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The crystal structure of the low-temperature Na4Ti5O12 (tetra­sodium penta­titanium dodeca­oxide) phase has been solved and refined from X-ray and neutron powder diffraction data at 295 K. The structure is trigonal, space group P3, with Z = 1, although it is pseudo-centrosymmetric. The O and Na atoms form a distorted close-packed structure, where Ti atoms occupy octahedral sites.

Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S0108270100014839/qd0006sup1.cif
Contains datablocks global, I

rtv

Rietveld powder data file (CIF format) https://doi.org/10.1107/S0108270100014839/qd0006Isup2.rtv
Contains datablock I

Comment top

Recently, it was reported (Nalbandyan, 2000) that the low-temperature sodium titanate earlier described as Na2Ti2O5 (Batygin, 1967), in fact corresponds to the formula Na4Ti5O12. It was found that the compound is stable below ca 973 K. Above this temperature, the compound decomposes to Na8Ti5O14 and Na2Ti3O7, and does not undergo the phase transition to any high-temperature form, because it was shown that previously described Na4Ti5O12 (Werthmann & Hoppe, 1984) does not exist in the Na2O-TiO2 system, and this structure type is actually stabilized by doping (Nalbandyan et al., 1998). The X-ray powder pattern of low-temperature Na4Ti5O12 was indexed and the parameters of hexagonal unit cell were found to be a = 5.319 Å and c = 9.556 Å. It was supposed that the structure is ABAC or ABAB close-packed with oxygen anions, and sodium and titanium occupy octahedral sites. However, neither that guess was checked nor the structure was solved ab initio. Therefore, we undertook the study of Na4Ti5O12 structure, and the results are reported here. The structure is based on the distorted close-packed layers consisting of large ions (oxygen and sodium) and the titanium ions occupy octahedral voids.

Experimental top

The title compound was prepared by solid-state method from TiO2 (anatase form) and Na2CO3 at ca 923 K (Nalbandyan, 2000). A colourless crystalline powder resulted.

Refinement top

The list of peak positions was obtained from the X-ray raw data using the XFIT program (Cheary & Coelho, 1997) and used for indexing by Crysfire suite (Shirley, 1999). A hexagonal cell [a = 5.31997 (14) Å and c = 9.5567 (3) Å] having FOM = 103 was found, in agreement with previous report (Nalbandyan, 2000). After that, the assumptions on close-packing ABAC or ABAB structure were checked. Since no systematical absence of reflections was observed, the space group P3 (No. 143) having the lowest possible symmetry within the system was chosen. In both cases, all the O atoms were placed at the special positions of close-packed structure, and all the cations were distributed over 12 octahedral voids uniformly. The occupancies of cation positions were considered as variables. However, no agreement of calculated and experimental profiles was obtained in both cases, and the refinement process was unstable, giving large negative occupancies of some cation sites. Therefore, ab initio structure determination has been performed. The structure-factor amplitudes were extracted by FULLPROF (Rodriguez-Carvajal, 1990) in profile matching mode with pseudo-Voight peak shape function (NPROF = 5). To prevent using the data from overlapping reflections, the reflection list was filtered by OVERLAP program (LeBail, 1999), and finally 68 Fo values were obtained. Patterson functions interpretation and Fourier syntheses were performed by SHELXS97 (Sheldrick, 1997). All the O atoms and cation sites were revealed and structural model obtained was used for Rietveld refinement with FULLPROF (pseudo-Voigt peak-shape function). The distribution of sodium and titanium over cation sites was refined using constraints occ(Na) + occ(Ti) = 1. The reasonable results were obtained: sodium allocated at distorted cubooctahedral voids, whereas titanium occupies octahedral ones.

The time-of-flight neutron data were collected using DN-2 diffractometer at IBR-2 source (Joint Institute for Nuclear Research, Dubna, Russia). The data were refined using MRIA program (Zlokazov et al., 1992). Since the resolution in the neutron data is rather low and peak overlapping is strong, the simultaneous refinement of all the variables resulted in unstable and mostly divergent process. Therefore, the positional and thermal parameters obtained by X-ray data refinement were fixed, and only the distribution of cations over nine non-equivalent sites was checked by neutron diffraction data refinement. Since sodium and titanium have opposite sign of the amplitude of coherent scattering of neutrons, the atoms can be distinguished easily by neutron diffraction. The refinement converged to the same results: sodium occupies large distorted cubooctahedral voids, forming together with O atoms distorted close-packed structure, whereas titanium occupies octahedral sites (Gaussian peak-shape function, Rp = 6.27, Rwp = 5.07, χ2 = 5.67).

The final coordinates are close to those obeying the P3 space group, where there is a pseudocentre of symmetry at the Ti4 atom. A refinement of the structure based on the X-ray data using P3 space group resulted in no improvement (Rp = 9.26, Rwp = 11.3 and χ2 = 7.62).

