Rb1x—O4—Rb2xiv | 96.47 (15) |
O1ii—Yb1—Px | 90.53 (13) | Rb2—O4—Rb2xiv | 163.52 (17) |
Symmetry codes: (i) −z+3/2, −x+1, y+1/2; (ii) −y+1, z−1/2, −x+3/2; (iii) y−1/2, −z+3/2, −x+1; (iv) x+1/2, −y+3/2, −z+2; (v) z−1/2, −x+1/2, −y+2; (vi) −x+1/2, −y+2, z+1/2; (vii) −z+1, x+1/2, −y+5/2; (viii) y−1, z, x+1; (ix) z−1, x, y; (x) x−1/2, −y+3/2, −z+2; (xi) −z+1, x+1/2, −y+3/2; (xii) −x+1/2, −y+1, z−1/2; (xiii) −y+3/2, −z+2, x+1/2; (xiv) −x+1/2, −y+2, z−1/2; (xv) −z+3/2, −x+1, y−1/2; (xvi) −x+1, y+1/2, −z+3/2; (xvii) x, y, z−1. |
Rb2YbTi(PO4)3 | Dx = 4.222 Mg m−3 |
Mr = 676.79 | Mo Kα radiation, λ = 0.71073 Å |
Cubic, P213 | Cell parameters from 7527 reflections |
Hall symbol: P_2ac_2ab_3 | θ = 2.8–32.9° |
a = 10.2111 (2) Å | µ = 19.08 mm−1 |
V = 1064.68 (4) Å3 | T = 150 K |
Z = 4 | Plate, colourless |
F(000) = 1228 | 0.08 × 0.07 × 0.05 mm |
Siemens SMART CCD diffractometer | 1342 independent reflections |
Radiation source: normal-focus sealed tube | 1333 reflections with F2 > 2σ(F2) |
Graphite monochromator | Rint = 0.044 |
ω scans | θmax = 33.1°, θmin = 2.8° |
Absorption correction: multi-scan (SADABS; Sheldrick 2001) | h = −15→15 |
Tmin = 0.25, Tmax = 0.385 | k = −15→15 |
19497 measured reflections | l = −15→15 |
Refinement on F2 | 8 constraints |
Least-squares matrix: full | w = 1/[σ2(Fo2) + (0.01P)2 + 7.1387P] where P = (Fo2 + 2Fc2)/3 |
R[F2 > 2σ(F2)] = 0.023 | (Δ/σ)max = 0.001 |
wR(F2) = 0.054 | Δρmax = 0.71 e Å−3 |
S = 1.28 | Δρmin = −1.22 e Å−3 |
1342 reflections | Absolute structure: Flack (1983) |
60 parameters | Absolute structure parameter: 0.017 (15) |
1 restraint |
Rb2YbTi(PO4)3 | Z = 4 |
Mr = 676.79 | Mo Kα radiation |
Cubic, P213 | µ = 19.08 mm−1 |
a = 10.2111 (2) Å | T = 150 K |
V = 1064.68 (4) Å3 | 0.08 × 0.07 × 0.05 mm |
Siemens SMART CCD diffractometer | 1342 independent reflections |
Absorption correction: multi-scan (SADABS; Sheldrick 2001) | 1333 reflections with F2 > 2σ(F2) |
Tmin = 0.25, Tmax = 0.385 | Rint = 0.044 |
19497 measured reflections |
R[F2 > 2σ(F2)] = 0.023 | 1 restraint |
wR(F2) = 0.054 | Δρmax = 0.71 e Å−3 |
S = 1.28 | Δρmin = −1.22 e Å−3 |
1342 reflections | Absolute structure: Flack (1983) |
60 parameters | Absolute structure parameter: 0.017 (15) |
Experimental. The data for (I) and (II) were collected with a laboratory Siemens diffractometer using Mo Kα radiation and at the Max II beamline 711 (Cerenius et al., 2000), respectively. Both data sets were normalized and corrected using SADABS within the SAINT-Plus program (Bruker, 1999). For (II), anomalous scattering factors for neutral atoms were taken from Sasaki (1989) and the linear absorption coefficient µ were calculated using mass attenuation coefficients from Sasaki (1990), both at wavelength 0.872 Å. The DSC measurements were made on a Perkin–Elmer Pyris with a cooling rate of 10 K min−1 and a sample weight of 23.6 mg. The measurements were made on a mixture of (I) and (II), the latter present in an insignificant amount. An exothermic peak was observed at around 183 K with an approximate enthalpy change of 1.1 kJ mol−1. |
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. Constraints used during the refinement: Equal Atomic Displacements parameters Ti1 Yb1 Equal Atomic Displacements parameters Ti2 Yb2 Occupancy of Ti1+Yb1 = 1.0 Occupancy of Ti2+Yb2 = 1.0 Atomic positions Ti1 =Yb1 and Ti2 =Yb2 Restraints used: Occupancy Ti1 + Ti2 = 1.0 |
x | y | z | Uiso*/Ueq | Occ. (<1) | |
Rb1 | 0.42962 (4) | 0.57038 (4) | 1.07038 (4) | 0.01426 (14) | |
Rb2 | 0.20787 (5) | 0.79213 (5) | 1.29213 (5) | 0.01597 (15) | |
Yb1 | 0.08332 (2) | 0.58332 (2) | 0.91668 (2) | 0.00616 (9) | 0.6744 (17) |
Ti1 | 0.08332 (2) | 0.58332 (2) | 0.91668 (2) | 0.00616 (9) | 0.3256 (17) |
Yb2 | 0.35221 (4) | 0.85221 (4) | 0.64779 (4) | 0.00751 (16) | 0.3256 (17) |
Ti2 | 0.35221 (4) | 0.85221 (4) | 0.64779 (4) | 0.00751 (16) | 0.6744 (17) |
P | 0.26476 (13) | 0.87871 (12) | 0.95816 (13) | 0.0143 (2) | |
O1 | 0.4028 (4) | 0.8522 (4) | 1.0053 (4) | 0.0262 (8) | |
O2 | 0.1802 (5) | 0.7567 (5) | 0.9798 (5) | 0.0329 (11) | |
O3 | 0.2638 (5) | 0.9172 (5) | 0.8120 (5) | 0.0306 (9) | |
O4 | 0.2036 (5) | 0.9910 (5) | 1.0376 (6) | 0.0377 (12) |
U11 | U22 | U33 | U12 | U13 | U23 | |
Rb1 | 0.01426 (14) | 0.01426 (14) | 0.01426 (14) | 0.00142 (15) | 0.00142 (15) | −0.00142 (15) |
Rb2 | 0.01597 (15) | 0.01597 (15) | 0.01597 (15) | 0.00084 (15) | 0.00084 (15) | −0.00084 (15) |
Yb1 | 0.00616 (9) | 0.00616 (9) | 0.00616 (9) | −0.00081 (7) | 0.00081 (7) | 0.00081 (7) |
Ti1 | 0.00616 (9) | 0.00616 (9) | 0.00616 (9) | −0.00081 (7) | 0.00081 (7) | 0.00081 (7) |
Yb2 | 0.00751 (16) | 0.00751 (16) | 0.00751 (16) | 0.00029 (11) | −0.00029 (11) | −0.00029 (11) |
Ti2 | 0.00751 (16) | 0.00751 (16) | 0.00751 (16) | 0.00029 (11) | −0.00029 (11) | −0.00029 (11) |
P | 0.0171 (5) | 0.0102 (5) | 0.0155 (5) | −0.0003 (4) | −0.0007 (4) | −0.0006 (4) |
O1 | 0.028 (2) | 0.0252 (19) | 0.0253 (19) | 0.0096 (17) | −0.0056 (16) | −0.0005 (16) |
O2 | 0.040 (3) | 0.025 (2) | 0.034 (2) | −0.0139 (19) | 0.005 (2) | −0.0043 (19) |
O3 | 0.039 (2) | 0.026 (2) | 0.028 (2) | −0.003 (2) | −0.0108 (18) | 0.0151 (18) |
O4 | 0.025 (2) | 0.027 (2) | 0.061 (3) | 0.0068 (18) | −0.008 (2) | −0.025 (2) |
Rb1—O1i | 2.966 (4) | Yb1—Pii | 3.5163 (14) |
Rb1—O1ii | 2.966 (4) | Yb1—Px | 3.5163 (14) |
Rb1—O1 | 2.966 (4) | Yb1—Rb1xii | 3.8710 (3) |
Rb1—O4iii | 3.072 (5) | Yb2—O3 | 2.017 (5) |
Rb1—O4iv | 3.072 (5) | Yb2—O3xi | 2.017 (5) |
Rb1—O4v | 3.072 (5) | Yb2—O3iii | 2.017 (5) |
Rb1—O2v | 3.151 (6) | Yb2—O4xiii | 2.039 (4) |
Rb1—O2iii | 3.151 (6) | Yb2—O4xiv | 2.039 (4) |
Rb1—O2iv | 3.151 (6) | Yb2—O4xv | 2.039 (4) |
Rb1—O2i | 3.311 (6) | Yb2—P | 3.3037 (14) |
Rb1—O2ii | 3.311 (6) | Yb2—Piii | 3.3037 (14) |
Rb1—O2 | 3.311 (6) | Yb2—Pxi | 3.3037 (14) |
Rb2—O3vi | 2.989 (5) | Yb2—Rb1xvi | 3.8586 (10) |
Rb2—O3vii | 2.989 (5) | Yb2—Rb2xvii | 3.9671 (4) |
Rb2—O3viii | 2.989 (5) | P—O1 | 1.514 (4) |
Rb2—O2i | 3.222 (5) | P—O2 | 1.532 (5) |
Rb2—O2ii | 3.222 (5) | P—O4 | 1.536 (5) |
Rb2—O2 | 3.222 (5) | P—O3 | 1.543 (5) |
Rb2—O4i | 3.299 (6) | P—Rb1x | 3.4736 (14) |
Rb2—O4ii | 3.299 (6) | P—Yb1v | 3.5163 (14) |
Rb2—O4 | 3.299 (6) | P—Rb2xv | 3.7747 (14) |
Rb2—O4vi | 3.464 (6) | O1—Ti1v | 2.113 (4) |
Rb2—O4vii | 3.464 (6) | O1—Yb1v | 2.113 (4) |
Rb2—O4viii | 3.464 (6) | O2—Rb1x | 3.151 (6) |
Yb1—O1ix | 2.113 (4) | O3—Rb2xv | 2.989 (5) |
Yb1—O1ii | 2.113 (4) | O3—Rb1x | 3.620 (5) |
Yb1—O1x | 2.113 (4) | O4—Ti2vi | 2.039 (4) |
Yb1—O2 | 2.128 (5) | O4—Yb2vi | 2.039 (4) |
Yb1—O2iii | 2.128 (5) | O4—Rb1x | 3.072 (5) |
Yb1—O2xi | 2.128 (5) | O4—Rb2xv | 3.464 (6) |
Yb1—Pix | 3.5163 (14) | ||
O1i—Rb1—O1ii | 98.53 (11) | O1x—Yb1—Px | 11.97 (12) |
O1i—Rb1—O1 | 98.53 (11) | O2—Yb1—Px | 103.19 (15) |
O1ii—Rb1—O1 | 98.53 (11) | O2iii—Yb1—Px | 166.40 (14) |
O1i—Rb1—O4iii | 150.60 (12) | O2xi—Yb1—Px | 88.34 (14) |
O1ii—Rb1—O4iii | 101.63 (13) | Pix—Yb1—Px | 78.81 (3) |
O1—Rb1—O4iii | 99.38 (14) | Pii—Yb1—Px | 78.81 (3) |
O1i—Rb1—O4iv | 101.63 (13) | O1ix—Yb1—Rb1xii | 49.38 (12) |
O1ii—Rb1—O4iv | 99.38 (14) | O1ii—Yb1—Rb1xii | 130.89 (12) |
O1—Rb1—O4iv | 150.60 (12) | O1x—Yb1—Rb1xii | 116.16 (12) |
O4iii—Rb1—O4iv | 54.15 (14) | O2—Yb1—Rb1xii | 129.04 (13) |
O1i—Rb1—O4v | 99.38 (14) | O2iii—Yb1—Rb1xii | 58.73 (15) |
O1ii—Rb1—O4v | 150.60 (12) | O2xi—Yb1—Rb1xii | 54.42 (15) |
O1—Rb1—O4v | 101.63 (13) | Pix—Yb1—Rb1xii | 60.78 (2) |
O4iii—Rb1—O4v | 54.15 (14) | Pii—Yb1—Rb1xii | 134.54 (2) |
O4iv—Rb1—O4v | 54.15 (14) | Px—Yb1—Rb1xii | 110.19 (2) |
O1i—Rb1—O2v | 85.65 (12) | O1ix—Yb1—Rb1 | 116.16 (12) |
O1ii—Rb1—O2v | 158.19 (12) | O1ii—Yb1—Rb1 | 49.38 (12) |
O1—Rb1—O2v | 59.65 (12) | O1x—Yb1—Rb1 | 130.89 (12) |
O4iii—Rb1—O2v | 83.54 (14) | O2—Yb1—Rb1 | 58.73 (15) |
O4iv—Rb1—O2v | 100.72 (14) | O2iii—Yb1—Rb1 | 54.42 (15) |
O4v—Rb1—O2v | 46.87 (12) | O2xi—Yb1—Rb1 | 129.04 (13) |
O1i—Rb1—O2iii | 158.19 (12) | Pix—Yb1—Rb1 | 110.19 (2) |
O1ii—Rb1—O2iii | 59.65 (12) | Pii—Yb1—Rb1 | 60.78 (2) |
O1—Rb1—O2iii | 85.65 (12) | Px—Yb1—Rb1 | 134.54 (2) |
O4iii—Rb1—O2iii | 46.87 (12) | Rb1xii—Yb1—Rb1 | 112.811 (5) |
O4iv—Rb1—O2iii | 83.54 (14) | O3—Yb2—O3xi | 92.79 (18) |
O4v—Rb1—O2iii | 100.72 (14) | O3—Yb2—O3iii | 92.79 (18) |
O2v—Rb1—O2iii | 114.47 (7) | O3xi—Yb2—O3iii | 92.79 (18) |
O1i—Rb1—O2iv | 59.65 (12) | O3—Yb2—O4xiii | 86.4 (2) |
O1ii—Rb1—O2iv | 85.65 (12) | O3xi—Yb2—O4xiii | 172.9 (2) |
O1—Rb1—O2iv | 158.19 (12) | O3iii—Yb2—O4xiii | 94.3 (2) |
O4iii—Rb1—O2iv | 100.72 (14) | O3—Yb2—O4xiv | 172.9 (2) |
O4iv—Rb1—O2iv | 46.87 (12) | O3xi—Yb2—O4xiv | 94.3 (2) |
O4v—Rb1—O2iv | 83.54 (14) | O3iii—Yb2—O4xiv | 86.4 (2) |
O2v—Rb1—O2iv | 114.47 (7) | O4xiii—Yb2—O4xiv | 86.6 (2) |
O2iii—Rb1—O2iv | 114.47 (7) | O3—Yb2—O4xv | 94.3 (2) |
O1i—Rb1—O2i | 46.29 (12) | O3xi—Yb2—O4xv | 86.4 (2) |
O1ii—Rb1—O2i | 112.97 (13) | O3iii—Yb2—O4xv | 172.9 (2) |
O1—Rb1—O2i | 53.71 (11) | O4xiii—Yb2—O4xv | 86.58 (19) |
O4iii—Rb1—O2i | 137.94 (15) | O4xiv—Yb2—O4xv | 86.58 (19) |
O4iv—Rb1—O2i | 135.86 (14) | O3—Yb2—P | 18.99 (12) |
O4v—Rb1—O2i | 96.23 (12) | O3xi—Yb2—P | 97.33 (13) |
O2v—Rb1—O2i | 55.62 (17) | O3iii—Yb2—P | 74.20 (13) |
O2iii—Rb1—O2i | 138.44 (9) | O4xiii—Yb2—P | 84.19 (14) |
O2iv—Rb1—O2i | 104.906 (13) | O4xiv—Yb2—P | 157.77 (17) |
O1i—Rb1—O2ii | 53.71 (11) | O4xv—Yb2—P | 112.94 (16) |
O1ii—Rb1—O2ii | 46.29 (12) | O3—Yb2—Piii | 97.33 (13) |
O1—Rb1—O2ii | 112.97 (13) | O3xi—Yb2—Piii | 74.20 (13) |
O4iii—Rb1—O2ii | 135.86 (14) | O3iii—Yb2—Piii | 18.99 (12) |
O4iv—Rb1—O2ii | 96.23 (12) | O4xiii—Yb2—Piii | 112.94 (16) |
O4v—Rb1—O2ii | 137.94 (14) | O4xiv—Yb2—Piii | 84.19 (14) |
O2v—Rb1—O2ii | 138.44 (9) | O4xv—Yb2—Piii | 157.77 (17) |
O2iii—Rb1—O2ii | 104.906 (12) | P—Yb2—Piii | 80.88 (3) |
O2iv—Rb1—O2ii | 55.62 (17) | O3—Yb2—Pxi | 74.20 (13) |
O2i—Rb1—O2ii | 86.19 (13) | O3xi—Yb2—Pxi | 18.99 (12) |
O1i—Rb1—O2 | 112.97 (13) | O3iii—Yb2—Pxi | 97.33 (13) |
O1ii—Rb1—O2 | 53.71 (11) | O4xiii—Yb2—Pxi | 157.77 (17) |
O1—Rb1—O2 | 46.29 (12) | O4xiv—Yb2—Pxi | 112.94 (16) |
O4iii—Rb1—O2 | 96.23 (12) | O4xv—Yb2—Pxi | 84.19 (14) |
O4iv—Rb1—O2 | 137.94 (15) | P—Yb2—Pxi | 80.88 (4) |
O4v—Rb1—O2 | 135.86 (14) | Piii—Yb2—Pxi | 80.88 (4) |
O2v—Rb1—O2 | 104.906 (12) | O3—Yb2—Rb1xvi | 123.27 (13) |
O2iii—Rb1—O2 | 55.62 (17) | O3xi—Yb2—Rb1xvi | 123.27 (13) |
O2iv—Rb1—O2 | 138.44 (9) | O3iii—Yb2—Rb1xvi | 123.27 (13) |
O2i—Rb1—O2 | 86.19 (13) | O4xiii—Yb2—Rb1xvi | 52.35 (13) |
O2ii—Rb1—O2 | 86.19 (13) | O4xiv—Yb2—Rb1xvi | 52.35 (13) |
O3vi—Rb2—O3vii | 92.02 (12) | O4xv—Yb2—Rb1xvi | 52.35 (13) |
O3vi—Rb2—O3viii | 92.02 (12) | P—Yb2—Rb1xvi | 131.50 (2) |
O3vii—Rb2—O3viii | 92.02 (12) | Piii—Yb2—Rb1xvi | 131.50 (2) |
O3vi—Rb2—O2i | 79.90 (14) | Pxi—Yb2—Rb1xvi | 131.50 (2) |
O3vii—Rb2—O2i | 100.80 (13) | O3—Yb2—Rb2xvii | 130.22 (13) |
O3viii—Rb2—O2i | 165.02 (13) | O3xi—Yb2—Rb2xvii | 47.21 (13) |
O3vi—Rb2—O2ii | 165.02 (13) | O3iii—Yb2—Rb2xvii | 113.79 (12) |
O3vii—Rb2—O2ii | 79.90 (13) | O4xiii—Yb2—Rb2xvii | 129.28 (14) |
O3viii—Rb2—O2ii | 100.80 (13) | O4xiv—Yb2—Rb2xvii | 56.14 (18) |
O2i—Rb2—O2ii | 89.17 (14) | O4xv—Yb2—Rb2xvii | 60.80 (18) |
O3vi—Rb2—O2 | 100.80 (13) | P—Yb2—Rb2xvii | 142.23 (3) |
O3vii—Rb2—O2 | 165.02 (13) | Piii—Yb2—Rb2xvii | 97.44 (2) |
O3viii—Rb2—O2 | 79.90 (13) | Pxi—Yb2—Rb2xvii | 61.76 (2) |
O2i—Rb2—O2 | 89.17 (14) | Rb1xvi—Yb2—Rb2xvii | 77.011 (9) |
O2ii—Rb2—O2 | 89.17 (14) | O1—P—O2 | 109.5 (3) |
O3vi—Rb2—O4i | 82.46 (13) | O1—P—O4 | 110.1 (3) |
O3vii—Rb2—O4i | 56.20 (12) | O2—P—O4 | 107.6 (3) |
O3viii—Rb2—O4i | 147.27 (12) | O1—P—O3 | 111.0 (3) |
O2i—Rb2—O4i | 44.60 (12) | O2—P—O3 | 110.1 (3) |
O2ii—Rb2—O4i | 82.56 (12) | O4—P—O3 | 108.5 (3) |
O2—Rb2—O4i | 132.83 (12) | O1—P—Yb2 | 92.23 (18) |
O3vi—Rb2—O4ii | 147.27 (12) | O2—P—Yb2 | 102.94 (19) |
O3vii—Rb2—O4ii | 82.46 (13) | O4—P—Yb2 | 132.6 (2) |
O3viii—Rb2—O4ii | 56.20 (12) | O1—P—Rb1x | 166.09 (18) |
O2i—Rb2—O4ii | 132.83 (12) | O2—P—Rb1x | 65.1 (2) |
O2ii—Rb2—O4ii | 44.60 (12) | O4—P—Rb1x | 62.12 (18) |
O2—Rb2—O4ii | 82.56 (12) | O3—P—Rb1x | 82.79 (19) |
O4i—Rb2—O4ii | 119.16 (3) | Yb2—P—Rb1x | 101.42 (4) |
O3vi—Rb2—O4 | 56.20 (12) | O2—P—Yb1v | 124.0 (2) |
O3vii—Rb2—O4 | 147.27 (12) | O4—P—Yb1v | 95.85 (18) |
O3viii—Rb2—O4 | 82.46 (13) | O3—P—Yb1v | 109.22 (19) |
O2i—Rb2—O4 | 82.56 (12) | Yb2—P—Yb1v | 96.18 (3) |
O2ii—Rb2—O4 | 132.83 (12) | Rb1x—P—Yb1v | 157.72 (4) |
O2—Rb2—O4 | 44.60 (12) | O1—P—Rb2 | 78.66 (18) |
O4i—Rb2—O4 | 119.16 (3) | O2—P—Rb2 | 64.49 (19) |
O4ii—Rb2—O4 | 119.16 (3) | O4—P—Rb2 | 67.3 (2) |
O3vi—Rb2—O4vi | 44.83 (12) | O3—P—Rb2 | 170.27 (19) |
O3vii—Rb2—O4vi | 50.31 (12) | Yb2—P—Rb2 | 160.04 (4) |
O3viii—Rb2—O4vi | 106.59 (12) | Rb1x—P—Rb2 | 87.53 (3) |
O2i—Rb2—O4vi | 76.53 (12) | Yb1v—P—Rb2 | 80.25 (3) |
O2ii—Rb2—O4vi | 122.68 (11) | O1—P—Rb1 | 48.30 (18) |
O2—Rb2—O4vi | 144.16 (11) | O2—P—Rb1 | 61.7 (2) |
O4i—Rb2—O4vi | 48.76 (16) | O4—P—Rb1 | 130.4 (2) |
O4ii—Rb2—O4vi | 130.91 (9) | O3—P—Rb1 | 120.8 (2) |
O4—Rb2—O4vi | 100.37 (2) | Yb2—P—Rb1 | 95.91 (3) |
O3vi—Rb2—O4vii | 106.59 (12) | Rb1x—P—Rb1 | 126.41 (4) |
O3vii—Rb2—O4vii | 44.83 (12) | Yb1v—P—Rb1 | 64.29 (2) |
O3viii—Rb2—O4vii | 50.31 (12) | Rb2—P—Rb1 | 64.74 (3) |
O2i—Rb2—O4vii | 144.16 (11) | O1—P—Rb2xv | 103.48 (19) |
O2ii—Rb2—O4vii | 76.53 (12) | O2—P—Rb2xv | 146.2 (2) |
O2—Rb2—O4vii | 122.68 (11) | O4—P—Rb2xv | 66.6 (2) |
O4i—Rb2—O4vii | 100.37 (2) | O3—P—Rb2xv | 48.66 (19) |
O4ii—Rb2—O4vii | 48.76 (16) | Yb2—P—Rb2xv | 67.80 (2) |
O4—Rb2—O4vii | 130.91 (9) | Rb1x—P—Rb2xv | 84.38 (3) |
O4vi—Rb2—O4vii | 83.86 (12) | Yb1v—P—Rb2xv | 89.80 (3) |
O3vi—Rb2—O4viii | 50.31 (12) | Rb2—P—Rb2xv | 131.41 (4) |
O3vii—Rb2—O4viii | 106.59 (12) | Rb1—P—Rb2xv | 148.39 (4) |
O3viii—Rb2—O4viii | 44.83 (12) | P—O1—Ti1v | 151.2 (3) |
O2i—Rb2—O4viii | 122.68 (11) | P—O1—Yb1v | 151.2 (3) |
O2ii—Rb2—O4viii | 144.16 (11) | P—O1—Rb1 | 109.3 (2) |
O2—Rb2—O4viii | 76.53 (12) | Ti1v—O1—Rb1 | 97.89 (15) |
O4i—Rb2—O4viii | 130.91 (9) | Yb1v—O1—Rb1 | 97.89 (15) |
O4ii—Rb2—O4viii | 100.37 (2) | P—O1—Rb2 | 76.94 (18) |
O4—Rb2—O4viii | 48.76 (16) | Ti1v—O1—Rb2 | 103.25 (15) |
O4vi—Rb2—O4viii | 83.86 (12) | Yb1v—O1—Rb2 | 103.25 (15) |
O4vii—Rb2—O4viii | 83.86 (12) | Rb1—O1—Rb2 | 72.72 (10) |
O1ix—Yb1—O1ii | 93.46 (16) | P—O2—Yb1 | 153.5 (3) |
O1ix—Yb1—O1x | 93.46 (16) | P—O2—Rb1x | 88.8 (2) |
O1ii—Yb1—O1x | 93.46 (16) | Yb1—O2—Rb1x | 92.27 (18) |
O1ix—Yb1—O2 | 174.4 (2) | P—O2—Rb2 | 90.1 (2) |
O1ii—Yb1—O2 | 84.53 (18) | Yb1—O2—Rb2 | 115.72 (18) |
O1x—Yb1—O2 | 91.85 (19) | Rb1x—O2—Rb2 | 99.74 (14) |
O1ix—Yb1—O2iii | 84.53 (18) | P—O2—Rb1 | 94.2 (2) |
O1ii—Yb1—O2iii | 91.85 (19) | Yb1—O2—Rb1 | 87.95 (17) |
O1x—Yb1—O2iii | 174.4 (2) | Rb1x—O2—Rb1 | 172.82 (17) |
O2—Yb1—O2iii | 90.34 (18) | Rb2—O2—Rb1 | 73.77 (12) |
O1ix—Yb1—O2xi | 91.85 (19) | P—O3—Yb2 | 135.8 (3) |
O1ii—Yb1—O2xi | 174.4 (2) | P—O3—Rb2xv | 108.5 (3) |
O1x—Yb1—O2xi | 84.53 (18) | Yb2—O3—Rb2xv | 103.11 (16) |
O2—Yb1—O2xi | 90.34 (18) | P—O3—Rb1x | 72.19 (19) |
O2iii—Yb1—O2xi | 90.34 (18) | Yb2—O3—Rb1x | 135.18 (19) |
O1ix—Yb1—Pix | 11.97 (12) | Rb2xv—O3—Rb1x | 94.53 (14) |
O1ii—Yb1—Pix | 81.99 (12) | P—O4—Ti2vi | 172.3 (3) |
O1x—Yb1—Pix | 90.73 (12) | P—O4—Yb2vi | 172.3 (3) |
O2—Yb1—Pix | 166.40 (14) | P—O4—Rb1x | 91.6 (2) |
O2iii—Yb1—Pix | 88.34 (14) | Ti2vi—O4—Rb1x | 95.94 (17) |
O2xi—Yb1—Pix | 103.19 (15) | Yb2vi—O4—Rb1x | 95.94 (17) |
O1ix—Yb1—Pii | 90.73 (12) | P—O4—Rb2 | 87.2 (2) |
O1ii—Yb1—Pii | 11.97 (12) | Ti2vi—O4—Rb2 | 93.0 (2) |
O1x—Yb1—Pii | 81.99 (12) | Yb2vi—O4—Rb2 | 93.0 (2) |
O2—Yb1—Pii | 88.34 (14) | Rb1x—O4—Rb2 | 99.74 (16) |
O2iii—Yb1—Pii | 103.19 (14) | P—O4—Rb2xv | 89.4 (3) |
O2xi—Yb1—Pii | 166.40 (14) | Ti2vi—O4—Rb2xv | 88.29 (18) |
Pix—Yb1—Pii | 78.81 (3) | Yb2vi—O4—Rb2xv | 88.29 (18) |
O1ix—Yb1—Px | 81.99 (12) | Rb1x—O4—Rb2xv | 96.23 (15) |
O1ii—Yb1—Px | 90.73 (12) | Rb2—O4—Rb2xv | 163.76 (16) |
Symmetry codes: (i) −z+3/2, −x+1, y+1/2; (ii) −y+1, z−1/2, −x+3/2; (iii) y−1/2, −z+3/2, −x+1; (iv) z−1/2, −x+1/2, −y+2; (v) x+1/2, −y+3/2, −z+2; (vi) −x+1/2, −y+2, z+1/2; (vii) −z+1, x+1/2, −y+5/2; (viii) y−1, z, x+1; (ix) z−1, x, y; (x) x−1/2, −y+3/2, −z+2; (xi) −z+1, x+1/2, −y+3/2; (xii) −x+1/2, −y+1, z−1/2; (xiii) −y+3/2, −z+2, x+1/2; (xiv) −z+3/2, −x+1, y−1/2; (xv) −x+1/2, −y+2, z−1/2; (xvi) −x+1, y+1/2, −z+3/2; (xvii) x, y, z−1. |
Rb2Yb0.32Ti1.68(PO4)3 | Dx = 3.664 Mg m−3 |
Mr = 591.07 | Synchrotron radiation, λ = 0.87200 Å |
Cubic, P213 | Cell parameters from 4133 reflections |
Hall symbol: P_2ac_2ab_3 | θ = 3.5–34.1° |
a = 10.2132 (2) Å | µ = 8.12 mm−1 |
V = 1065.33 (4) Å3 | T = 293 K |
Z = 4 | Plate, blue |
F(000) = 1096 | 0.04 × 0.04 × 0.01 mm |
Siemens SMART CCD diffractometer | 766 reflections with F2 > 2σ(F2) |
Graphite monochromator | Rint = 0.070 |
ω scan | θmax = 32.1°, θmin = 3.5° |
Absorption correction: multi-scan (SADABS; Sheldrick, 2001) | h = −11→12 |
Tmin = 0.75, Tmax = 0.96 | k = −11→11 |
2811 measured reflections | l = −12→7 |
771 independent reflections |
Refinement on F2 | 8 constraints |
Least-squares matrix: full | w = 1/[σ2(Fo2) + (0.0654P)2 + 5P] where P = (Fo2 + 2Fc2)/3 |
R[F2 > 2σ(F2)] = 0.044 | (Δ/σ)max < 0.001 |
wR(F2) = 0.118 | Δρmax = 0.98 e Å−3 |
S = 1.18 | Δρmin = −1.07 e Å−3 |
771 reflections | Absolute structure: Flack (1983) |
61 parameters | Absolute structure parameter: 0.41 (3) |
0 restraints |
Rb2Yb0.32Ti1.68(PO4)3 | Z = 4 |
Mr = 591.07 | Synchrotron radiation, λ = 0.87200 Å |
Cubic, P213 | µ = 8.12 mm−1 |
a = 10.2132 (2) Å | T = 293 K |
V = 1065.33 (4) Å3 | 0.04 × 0.04 × 0.01 mm |
Siemens SMART CCD diffractometer | 771 independent reflections |
Absorption correction: multi-scan (SADABS; Sheldrick, 2001) | 766 reflections with F2 > 2σ(F2) |
Tmin = 0.75, Tmax = 0.96 | Rint = 0.070 |
2811 measured reflections |
R[F2 > 2σ(F2)] = 0.044 | 0 restraints |
wR(F2) = 0.118 | Δρmax = 0.98 e Å−3 |
S = 1.18 | Δρmin = −1.07 e Å−3 |
771 reflections | Absolute structure: Flack (1983) |
61 parameters | Absolute structure parameter: 0.41 (3) |
Experimental. The data for (I) and (II) were collected with a laboratory Siemens diffractometer using Mo Kα radiation and at the Max II beamline 711 (Cerenius et al., 2000), respectively. Both data sets were normalized and corrected using SADABS within the SAINT-Plus program (Bruker, 1999). For (II), anomalous scattering factors for neutral atoms were taken from Sasaki (1989) and the linear absorption coefficient µ were calculated using mass attenuation coefficients from Sasaki (1990), both at wavelength 0.872 Å. The DSC measurements were made on a Perkin–Elmer Pyris with a cooling rate of 10 K min−1 and a sample weight of 23.6 mg. The measurements were made on a mixture of (I) and (II), the latter present in an insignificant amount. An exothermic peak was observed at around 183 K with an approximate enthalpy change of 1.1 kJ mol−1. |
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. Constraints used during the refinement: Equal Atomic Displacements parameters Ti1 Yb1 Equal Atomic Displacements parameters Ti2 Yb2 Occupancy of Ti1+Yb1 = 1.0 Occupancy of Ti2+Yb2 = 1.0 Atomic positions Ti1 =Yb1 and Ti2 =Yb2 |
x | y | z | Uiso*/Ueq | Occ. (<1) | |
Rb1 | 0.56997 (9) | 0.43003 (9) | −0.06997 (9) | 0.0193 (4) | |
Rb2 | 0.79226 (10) | 0.20774 (10) | −0.29226 (10) | 0.0230 (4) | |
Ti1 | 0.91655 (8) | 0.41655 (8) | 0.08345 (8) | 0.0081 (5) | 0.800 (6) |
Yb1 | 0.91655 (8) | 0.41655 (8) | 0.08345 (8) | 0.0081 (5) | 0.200 (6) |
Ti2 | 0.64711 (10) | 0.14711 (10) | 0.35289 (10) | 0.0110 (6) | 0.885 (5) |
Yb2 | 0.64711 (10) | 0.14711 (10) | 0.35289 (10) | 0.0110 (6) | 0.115 (5) |
P | 0.7354 (2) | 0.1214 (2) | 0.0408 (2) | 0.0170 (5) | |
O1 | 0.5962 (7) | 0.1475 (8) | −0.0048 (8) | 0.0350 (18) | |
O2 | 0.8172 (9) | 0.2420 (8) | 0.0208 (8) | 0.040 (2) | |
O3 | 0.7368 (9) | 0.0807 (8) | 0.1856 (8) | 0.0371 (19) | |
O4 | 0.7958 (8) | 0.0116 (9) | −0.0390 (10) | 0.044 (2) |
U11 | U22 | U33 | U12 | U13 | U23 | |
Rb1 | 0.0193 (4) | 0.0193 (4) | 0.0193 (4) | 0.0017 (3) | 0.0017 (3) | −0.0017 (3) |
Rb2 | 0.0230 (4) | 0.0230 (4) | 0.0230 (4) | 0.0004 (4) | 0.0004 (4) | −0.0004 (4) |
Ti1 | 0.0081 (5) | 0.0081 (5) | 0.0081 (5) | −0.0007 (3) | 0.0007 (3) | 0.0007 (3) |
Yb1 | 0.0081 (5) | 0.0081 (5) | 0.0081 (5) | −0.0007 (3) | 0.0007 (3) | 0.0007 (3) |
Ti2 | 0.0110 (6) | 0.0110 (6) | 0.0110 (6) | 0.0012 (4) | −0.0012 (4) | −0.0012 (4) |
Yb2 | 0.0110 (6) | 0.0110 (6) | 0.0110 (6) | 0.0012 (4) | −0.0012 (4) | −0.0012 (4) |
P | 0.0176 (10) | 0.0127 (10) | 0.0206 (11) | −0.0008 (7) | 0.0002 (8) | 0.0008 (8) |
O1 | 0.027 (4) | 0.040 (5) | 0.038 (4) | 0.010 (3) | −0.008 (3) | 0.005 (4) |
O2 | 0.058 (6) | 0.026 (4) | 0.035 (4) | −0.022 (4) | 0.008 (4) | −0.001 (3) |
O3 | 0.050 (5) | 0.029 (4) | 0.033 (4) | 0.002 (4) | −0.012 (3) | 0.018 (3) |
O4 | 0.034 (4) | 0.040 (5) | 0.060 (6) | 0.005 (4) | −0.005 (4) | −0.023 (4) |
Rb1—O1i | 2.974 (8) | Ti1—O2iii | 2.149 (8) |
Rb1—O1ii | 2.974 (8) | Ti1—Rb1xii | 3.8735 (6) |
Rb1—O1 | 2.974 (8) | Ti1—Rb1x | 3.8735 (6) |
Rb1—O4iii | 3.071 (8) | Ti2—O4xiii | 2.046 (8) |
Rb1—O4iv | 3.071 (8) | Ti2—O4xiv | 2.046 (8) |
Rb1—O4v | 3.071 (8) | Ti2—O4xv | 2.046 (8) |
Rb1—O2iii | 3.163 (9) | Ti2—O3xi | 2.054 (9) |
Rb1—O2v | 3.163 (9) | Ti2—O3 | 2.054 (9) |
Rb1—O2iv | 3.163 (9) | Ti2—O3iii | 2.054 (9) |
Rb1—O2i | 3.305 (9) | Ti2—Rb1xvi | 3.840 (2) |
Rb1—O2 | 3.305 (9) | Ti2—Rb2xvii | 3.9643 (8) |
Rb1—O2ii | 3.305 (9) | Ti2—Rb2xiv | 3.9643 (8) |
Rb2—O3vi | 2.969 (8) | Ti2—Rb2v | 3.9643 (8) |
Rb2—O3vii | 2.969 (8) | P—O2 | 1.503 (8) |
Rb2—O3viii | 2.969 (8) | P—O4 | 1.517 (8) |
Rb2—O2ii | 3.226 (8) | P—O1 | 1.519 (8) |
Rb2—O2i | 3.226 (8) | P—O3 | 1.536 (8) |
Rb2—O2 | 3.226 (8) | P—Rb1x | 3.470 (2) |
Rb2—O4i | 3.272 (10) | P—Yb1v | 3.516 (2) |
Rb2—O4ii | 3.272 (10) | P—Rb2xiv | 3.779 (2) |
Rb2—O4 | 3.272 (10) | O1—Yb1v | 2.107 (8) |
Rb2—O4vi | 3.490 (11) | O1—Ti1v | 2.107 (8) |
Rb2—O4vii | 3.490 (10) | O2—Rb1x | 3.163 (9) |
Rb2—O4viii | 3.490 (11) | O3—Rb2xiv | 2.969 (8) |
Ti1—O1ix | 2.107 (8) | O3—Rb1x | 3.604 (9) |
Ti1—O1ii | 2.107 (8) | O4—Yb2vi | 2.046 (8) |
Ti1—O1x | 2.107 (8) | O4—Ti2vi | 2.046 (8) |
Ti1—O2xi | 2.149 (8) | O4—Rb1x | 3.071 (8) |
Ti1—O2 | 2.149 (8) | O4—Rb2xiv | 3.490 (10) |
O1i—Rb1—O1ii | 98.6 (2) | O1x—Ti1—O2iii | 174.2 (3) |
O1i—Rb1—O1 | 98.6 (2) | O2xi—Ti1—O2iii | 89.8 (3) |
O1ii—Rb1—O1 | 98.6 (2) | O2—Ti1—O2iii | 89.8 (3) |
O1i—Rb1—O4iii | 150.9 (2) | O1ix—Ti1—Rb1xii | 49.5 (2) |
O1ii—Rb1—O4iii | 100.9 (2) | O1ii—Ti1—Rb1xii | 130.7 (2) |
O1—Rb1—O4iii | 99.5 (2) | O1x—Ti1—Rb1xii | 116.3 (2) |
O1i—Rb1—O4iv | 100.9 (2) | O2xi—Ti1—Rb1xii | 54.7 (3) |
O1ii—Rb1—O4iv | 99.5 (2) | O2—Ti1—Rb1xii | 128.6 (2) |
O1—Rb1—O4iv | 150.9 (2) | O2iii—Ti1—Rb1xii | 58.5 (2) |
O4iii—Rb1—O4iv | 54.7 (3) | O1ix—Ti1—Rb1 | 116.3 (2) |
O1i—Rb1—O4v | 99.5 (2) | O1ii—Ti1—Rb1 | 49.5 (2) |
O1ii—Rb1—O4v | 150.9 (2) | O1x—Ti1—Rb1 | 130.7 (2) |
O1—Rb1—O4v | 100.9 (2) | O2xi—Ti1—Rb1 | 128.6 (2) |
O4iii—Rb1—O4v | 54.7 (3) | O2—Ti1—Rb1 | 58.5 (2) |
O4iv—Rb1—O4v | 54.7 (3) | O2iii—Ti1—Rb1 | 54.7 (3) |
O1i—Rb1—O2iii | 158.6 (2) | Rb1xii—Ti1—Rb1 | 112.815 (18) |
O1ii—Rb1—O2iii | 59.9 (2) | O1ix—Ti1—Rb1x | 130.7 (2) |
O1—Rb1—O2iii | 85.5 (2) | O1ii—Ti1—Rb1x | 116.3 (2) |
O4iii—Rb1—O2iii | 46.1 (2) | O1x—Ti1—Rb1x | 49.5 (2) |
O4iv—Rb1—O2iii | 84.2 (2) | O2xi—Ti1—Rb1x | 58.5 (2) |
O4v—Rb1—O2iii | 100.4 (2) | O2—Ti1—Rb1x | 54.7 (3) |
O1i—Rb1—O2v | 85.5 (2) | O2iii—Ti1—Rb1x | 128.6 (2) |
O1ii—Rb1—O2v | 158.6 (2) | Rb1xii—Ti1—Rb1x | 112.815 (18) |
O1—Rb1—O2v | 59.9 (2) | Rb1—Ti1—Rb1x | 112.815 (18) |
O4iii—Rb1—O2v | 84.2 (2) | O4xiii—Ti2—O4xiv | 87.2 (3) |
O4iv—Rb1—O2v | 100.4 (2) | O4xiii—Ti2—O4xv | 87.2 (3) |
O4v—Rb1—O2v | 46.1 (2) | O4xiv—Ti2—O4xv | 87.2 (3) |
O2iii—Rb1—O2v | 114.33 (11) | O4xiii—Ti2—O3xi | 173.6 (4) |
O1i—Rb1—O2iv | 59.9 (2) | O4xiv—Ti2—O3xi | 86.5 (3) |
O1ii—Rb1—O2iv | 85.5 (2) | O4xv—Ti2—O3xi | 93.5 (3) |
O1—Rb1—O2iv | 158.6 (2) | O4xiii—Ti2—O3 | 86.5 (3) |
O4iii—Rb1—O2iv | 100.4 (2) | O4xiv—Ti2—O3 | 93.5 (3) |
O4iv—Rb1—O2iv | 46.1 (2) | O4xv—Ti2—O3 | 173.6 (4) |
O4v—Rb1—O2iv | 84.2 (2) | O3xi—Ti2—O3 | 92.9 (3) |
O2iii—Rb1—O2iv | 114.33 (11) | O4xiii—Ti2—O3iii | 93.5 (3) |
O2v—Rb1—O2iv | 114.33 (11) | O4xiv—Ti2—O3iii | 173.6 (4) |
O1i—Rb1—O2i | 45.9 (2) | O4xv—Ti2—O3iii | 86.5 (3) |
O1ii—Rb1—O2i | 113.0 (2) | O3xi—Ti2—O3iii | 92.9 (3) |
O1—Rb1—O2i | 54.1 (2) | O3—Ti2—O3iii | 92.9 (3) |
O4iii—Rb1—O2i | 138.8 (2) | O4xiii—Ti2—Rb1xvi | 52.8 (2) |
O4iv—Rb1—O2i | 135.0 (2) | O4xiv—Ti2—Rb1xvi | 52.8 (2) |
O4v—Rb1—O2i | 95.9 (2) | O4xv—Ti2—Rb1xvi | 52.8 (2) |
O2iii—Rb1—O2i | 138.71 (16) | O3xi—Ti2—Rb1xvi | 123.2 (2) |
O2v—Rb1—O2i | 55.9 (3) | O3—Ti2—Rb1xvi | 123.2 (2) |
O2iv—Rb1—O2i | 104.85 (2) | O3iii—Ti2—Rb1xvi | 123.2 (2) |
O1i—Rb1—O2 | 113.0 (2) | O4xiii—Ti2—Rb2xvii | 129.9 (2) |
O1ii—Rb1—O2 | 54.1 (2) | O4xiv—Ti2—Rb2xvii | 61.6 (3) |
O1—Rb1—O2 | 45.9 (2) | O4xv—Ti2—Rb2xvii | 55.5 (3) |
O4iii—Rb1—O2 | 95.9 (2) | O3xi—Ti2—Rb2xvii | 46.9 (2) |
O4iv—Rb1—O2 | 138.8 (2) | O3—Ti2—Rb2xvii | 130.2 (2) |
O4v—Rb1—O2 | 135.0 (2) | O3iii—Ti2—Rb2xvii | 113.7 (2) |
O2iii—Rb1—O2 | 55.9 (3) | Rb1xvi—Ti2—Rb2xvii | 77.19 (3) |
O2v—Rb1—O2 | 104.85 (2) | O4xiii—Ti2—Rb2xiv | 61.6 (3) |
O2iv—Rb1—O2 | 138.71 (16) | O4xiv—Ti2—Rb2xiv | 55.5 (3) |
O2i—Rb1—O2 | 86.2 (2) | O4xv—Ti2—Rb2xiv | 129.9 (2) |
O1i—Rb1—O2ii | 54.1 (2) | O3xi—Ti2—Rb2xiv | 113.7 (2) |
O1ii—Rb1—O2ii | 45.9 (2) | O3—Ti2—Rb2xiv | 46.9 (2) |
O1—Rb1—O2ii | 113.0 (2) | O3iii—Ti2—Rb2xiv | 130.2 (2) |
O4iii—Rb1—O2ii | 135.0 (2) | Rb1xvi—Ti2—Rb2xiv | 77.19 (3) |
O4iv—Rb1—O2ii | 95.9 (2) | Rb2xvii—Ti2—Rb2xiv | 115.230 (18) |
O4v—Rb1—O2ii | 138.8 (2) | O4xiii—Ti2—Rb2v | 55.5 (3) |
O2iii—Rb1—O2ii | 104.85 (2) | O4xiv—Ti2—Rb2v | 129.9 (2) |
O2v—Rb1—O2ii | 138.71 (16) | O4xv—Ti2—Rb2v | 61.6 (3) |
O2iv—Rb1—O2ii | 55.9 (3) | O3xi—Ti2—Rb2v | 130.2 (2) |
O2i—Rb1—O2ii | 86.2 (2) | O3—Ti2—Rb2v | 113.7 (2) |
O2—Rb1—O2ii | 86.2 (2) | O3iii—Ti2—Rb2v | 46.9 (2) |
O3vi—Rb2—O3vii | 91.8 (2) | Rb1xvi—Ti2—Rb2v | 77.19 (3) |
O3vi—Rb2—O3viii | 91.8 (2) | Rb2xvii—Ti2—Rb2v | 115.230 (18) |
O3vii—Rb2—O3viii | 91.8 (2) | Rb2xiv—Ti2—Rb2v | 115.230 (18) |
O3vi—Rb2—O2ii | 165.1 (2) | O2—P—O4 | 107.8 (5) |
O3vii—Rb2—O2ii | 80.3 (2) | O2—P—O1 | 109.6 (5) |
O3viii—Rb2—O2ii | 101.0 (2) | O4—P—O1 | 110.2 (5) |
O3vi—Rb2—O2i | 80.3 (2) | O2—P—O3 | 110.3 (5) |
O3vii—Rb2—O2i | 101.0 (2) | O4—P—O3 | 108.3 (5) |
O3viii—Rb2—O2i | 165.1 (2) | O1—P—O3 | 110.6 (5) |
O2ii—Rb2—O2i | 88.8 (2) | O2—P—Rb1x | 65.7 (4) |
O3vi—Rb2—O2 | 101.0 (2) | O4—P—Rb1x | 62.2 (3) |
O3vii—Rb2—O2 | 165.1 (2) | O1—P—Rb1x | 166.9 (3) |
O3viii—Rb2—O2 | 80.3 (2) | O3—P—Rb1x | 82.4 (3) |
O2ii—Rb2—O2 | 88.8 (2) | O2—P—Yb1v | 123.8 (4) |
O2i—Rb2—O2 | 88.8 (2) | O4—P—Yb1v | 95.8 (3) |
O3vi—Rb2—O4i | 82.1 (2) | O3—P—Yb1v | 109.1 (3) |
O3vii—Rb2—O4i | 56.9 (2) | Rb1x—P—Yb1v | 157.86 (8) |
O3viii—Rb2—O4i | 147.6 (2) | O2—P—Rb2 | 64.9 (3) |
O2ii—Rb2—O4i | 82.9 (2) | O4—P—Rb2 | 66.6 (4) |
O2i—Rb2—O4i | 44.1 (2) | O1—P—Rb2 | 79.4 (3) |
O2—Rb2—O4i | 132.1 (2) | O3—P—Rb2 | 170.0 (4) |
O3vi—Rb2—O4ii | 147.6 (2) | Rb1x—P—Rb2 | 87.64 (5) |
O3vii—Rb2—O4ii | 82.1 (2) | Yb1v—P—Rb2 | 80.42 (5) |
O3viii—Rb2—O4ii | 56.9 (2) | O2—P—Rb1 | 61.3 (4) |
O2ii—Rb2—O4ii | 44.1 (2) | O4—P—Rb1 | 129.9 (4) |
O2i—Rb2—O4ii | 132.1 (2) | O1—P—Rb1 | 48.6 (3) |
O2—Rb2—O4ii | 82.9 (2) | O3—P—Rb1 | 121.5 (3) |
O4i—Rb2—O4ii | 119.08 (5) | Rb1x—P—Rb1 | 126.62 (7) |
O3vi—Rb2—O4 | 56.9 (2) | Yb1v—P—Rb1 | 64.32 (4) |
O3vii—Rb2—O4 | 147.6 (2) | Rb2—P—Rb1 | 64.99 (5) |
O3viii—Rb2—O4 | 82.1 (2) | O2—P—Rb2xiv | 146.3 (4) |
O2ii—Rb2—O4 | 132.1 (2) | O4—P—Rb2xiv | 67.4 (4) |
O2i—Rb2—O4 | 82.9 (2) | O1—P—Rb2xiv | 103.0 (3) |
O2—Rb2—O4 | 44.1 (2) | O3—P—Rb2xiv | 47.6 (3) |
O4i—Rb2—O4 | 119.08 (5) | Rb1x—P—Rb2xiv | 84.28 (5) |
O4ii—Rb2—O4 | 119.08 (5) | Yb1v—P—Rb2xiv | 89.75 (5) |
O3vi—Rb2—O4vi | 44.1 (2) | Rb2—P—Rb2xiv | 131.54 (7) |
O3vii—Rb2—O4vi | 50.8 (2) | Rb1—P—Rb2xiv | 148.19 (7) |
O3viii—Rb2—O4vi | 106.2 (2) | P—O1—Yb1v | 151.3 (5) |
O2ii—Rb2—O4vi | 123.46 (19) | P—O1—Ti1v | 151.3 (5) |
O2i—Rb2—O4vi | 76.8 (2) | P—O1—Rb1 | 108.9 (4) |
O2—Rb2—O4vi | 143.65 (19) | Yb1v—O1—Rb1 | 97.9 (3) |
O4i—Rb2—O4vi | 49.2 (3) | Ti1v—O1—Rb1 | 97.9 (3) |
O4ii—Rb2—O4vi | 131.10 (17) | P—O1—Rb2 | 76.1 (3) |
O4—Rb2—O4vi | 100.41 (4) | Yb1v—O1—Rb2 | 103.1 (3) |
O3vi—Rb2—O4vii | 106.2 (2) | Ti1v—O1—Rb2 | 103.1 (3) |
O3vii—Rb2—O4vii | 44.1 (2) | Rb1—O1—Rb2 | 72.68 (18) |
O3viii—Rb2—O4vii | 50.8 (2) | P—O2—Ti1 | 154.5 (5) |
O2ii—Rb2—O4vii | 76.8 (2) | P—O2—Rb1x | 88.7 (4) |
O2i—Rb2—O4vii | 143.65 (19) | Ti1—O2—Rb1x | 91.6 (3) |
O2—Rb2—O4vii | 123.5 (2) | P—O2—Rb2 | 90.1 (4) |
O4i—Rb2—O4vii | 100.41 (4) | Ti1—O2—Rb2 | 115.0 (3) |
O4ii—Rb2—O4vii | 49.2 (3) | Rb1x—O2—Rb2 | 99.3 (2) |
O4—Rb2—O4vii | 131.10 (17) | P—O2—Rb1 | 95.1 (4) |
O4vi—Rb2—O4vii | 83.6 (2) | Ti1—O2—Rb1 | 87.8 (3) |
O3vi—Rb2—O4viii | 50.8 (2) | Rb1x—O2—Rb1 | 172.3 (3) |
O3vii—Rb2—O4viii | 106.2 (2) | Rb2—O2—Rb1 | 74.02 (19) |
O3viii—Rb2—O4viii | 44.1 (2) | P—O3—Ti2 | 135.0 (5) |
O2ii—Rb2—O4viii | 143.65 (19) | P—O3—Rb2xiv | 109.9 (4) |
O2i—Rb2—O4viii | 123.5 (2) | Ti2—O3—Rb2xiv | 102.7 (3) |
O2—Rb2—O4viii | 76.8 (2) | P—O3—Rb1x | 72.6 (3) |
O4i—Rb2—O4viii | 131.10 (17) | Ti2—O3—Rb1x | 134.7 (3) |
O4ii—Rb2—O4viii | 100.41 (4) | Rb2xiv—O3—Rb1x | 95.1 (2) |
O4—Rb2—O4viii | 49.2 (3) | P—O4—Yb2vi | 172.3 (6) |
O4vi—Rb2—O4viii | 83.6 (2) | P—O4—Ti2vi | 172.3 (6) |
O4vii—Rb2—O4viii | 83.6 (2) | P—O4—Rb1x | 91.9 (4) |
O1ix—Ti1—O1ii | 93.2 (3) | Yb2vi—O4—Rb1x | 95.1 (3) |
O1ix—Ti1—O1x | 93.2 (3) | Ti2vi—O4—Rb1x | 95.1 (3) |
O1ii—Ti1—O1x | 93.2 (3) | P—O4—Rb2 | 88.2 (4) |
O1ix—Ti1—O2xi | 92.3 (3) | Yb2vi—O4—Rb2 | 93.5 (3) |
O1ii—Ti1—O2xi | 174.2 (3) | Ti2vi—O4—Rb2 | 93.5 (3) |
O1x—Ti1—O2xi | 84.9 (3) | Rb1x—O4—Rb2 | 100.2 (3) |
O1ix—Ti1—O2 | 174.2 (3) | P—O4—Rb2xiv | 88.9 (4) |
O1ii—Ti1—O2 | 84.9 (3) | Yb2vi—O4—Rb2xiv | 87.4 (3) |
O1x—Ti1—O2 | 92.3 (3) | Ti2vi—O4—Rb2xiv | 87.4 (3) |
O2xi—Ti1—O2 | 89.8 (3) | Rb1x—O4—Rb2xiv | 95.6 (3) |
O1ix—Ti1—O2iii | 84.9 (3) | Rb2—O4—Rb2xiv | 163.9 (3) |
O1ii—Ti1—O2iii | 92.3 (3) |
Symmetry codes: (i) −z+1/2, −x+1, y−1/2; (ii) −y+1, z+1/2, −x+1/2; (iii) y+1/2, −z+1/2, −x+1; (iv) z+1/2, −x+3/2, −y; (v) x−1/2, −y+1/2, −z; (vi) −x+3/2, −y, z−1/2; (vii) −z+1, x−1/2, −y−1/2; (viii) y+1, z, x−1; (ix) z+1, x, y; (x) x+1/2, −y+1/2, −z; (xi) −z+1, x−1/2, −y+1/2; (xii) −x+3/2, −y+1, z+1/2; (xiii) −y+1/2, −z, x−1/2; (xiv) −x+3/2, −y, z+1/2; (xv) −z+1/2, −x+1, y+1/2; (xvi) −x+1, y−1/2, −z+1/2; (xvii) x, y, z+1. |
Rb2Yb0.32Ti1.68(PO4)3 | Dx = 3.675 Mg m−3 |
Mr = 591.07 | Synchrotron radiation, λ = 0.872 Å |
Cubic, P213 | Cell parameters from 7416 reflections |
Hall symbol: P 2ac 2ab 3 | θ = 3.5–31.1° |
a = 10.2228 (5) Å | µ = 8.10 mm−1 |
V = 1068.34 (9) Å3 | T = 150 K |
Z = 4 | Plate, blue |
F(000) = 1096 | 0.04 × 0.04 × 0.01 mm |
Bruker SMART CCD diffractometer | 784 reflections with F2 > 2σ(F2) |
Graphite monochromator | Rint = 0.085 |
ω scan | θmax = 34.1°, θmin = 3.5° |
Absorption correction: multi-scan (SADABS; Sheldrick 2001) | h = −12→13 |
Tmin = 0.75, Tmax = 0.96 | k = −13→12 |
7663 measured reflections | l = −12→12 |
785 independent reflections |
Refinement on F2 | 8 constraints |
Least-squares matrix: full | w = 1/[σ2(Fo2) + (0.0264P)2 + 1.609P] where P = (Fo2 + 2Fc2)/3 |
R[F2 > 2σ(F2)] = 0.024 | (Δ/σ)max < 0.001 |
wR(F2) = 0.063 | Δρmax = 0.62 e Å−3 |
S = 1.21 | Δρmin = −0.47 e Å−3 |
785 reflections | Absolute structure: Flack (1983) |
61 parameters | Absolute structure parameter: 0.42 (2) |
0 restraints |
Rb2Yb0.32Ti1.68(PO4)3 | Z = 4 |
Mr = 591.07 | Synchrotron radiation, λ = 0.872 Å |
Cubic, P213 | µ = 8.10 mm−1 |
a = 10.2228 (5) Å | T = 150 K |
V = 1068.34 (9) Å3 | 0.04 × 0.04 × 0.01 mm |
Bruker SMART CCD diffractometer | 785 independent reflections |
Absorption correction: multi-scan (SADABS; Sheldrick 2001) | 784 reflections with F2 > 2σ(F2) |
Tmin = 0.75, Tmax = 0.96 | Rint = 0.085 |
7663 measured reflections |
R[F2 > 2σ(F2)] = 0.024 | 0 restraints |
wR(F2) = 0.063 | Δρmax = 0.62 e Å−3 |
S = 1.21 | Δρmin = −0.47 e Å−3 |
785 reflections | Absolute structure: Flack (1983) |
61 parameters | Absolute structure parameter: 0.42 (2) |
Experimental. The data for (I) and (II) were collected with a laboratory Siemens diffractometer using Mo Kα radiation and at the Max II beamline 711 (Cerenius et al., 2000), respectively. Both data sets were normalized and corrected using SADABS within the SAINT-Plus program (Bruker, 1999). For (II), anomalous scattering factors for neutral atoms were taken from Sasaki (1989) and the linear absorption coefficient µ were calculated using mass attenuation coefficients from Sasaki (1990), both at wavelength 0.872 Å. The DSC measurements were made on a Perkin–Elmer Pyris with a cooling rate of 10 K min−1 and a sample weight of 23.6 mg. The measurements were made on a mixture of (I) and (II), the latter present in an insignificant amount. An exothermic peak was observed at around 183 K with an approximate enthalpy change of 1.1 kJ mol−1. |
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. Constraints used during the refinement: Equal Atomic Displacements parameters Ti1 Yb1 Equal Atomic Displacements parameters Ti2 Yb2 Occupancy of Ti1+Yb1 = 1.0 Occupancy of Ti2+Yb2 = 1.0 Atomic positions Ti1 = Yb1 and Ti2 = Yb2 |
x | y | z | Uiso*/Ueq | Occ. (<1) | |
Rb1 | 0.57007 (5) | 0.42993 (5) | −0.07007 (5) | 0.0157 (2) | |
Rb2 | 0.79247 (5) | 0.20753 (5) | −0.29247 (5) | 0.0177 (2) | |
Ti1 | 0.91673 (5) | 0.41673 (5) | 0.08327 (5) | 0.0087 (3) | 0.798 (3) |
Yb1 | 0.91673 (5) | 0.41673 (5) | 0.08327 (5) | 0.0087 (3) | 0.202 (3) |
Ti2 | 0.64739 (6) | 0.14739 (6) | 0.35261 (6) | 0.0111 (3) | 0.887 (3) |
Yb2 | 0.64739 (6) | 0.14739 (6) | 0.35261 (6) | 0.0111 (3) | 0.113 (3) |
P | 0.73540 (13) | 0.12203 (12) | 0.04069 (13) | 0.0178 (3) | |
O1 | 0.5972 (4) | 0.1486 (5) | −0.0059 (4) | 0.0323 (10) | |
O2 | 0.8194 (5) | 0.2433 (4) | 0.0193 (4) | 0.0402 (12) | |
O3 | 0.7356 (5) | 0.0814 (4) | 0.1863 (4) | 0.0337 (10) | |
O4 | 0.7971 (5) | 0.0107 (5) | −0.0399 (5) | 0.0424 (12) |
U11 | U22 | U33 | U12 | U13 | U23 | |
Rb1 | 0.0157 (2) | 0.0157 (2) | 0.0157 (2) | 0.00166 (19) | 0.00166 (19) | −0.00166 (19) |
Rb2 | 0.0177 (2) | 0.0177 (2) | 0.0177 (2) | 0.00028 (19) | 0.00028 (19) | −0.00028 (19) |
Ti1 | 0.0087 (3) | 0.0087 (3) | 0.0087 (3) | 0.00000 (18) | 0.00000 (18) | 0.00000 (18) |
Yb1 | 0.0087 (3) | 0.0087 (3) | 0.0087 (3) | 0.00000 (18) | 0.00000 (18) | 0.00000 (18) |
Ti2 | 0.0111 (3) | 0.0111 (3) | 0.0111 (3) | 0.0006 (2) | −0.0006 (2) | −0.0006 (2) |
Yb2 | 0.0111 (3) | 0.0111 (3) | 0.0111 (3) | 0.0006 (2) | −0.0006 (2) | −0.0006 (2) |
P | 0.0199 (6) | 0.0141 (6) | 0.0195 (6) | −0.0011 (5) | −0.0006 (5) | −0.0006 (5) |
O1 | 0.033 (2) | 0.033 (2) | 0.031 (2) | 0.011 (2) | −0.0064 (18) | 0.0027 (19) |
O2 | 0.060 (3) | 0.031 (2) | 0.030 (2) | −0.017 (2) | 0.013 (2) | −0.001 (2) |
O3 | 0.043 (2) | 0.027 (2) | 0.031 (2) | −0.006 (2) | −0.0107 (19) | 0.0128 (18) |
O4 | 0.032 (2) | 0.032 (2) | 0.063 (3) | 0.005 (2) | −0.006 (2) | −0.021 (2) |
Rb1—O1i | 2.963 (5) | Ti1—O2xi | 2.136 (5) |
Rb1—O1ii | 2.963 (5) | Ti1—Rb1xii | 3.8774 (4) |
Rb1—O1 | 2.963 (5) | Ti1—Rb1x | 3.8774 (4) |
Rb1—O4iii | 3.069 (5) | Ti2—O4xiii | 2.035 (5) |
Rb1—O4iv | 3.069 (5) | Ti2—O4xiv | 2.035 (5) |
Rb1—O4v | 3.069 (5) | Ti2—O4xv | 2.035 (5) |
Rb1—O2iii | 3.158 (5) | Ti2—O3xi | 2.039 (5) |
Rb1—O2iv | 3.158 (5) | Ti2—O3v | 2.039 (5) |
Rb1—O2v | 3.158 (5) | Ti2—O3 | 2.039 (5) |
Rb1—O2i | 3.312 (5) | Ti2—Rb1xvi | 3.8504 (14) |
Rb1—O2 | 3.312 (5) | Ti2—Rb2xvii | 3.9676 (5) |
Rb1—O2ii | 3.312 (5) | Ti2—Rb2xiv | 3.9676 (5) |
Rb2—O3vi | 2.976 (4) | Ti2—Rb2iv | 3.9676 (5) |
Rb2—O3vii | 2.976 (4) | P—O1 | 1.516 (4) |
Rb2—O3viii | 2.976 (4) | P—O2 | 1.524 (5) |
Rb2—O2ii | 3.220 (4) | P—O4 | 1.540 (5) |
Rb2—O2i | 3.220 (4) | P—O3 | 1.545 (4) |
Rb2—O2 | 3.220 (4) | P—Rb1x | 3.4752 (14) |
Rb2—O4i | 3.274 (6) | P—Yb1iv | 3.5179 (14) |
Rb2—O4ii | 3.274 (6) | P—Rb2xiv | 3.7869 (15) |
Rb2—O4 | 3.274 (6) | O1—Yb1iv | 2.115 (4) |
Rb2—O4vi | 3.494 (6) | O1—Ti1iv | 2.115 (4) |
Rb2—O4vii | 3.494 (6) | O2—Rb1x | 3.158 (5) |
Rb2—O4viii | 3.494 (6) | O3—Rb2xiv | 2.976 (4) |
Ti1—O1ix | 2.115 (4) | O3—Rb1x | 3.622 (5) |
Ti1—O1ii | 2.115 (4) | O4—Yb2vi | 2.035 (5) |
Ti1—O1x | 2.115 (4) | O4—Ti2vi | 2.035 (5) |
Ti1—O2 | 2.136 (5) | O4—Rb1x | 3.069 (5) |
Ti1—O2v | 2.136 (5) | O4—Rb2xiv | 3.494 (6) |
O1i—Rb1—O1ii | 98.34 (11) | O1x—Ti1—O2xi | 84.05 (17) |
O1i—Rb1—O1 | 98.34 (11) | O2—Ti1—O2xi | 90.59 (16) |
O1ii—Rb1—O1 | 98.34 (11) | O2v—Ti1—O2xi | 90.59 (16) |
O1i—Rb1—O4iii | 101.30 (12) | O1ix—Ti1—Rb1 | 116.05 (12) |
O1ii—Rb1—O4iii | 99.94 (13) | O1ii—Ti1—Rb1 | 49.14 (12) |
O1—Rb1—O4iii | 150.81 (12) | O1x—Ti1—Rb1 | 131.05 (12) |
O1i—Rb1—O4iv | 99.94 (13) | O2—Ti1—Rb1 | 58.62 (15) |
O1ii—Rb1—O4iv | 150.81 (12) | O2v—Ti1—Rb1 | 54.47 (15) |
O1—Rb1—O4iv | 101.30 (12) | O2xi—Ti1—Rb1 | 129.19 (12) |
O4iii—Rb1—O4iv | 54.17 (14) | O1ix—Ti1—Rb1xii | 49.14 (12) |
O1i—Rb1—O4v | 150.81 (12) | O1ii—Ti1—Rb1xii | 131.05 (12) |
O1ii—Rb1—O4v | 101.30 (12) | O1x—Ti1—Rb1xii | 116.05 (12) |
O1—Rb1—O4v | 99.94 (13) | O2—Ti1—Rb1xii | 129.19 (12) |
O4iii—Rb1—O4v | 54.17 (14) | O2v—Ti1—Rb1xii | 58.62 (15) |
O4iv—Rb1—O4v | 54.17 (14) | O2xi—Ti1—Rb1xii | 54.47 (15) |
O1i—Rb1—O2iii | 59.67 (12) | Rb1—Ti1—Rb1xii | 112.784 (10) |
O1ii—Rb1—O2iii | 85.84 (11) | O1ix—Ti1—Rb1x | 131.05 (12) |
O1—Rb1—O2iii | 158.01 (12) | O1ii—Ti1—Rb1x | 116.05 (12) |
O4iii—Rb1—O2iii | 46.60 (12) | O1x—Ti1—Rb1x | 49.14 (12) |
O4iv—Rb1—O2iii | 83.99 (13) | O2—Ti1—Rb1x | 54.47 (15) |
O4v—Rb1—O2iii | 100.38 (13) | O2v—Ti1—Rb1x | 129.19 (12) |
O1i—Rb1—O2iv | 85.84 (11) | O2xi—Ti1—Rb1x | 58.62 (15) |
O1ii—Rb1—O2iv | 158.01 (12) | Rb1—Ti1—Rb1x | 112.784 (10) |
O1—Rb1—O2iv | 59.67 (12) | Rb1xii—Ti1—Rb1x | 112.784 (10) |
O4iii—Rb1—O2iv | 100.38 (13) | O4xiii—Ti2—O4xiv | 86.8 (2) |
O4iv—Rb1—O2iv | 46.60 (12) | O4xiii—Ti2—O4xv | 86.8 (2) |
O4v—Rb1—O2iv | 83.99 (13) | O4xiv—Ti2—O4xv | 86.8 (2) |
O2iii—Rb1—O2iv | 114.45 (7) | O4xiii—Ti2—O3xi | 173.3 (2) |
O1i—Rb1—O2v | 158.01 (12) | O4xiv—Ti2—O3xi | 86.55 (18) |
O1ii—Rb1—O2v | 59.67 (12) | O4xv—Ti2—O3xi | 93.69 (19) |
O1—Rb1—O2v | 85.84 (11) | O4xiii—Ti2—O3v | 93.69 (19) |
O4iii—Rb1—O2v | 83.99 (13) | O4xiv—Ti2—O3v | 173.3 (2) |
O4iv—Rb1—O2v | 100.38 (13) | O4xv—Ti2—O3v | 86.55 (18) |
O4v—Rb1—O2v | 46.60 (12) | O3xi—Ti2—O3v | 93.06 (16) |
O2iii—Rb1—O2v | 114.45 (7) | O4xiii—Ti2—O3 | 86.55 (18) |
O2iv—Rb1—O2v | 114.45 (7) | O4xiv—Ti2—O3 | 93.69 (19) |
O1i—Rb1—O2i | 46.20 (12) | O4xv—Ti2—O3 | 173.3 (2) |
O1ii—Rb1—O2i | 112.60 (12) | O3xi—Ti2—O3 | 93.06 (16) |
O1—Rb1—O2i | 53.59 (12) | O3v—Ti2—O3 | 93.06 (16) |
O4iii—Rb1—O2i | 135.45 (13) | O4xiii—Ti2—Rb1xvi | 52.47 (14) |
O4iv—Rb1—O2i | 96.46 (11) | O4xiv—Ti2—Rb1xvi | 52.47 (14) |
O4v—Rb1—O2i | 138.68 (13) | O4xv—Ti2—Rb1xvi | 52.47 (14) |
O2iii—Rb1—O2i | 104.838 (12) | O3xi—Ti2—Rb1xvi | 123.07 (12) |
O2iv—Rb1—O2i | 55.91 (16) | O3v—Ti2—Rb1xvi | 123.07 (12) |
O2v—Rb1—O2i | 138.47 (9) | O3—Ti2—Rb1xvi | 123.07 (12) |
O1i—Rb1—O2 | 112.60 (12) | O4xiii—Ti2—Rb2xvii | 129.47 (14) |
O1ii—Rb1—O2 | 53.59 (12) | O4xiv—Ti2—Rb2xvii | 61.63 (16) |
O1—Rb1—O2 | 46.20 (12) | O4xv—Ti2—Rb2xvii | 55.43 (16) |
O4iii—Rb1—O2 | 138.68 (13) | O3xi—Ti2—Rb2xvii | 46.95 (12) |
O4iv—Rb1—O2 | 135.45 (13) | O3v—Ti2—Rb2xvii | 113.50 (12) |
O4v—Rb1—O2 | 96.46 (11) | O3—Ti2—Rb2xvii | 130.42 (12) |
O2iii—Rb1—O2 | 138.47 (9) | Rb1xvi—Ti2—Rb2xvii | 77.133 (15) |
O2iv—Rb1—O2 | 104.838 (12) | O4xiii—Ti2—Rb2xiv | 61.63 (16) |
O2v—Rb1—O2 | 55.91 (16) | O4xiv—Ti2—Rb2xiv | 55.43 (16) |
O2i—Rb1—O2 | 85.86 (11) | O4xv—Ti2—Rb2xiv | 129.47 (14) |
O1i—Rb1—O2ii | 53.59 (12) | O3xi—Ti2—Rb2xiv | 113.50 (12) |
O1ii—Rb1—O2ii | 46.20 (12) | O3v—Ti2—Rb2xiv | 130.42 (12) |
O1—Rb1—O2ii | 112.60 (12) | O3—Ti2—Rb2xiv | 46.95 (11) |
O4iii—Rb1—O2ii | 96.46 (11) | Rb1xvi—Ti2—Rb2xiv | 77.133 (15) |
O4iv—Rb1—O2ii | 138.68 (13) | Rb2xvii—Ti2—Rb2xiv | 115.190 (11) |
O4v—Rb1—O2ii | 135.45 (13) | O4xiii—Ti2—Rb2iv | 55.43 (16) |
O2iii—Rb1—O2ii | 55.91 (16) | O4xiv—Ti2—Rb2iv | 129.47 (14) |
O2iv—Rb1—O2ii | 138.47 (9) | O4xv—Ti2—Rb2iv | 61.63 (16) |
O2v—Rb1—O2ii | 104.838 (12) | O3xi—Ti2—Rb2iv | 130.42 (12) |
O2i—Rb1—O2ii | 85.86 (11) | O3v—Ti2—Rb2iv | 46.95 (12) |
O2—Rb1—O2ii | 85.86 (11) | O3—Ti2—Rb2iv | 113.50 (12) |
O3vi—Rb2—O3vii | 91.74 (12) | Rb1xvi—Ti2—Rb2iv | 77.133 (15) |
O3vi—Rb2—O3viii | 91.74 (12) | Rb2xvii—Ti2—Rb2iv | 115.190 (11) |
O3vii—Rb2—O3viii | 91.74 (12) | Rb2xiv—Ti2—Rb2iv | 115.190 (11) |
O3vi—Rb2—O2ii | 164.89 (12) | O1—P—O2 | 109.5 (3) |
O3vii—Rb2—O2ii | 80.10 (13) | O1—P—O4 | 110.3 (3) |
O3viii—Rb2—O2ii | 101.13 (12) | O2—P—O4 | 107.1 (3) |
O3vi—Rb2—O2i | 80.10 (13) | O1—P—O3 | 110.6 (3) |
O3vii—Rb2—O2i | 101.13 (12) | O2—P—O3 | 110.9 (3) |
O3viii—Rb2—O2i | 164.89 (12) | O4—P—O3 | 108.4 (3) |
O2ii—Rb2—O2i | 88.97 (14) | O1—P—Rb1x | 166.51 (18) |
O3vi—Rb2—O2 | 101.13 (12) | O2—P—Rb1x | 65.3 (2) |
O3vii—Rb2—O2 | 164.89 (12) | O4—P—Rb1x | 61.98 (18) |
O3viii—Rb2—O2 | 80.10 (13) | O3—P—Rb1x | 82.79 (19) |
O2ii—Rb2—O2 | 88.97 (14) | O2—P—Yb1iv | 124.2 (2) |
O2i—Rb2—O2 | 88.97 (14) | O4—P—Yb1iv | 95.92 (18) |
O3vi—Rb2—O4i | 82.24 (13) | O3—P—Yb1iv | 108.53 (18) |
O3vii—Rb2—O4i | 56.55 (12) | Rb1x—P—Yb1iv | 157.75 (4) |
O3viii—Rb2—O4i | 147.25 (12) | O1—P—Rb2 | 78.97 (17) |
O2ii—Rb2—O4i | 82.65 (12) | O2—P—Rb2 | 64.60 (18) |
O2i—Rb2—O4i | 44.59 (11) | O4—P—Rb2 | 66.6 (2) |
O2—Rb2—O4i | 132.65 (12) | O3—P—Rb2 | 170.44 (19) |
O3vi—Rb2—O4ii | 147.25 (12) | Rb1x—P—Rb2 | 87.65 (3) |
O3vii—Rb2—O4ii | 82.24 (13) | Yb1iv—P—Rb2 | 80.50 (3) |
O3viii—Rb2—O4ii | 56.55 (12) | O1—P—Rb1 | 48.25 (18) |
O2ii—Rb2—O4ii | 44.59 (11) | O2—P—Rb1 | 61.8 (2) |
O2i—Rb2—O4ii | 132.65 (12) | O4—P—Rb1 | 130.1 (2) |
O2—Rb2—O4ii | 82.65 (12) | O3—P—Rb1 | 121.14 (19) |
O4i—Rb2—O4ii | 119.16 (3) | Rb1x—P—Rb1 | 126.76 (4) |
O3vi—Rb2—O4 | 56.55 (12) | Yb1iv—P—Rb1 | 64.41 (2) |
O3vii—Rb2—O4 | 147.25 (12) | Rb2—P—Rb1 | 65.11 (3) |
O3viii—Rb2—O4 | 82.24 (13) | O1—P—Rb2xiv | 103.34 (19) |
O2ii—Rb2—O4 | 132.65 (12) | O2—P—Rb2xiv | 146.2 (2) |
O2i—Rb2—O4 | 82.65 (12) | O4—P—Rb2xiv | 67.3 (2) |
O2—Rb2—O4 | 44.59 (11) | O3—P—Rb2xiv | 47.72 (17) |
O4i—Rb2—O4 | 119.16 (3) | Rb1x—P—Rb2xiv | 84.21 (3) |
O4ii—Rb2—O4 | 119.16 (3) | Yb1iv—P—Rb2xiv | 89.56 (3) |
O3vi—Rb2—O4vi | 44.63 (11) | Rb2—P—Rb2xiv | 131.36 (4) |
O3vii—Rb2—O4vi | 50.37 (12) | Rb1—P—Rb2xiv | 148.14 (4) |
O3viii—Rb2—O4vi | 106.45 (11) | P—O1—Yb1iv | 150.9 (3) |
O2ii—Rb2—O4vi | 122.70 (11) | P—O1—Ti1iv | 150.9 (3) |
O2i—Rb2—O4vi | 76.60 (12) | P—O1—Rb1 | 109.3 (2) |
O2—Rb2—O4vi | 144.23 (11) | Yb1iv—O1—Rb1 | 98.17 (14) |
O4i—Rb2—O4vi | 48.65 (16) | Ti1iv—O1—Rb1 | 98.17 (14) |
O4ii—Rb2—O4vi | 130.85 (9) | P—O1—Rb2 | 76.60 (17) |
O4—Rb2—O4vi | 100.50 (2) | Yb1iv—O1—Rb2 | 103.43 (14) |
O3vi—Rb2—O4vii | 106.45 (11) | Ti1iv—O1—Rb2 | 103.43 (14) |
O3vii—Rb2—O4vii | 44.63 (11) | Rb1—O1—Rb2 | 73.07 (10) |
O3viii—Rb2—O4vii | 50.37 (12) | P—O2—Ti1 | 153.4 (3) |
O2ii—Rb2—O4vii | 76.60 (12) | P—O2—Rb1x | 88.7 (2) |
O2i—Rb2—O4vii | 144.23 (11) | Ti1—O2—Rb1x | 92.13 (18) |
O2—Rb2—O4vii | 122.70 (11) | P—O2—Rb2 | 90.1 (2) |
O4i—Rb2—O4vii | 100.50 (2) | Ti1—O2—Rb2 | 115.93 (16) |
O4ii—Rb2—O4vii | 48.65 (16) | Rb1x—O2—Rb2 | 99.70 (13) |
O4—Rb2—O4vii | 130.85 (9) | P—O2—Rb1 | 94.3 (2) |
O4vi—Rb2—O4vii | 83.96 (12) | Ti1—O2—Rb1 | 87.98 (15) |
O3vi—Rb2—O4viii | 50.37 (12) | Rb1x—O2—Rb1 | 173.13 (15) |
O3vii—Rb2—O4viii | 106.45 (11) | Rb2—O2—Rb1 | 74.14 (11) |
O3viii—Rb2—O4viii | 44.63 (11) | P—O3—Ti2 | 135.5 (3) |
O2ii—Rb2—O4viii | 144.23 (11) | P—O3—Rb2xiv | 109.7 (2) |
O2i—Rb2—O4viii | 122.70 (11) | Ti2—O3—Rb2xiv | 103.00 (16) |
O2—Rb2—O4viii | 76.60 (12) | P—O3—Rb1x | 72.16 (18) |
O4i—Rb2—O4viii | 130.85 (9) | Ti2—O3—Rb1x | 134.55 (18) |
O4ii—Rb2—O4viii | 100.50 (2) | Rb2xiv—O3—Rb1x | 94.77 (13) |
O4—Rb2—O4viii | 48.65 (16) | P—O4—Yb2vi | 171.9 (3) |
O4vi—Rb2—O4viii | 83.96 (12) | P—O4—Ti2vi | 171.9 (3) |
O4vii—Rb2—O4viii | 83.96 (12) | P—O4—Rb1x | 91.7 (2) |
O1ix—Ti1—O1ii | 93.86 (17) | Yb2vi—O4—Rb1x | 95.81 (17) |
O1ix—Ti1—O1x | 93.86 (17) | Ti2vi—O4—Rb1x | 95.81 (17) |
O1ii—Ti1—O1x | 93.86 (17) | P—O4—Rb2 | 87.8 (2) |
O1ix—Ti1—O2 | 174.19 (19) | Yb2vi—O4—Rb2 | 93.79 (19) |
O1ii—Ti1—O2 | 84.05 (17) | Ti2vi—O4—Rb2 | 93.79 (19) |
O1x—Ti1—O2 | 91.69 (18) | Rb1x—O4—Rb2 | 100.39 (15) |
O1ix—Ti1—O2v | 84.05 (17) | P—O4—Rb2xiv | 88.7 (2) |
O1ii—Ti1—O2v | 91.69 (18) | Yb2vi—O4—Rb2xiv | 87.54 (17) |
O1x—Ti1—O2v | 174.19 (19) | Ti2vi—O4—Rb2xiv | 87.54 (17) |
O2—Ti1—O2v | 90.59 (16) | Rb1x—O4—Rb2xiv | 95.71 (14) |
O1ix—Ti1—O2xi | 91.69 (18) | Rb2—O4—Rb2xiv | 163.62 (16) |
O1ii—Ti1—O2xi | 174.19 (19) |
Symmetry codes: (i) −z+1/2, −x+1, y−1/2; (ii) −y+1, z+1/2, −x+1/2; (iii) z+1/2, −x+3/2, −y; (iv) x−1/2, −y+1/2, −z; (v) y+1/2, −z+1/2, −x+1; (vi) −x+3/2, −y, z−1/2; (vii) −z+1, x−1/2, −y−1/2; (viii) y+1, z, x−1; (ix) z+1, x, y; (x) x+1/2, −y+1/2, −z; (xi) −z+1, x−1/2, −y+1/2; (xii) −x+3/2, −y+1, z+1/2; (xiii) −y+1/2, −z, x−1/2; (xiv) −x+3/2, −y, z+1/2; (xv) −z+1/2, −x+1, y+1/2; (xvi) −x+1, y−1/2, −z+1/2; (xvii) x, y, z+1. |
Experimental details
(I_293_K) | (I_150_K) | (II_293_K) | (II_150_K) | |
Crystal data | ||||
Chemical formula | Rb2YbTi(PO4)3 | Rb2YbTi(PO4)3 | Rb2Yb0.32Ti1.68(PO4)3 | Rb2Yb0.32Ti1.68(PO4)3 |
Mr | 676.79 | 676.79 | 591.07 | 591.07 |
Crystal system, space group | Cubic, P213 | Cubic, P213 | Cubic, P213 | Cubic, P213 |
Temperature (K) | 293 | 150 | 293 | 150 |
a (Å) | 10.2083 (2) | 10.2111 (2) | 10.2132 (2) | 10.2228 (5) |
V (Å3) | 1063.80 (4) | 1064.68 (4) | 1065.33 (4) | 1068.34 (9) |
Z | 4 | 4 | 4 | 4 |
Radiation type | Mo Kα | Mo Kα | Synchrotron, λ = 0.87200 Å | Synchrotron, λ = 0.872 Å |
µ (mm−1) | 19.09 | 19.08 | 8.12 | 8.10 |
Crystal size (mm) | 0.07 × 0.06 × 0.05 | 0.08 × 0.07 × 0.05 | 0.04 × 0.04 × 0.01 | 0.04 × 0.04 × 0.01 |
Data collection | ||||
Diffractometer | Siemens SMART CCD diffractometer | Siemens SMART CCD diffractometer | Siemens SMART CCD diffractometer | Bruker SMART CCD diffractometer |
Absorption correction | Multi-scan (SADABS; Sheldrick 2001) | Multi-scan (SADABS; Sheldrick 2001) | Multi-scan (SADABS; Sheldrick, 2001) | Multi-scan (SADABS; Sheldrick 2001) |
Tmin, Tmax | 0.257, 0.385 | 0.25, 0.385 | 0.75, 0.96 | 0.75, 0.96 |
No. of measured, independent and observed [F2 > 2σ(F2)] reflections | 19443, 1338, 1326 | 19497, 1342, 1333 | 2811, 771, 766 | 7663, 785, 784 |
Rint | 0.053 | 0.044 | 0.070 | 0.085 |
(sin θ/λ)max (Å−1) | 0.768 | 0.768 | 0.609 | 0.643 |
Refinement | ||||
R[F2 > 2σ(F2)], wR(F2), S | 0.024, 0.056, 1.24 | 0.023, 0.054, 1.28 | 0.044, 0.118, 1.18 | 0.024, 0.063, 1.21 |
No. of reflections | 1338 | 1342 | 771 | 785 |
No. of parameters | 60 | 60 | 61 | 61 |
No. of restraints | 1 | 1 | 0 | 0 |
Δρmax, Δρmin (e Å−3) | 0.63, −1.35 | 0.71, −1.22 | 0.98, −1.07 | 0.62, −0.47 |
Absolute structure | Flack (1983) | Flack (1983) | Flack (1983) | Flack (1983) |
Absolute structure parameter | 0.021 (16) | 0.017 (15) | 0.41 (3) | 0.42 (2) |
Computer programs: SMART (Siemens, 1995), SMART-NT (Bruker, 1998), SAINT (Siemens, 1995) or SAINT-Plus? (Bruker, 1999), SAINT and SADABS (Sheldrick, 2001), SAINT-Plus (Bruker, 1999) and SADABS (Sheldrick, 2001), SMART-NT and SADABS (Sheldrick, 2001), SAINT-Plus and SADABS (Sheldrick, 2001), SHELXS97 (Sheldrick, 1997), Coordinates from RA, Coordinates from (I), Coordinates from (II) at 293K, SHELXL97 (Sheldrick, 1997), 'ORTEP-3 for Windows (Farrugia, 1997) and DIAMOND (Brandenburg, 2000)', WinGX (Farrugia, 1999).
RYbTP-I 293 K | RYbTP-I 150 K | RYbTP-II 293 K | RYbTP-II 150 K | |
Yb1/Ti1 - O1ii | 2.115 (5) | 2.113 (4) | 2.107 (8) | 2.115 (4) |
Yb1/Ti1 - O2 | 2.128 (5) | 2.128 (5) | 2.149 (8) | 2.136 (5) |
Yb2/Ti2 - O3 | 2.019 (6) | 2.017 (5) | 2.054 (9) | 2.035 (5) |
Yb2/Ti2 - O4viii | 2.041 (5) | 2.039 (4) | 2.046 (8) | 2.039 (5) |
[Symmetry codes as in Fig 1] |
RYbTP-I 293 K | RYbTP-I 150 K | RYbTP-II 293 K | RYbTP-II 150 K | |
Rb1 | 1.06 | 1.06 | 1.04 | 1.06 |
Rb2 | 0.82 | 0.83 | 0.86 | 0.85 |
Yb1 | 3.93 | 3.94 | 3.87 | 3.95 |
Ti1(IV) | 2.62 | 2.63 | 2.58 | 2.60 |
Ti1(III) | - | - | 2.42 | 2.43 |
Yb2 | 5.00 | 5.06 | 4.78 | 4.93 |
Ti2(IV) | 3.36 | 3.38 | 3.18 | 3.31 |
Ti1(III) | - | - | 2.98 | 3.08 |
P | 5.10 | 5.05 | 5.22 | 5.04 |
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KTP (KTiOPO4) and its analogues RTP (RbTiOPO4) and CTA (CsTiOAsO4) are well known ferroelectric materials with excellent nonlinear optical properties (Satyanarayan et al., 1999). The optical properties of these compounds can be changed by modifying the composition, for example, by replacing some of the titanium in RTP by ytterbium. In an attempt to prepare ytterbium-doped RTP by adding Yb2O3 to the flux, crystals of RTP were grown. Simultaneously, well shaped colourless tetrahedral crystals were found, a small number of them showing a bluish colour. Upon analysis, these crystals were found to belong to the langbeinite structure type. All examined crystals from the same growth experiment had either of two compositions, viz. Rb2YbTi(PO4)3, (I) (colourless), or Rb2Yb0.32Ti1.68(PO4)3, (II) (blue). Differential scanning calorimetry (DSC) indicated a phase transition at 183 K for (I). We present here a detailed crystallographic investigation of the two new phosphate langbeinites at two different temperatures.
The title compounds belong to the large group of synthetic AxM2(XO4)3 compounds named after the mineral langbeinite, K2Mg2(SO4)3 (Zemann & Zemann, 1957). Langbeinite compounds have attracted a significant amount of interest due to their ferroelectric and ferroelastic behaviour, for example, (NH4)2Cd2(SO4)3 (Jona & Pepinsky, 1956), Tl2Cd2(SO4)3 (Brezina & Glogarova, 1972) and K2Cd2(SO4)3 (Abrahams & Bernstein, 1977). All known langbeinites crystallize in a common high-temperature cubic phase, in space group P213. Below room temperature, most of them undergo one or several phase transitions, with two possible transitions paths. The first path includes several steps from P213 to the final orthorhombic space group P212121, which is exemplified by the phase transitions of Tl2Cd2(SO4)3 (Brezina & Glogarova, 1972; Guelylah et al., 2000): P213 (RT) → P21 (128 K) → P1 (119 K) → P212121 (98 K).
In the second path, the transformation proceeds directly from the high-temperature P213 phase to the orthorhombic low-temperature P212121 phase. Several different mechanisms for these transitions have been suggested (e.g. Percival et al., 1989; Moriyoshi et al., 1996).
Phosphate langbeinites containing titanium form a small group of compounds, including KTi2(PO4)3, K2Ti2(PO4)3, K1 + xTi2 − yAly(PO4)3, K2MTi(PO4)3 (M = Er, Yb or Y) and Rb2ErTi(PO4)3 (Masse et al., 1972; Leclaire et al., 1989; Slobodyanik et al., 1991; Norberg, 2002; Carvajal et al., 2002). Some of these compounds contain mixed-valence octahedral cations, such as Ti3+/Ti4+ in K2Ti2(PO4)3. This is also the case for the present compound (II). The small number of phosphate langbeinites is a result of the fact that most AxM2(PO4)3 compounds tend to crystallize in the closely related nasicon structure, Na3Zr2(PO4)(SiO4)2 (Sljukic et al., 1967; von Alpen et al., 1979). There are also examples of the same compound crystallizing in both the langbeinite and the nasicon structure (Masse et al., 1972). One important difference between the two structures is that, in langbeinites, the alkali cations are located in cages, while in nasicon, they are found in tunnels. The langbeinite framework is built of MO6 octahedra sharing corners with PO4 tetrahedra (Fig. 1). An alternative description of the framework is based on [M2X3O18] units composed of two MO6 octahedra linked together by three XO4 tetrahedra. Another description based on M5X6O39 units has recently been presented by Norberg (2002), which gives an improved visualization of the cages and tunnels formed in langbeinite and nasicon, respectively. An alternative description of the langbeinite structure, in terms of packed <111> rods, has been given by O'Keeffe & Andersson (1977).
Within the langbeinite framework, large cages are formed, in which the alkali cations are located. Each cage contains two Rb ions separated by 3.917 (1) and 3.932 (2) Å at room temperature in (I) and (II), respectively. These distances are longer than the sum of ionic radii for nine-coordinated Rb+ ions (3.38 Å; Shannon, 1976). The cages have a volume of approximately 5 x 5 x 11 Å and are isolated from one another, making langbeinites poor ionic conductors. The Rb1+ and Rb2+ cations are best described as twelve- and nine-coordinate, respectively. Atom Rb1 can also be described as surrounded by four MO6 octahedra in a tetrahedral arrangement, while atom Rb2 is surrounded by six MO6 octahedra in an octahedral geometry. These large polyhedra are regular and share one triangular face to form a cage of seven MO6 octahedra about two Rb+ ions (Fig. 2). The Rb—M distances in the cage are in the range 3.85–3.97 Å. The arrangement of the seven MO6 octahedra around the Rb atoms results in an opening in the cage located opposite to the tetrahedron. This opening is closed by an eigth octahedron, at a M—Rb distance of about 5.15 Å for both compounds at both temperatures. Thus, the two Rb atoms are located at one end of the cage with room to accommodate another small cation in the empty part of the cage (Fig. 2). To the best of our knowledge, no langbeinite structure has yet been found where all three positions are occupied. Bond-valence sums (Brown 1981, 1985) for (I) and (II) have been calculated (Table 2). The difference between the two Rb sites reflects the difference in coordination and the lower bond-valence sum for Rb2 indicates underbonding.
Selected bond distances for the two compounds are given in Table 1. The two crystallographically independent MO6 (M = Ti/Yb) octahedra are regular, with the metal atom slightly off-centre by 0.0380 (8) Å (M1) and 0.0707 (9) Å (M2) in (I), and 0.050 (2) Å (M1) and 0.0564 (8) Å (M2) in (II). The centre of the octahedra was calculated as the geometric mean for the six O-atom positions at the vertices.
The distribution between the Ti and Yb atoms is not equal in the two octahedral sites, as two-thirds of the Yb atoms are found in the M1O6 octahedra and one-third are found in the M2O6 - octahedra. The M1O6 octahedra define the shared triangular face between the Rb2 (MO6)6 octahedra and the Rb1 (MO6)4 tetrahedra (Fig 2). The M1O6 octahedra are thus more influenced by the Rb+ cations than the M2O6 octahedra, which might have an impact on the distribution of Yb.
The geometry of the phosphate groups in (I) and (II) is as expected. The displacement parameters for the O atoms are large and the ellipsoids are mostly oriented with the major axis perpendicular to the P—O bond (Fig. 3). This result is an indication of O-atom disorder or rotation of the phosphate group, which has been interpreted as the initial stages of a phase transition in langbeinites (Lissalde et al., 1979). The displacement parameters of the O atoms are not affected by the change in temperature, while those of the metal atoms decrease by approximately 25%. The temperature decrease from 298 to 150 K does not affect the cell parameters and a slight increase (0.3%) of the cell volume is even observed for (II).
As mentioned above, DSC data indicated a phase transition at 183 K. Data were therefore collected for both compounds at 150 K in order to investigate the formation of a possible low-temperature phase. However, the structure refinements did not reveal a phase transition. In an attempt to obtain an indication of how close these structures are to a phase transition, the instability index GII was calculated [GII is the r.m.s. deviation between the valence sums and oxidation states averaged over all atoms in the structure (Salinas-Sanchez et al., 1992)]. A GII value above 0.05 is an indication of a strained structure (Rao et al., 1998), while structures with values above 0.20 are considered unstable. For both (I) and (II), the calculated GII indices are about 0.10 at 150 K.