Computing details top

Data collection: D/MAX-B (Rigaku, 1992); cell refinement: FULLPROF (Rodriguez-Carvajal, 1990); program(s) used to solve structure: SHELXS97 (Sheldrick, 1997); molecular graphics: DIAMOND (Bergerhoff et al., 1996); software used to prepare material for publication: WINPLOTR (Roisnel & Rodruguez-Carvajal, 1999).

sodium titanate top
Crystal data top
Na4Ti5O12Z = 1
Mr = 522.30Dx = 3.710 Mg m3
Trigonal, P3Melting point: unstable above 700°C K
Hall symbol: P 3Cu Kα1, Cu Kα2 radiation, λ = 1.54056, 1.54439 Å
a = 5.31997 (14) ÅT = 295 K
c = 9.5567 (3) Åcolourless
V = 234.24 (1) Å3flat sheet, 18 × 20 mm
Data collection top
Rigaku D/MAX-B
diffractometer
Data collection mode: reflection
Radiation source: sealed X-ray tube, sealed X-ray tubeScan method: step
Curved graphite (002) monochromator2θmin = 18.0°, 2θmax = 120.0°, 2θstep = 0.02°
Specimen mounting: drifted powder on off-cut glass
Refinement top
Refinement on InetProfile function: pseudo-Voigt
Least-squares matrix: full with fixed elements per cycle60 parameters
Rp = 6.859 constraints
Rwp = 9.44Weighting scheme based on measured s.u.'s
Rexp = 4.07(Δ/σ)max < 0.01
χ2 = 28.837Background function: 4rd order polynomial function
5101 data pointsPreferred orientation correction: G2+(1-G2)*exp(G1*a2*)
Crystal data top
Na4Ti5O12V = 234.24 (1) Å3
Mr = 522.30Z = 1
Trigonal, P3Cu Kα1, Cu Kα2 radiation, λ = 1.54056, 1.54439 Å
a = 5.31997 (14) ÅT = 295 K
c = 9.5567 (3) Åflat sheet, 18 × 20 mm
Data collection top
Rigaku D/MAX-B
diffractometer
Scan method: step
Specimen mounting: drifted powder on off-cut glass2θmin = 18.0°, 2θmax = 120.0°, 2θstep = 0.02°
Data collection mode: reflection
Refinement top
Rp = 6.85χ2 = 28.837
Rwp = 9.445101 data points
Rexp = 4.0760 parameters
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Ti10.333330.666670.273 (8)0.043 (4)*
Ti20.333330.666670.035 (8)0.030 (4)*
Ti30.333330.333330.044 (8)0.121 (4)*
Ti40.000000.000000.525 (8)0.044 (2)*
Ti50.333330.333330.261 (8)0.019 (3)*
Na10.000000.000000.216 (8)0.045 (4)*
Na20.666670.333330.423 (8)0.026 (8)*
Na30.333330.666670.601 (8)0.061 (5)*
Na40.000000.000000.151 (8)0.020 (6)*
O10.2343 (3)0.3331 (4)0.367 (8)0.021 (4)*
O20.0426 (3)0.4340 (4)0.141 (8)0.075 (8)*
O30.9292 (4)0.2267 (4)0.636 (8)0.078 (11)*
O40.0097 (3)0.5575 (2)0.131 (8)0.010 (2)*
Geometric parameters (Å, º) top
Ti1—O1i1.82 (5)Na1—O2ii3.21 (2)
Ti1—O1ii1.82 (5)Na1—O2xiii3.21 (2)
Ti1—O11.82 (5)Na1—O2iii3.21 (2)
Ti1—O2i1.90 (7)Na2—O1vi2.36 (2)
Ti1—O21.90 (7)Na2—O12.36 (2)
Ti1—O2ii1.90 (7)Na2—O1xiv2.36 (2)
Ti2—O41.86 (5)Na2—O3xiv2.67 (8)
Ti2—O4i1.86 (5)Na2—O3vi2.67 (8)
Ti2—O4ii1.86 (5)Na2—O32.67 (8)
Ti2—O2i2.20 (8)Na2—O1ii3.07 (2)
Ti2—O22.20 (8)Na2—O1xv3.07 (2)
Ti2—O2ii2.20 (8)Na2—O1ix3.07 (2)
TI3—O22.02 (5)Na2—O2xv3.24 (9)
TI3—O2iii2.02 (5)Na2—O2ii3.24 (9)
TI3—O2iv2.02 (5)Na2—O2ix3.24 (9)
TI3—O4iii2.27 (8)Na3—O3xiv2.28 (2)
TI3—O42.27 (8)Na3—O3xvi2.28 (2)
TI3—O4iv2.27 (8)Na3—O3vii2.28 (2)
TI4—O3v1.78 (6)Na3—O12.74 (9)
TI4—O3vi1.78 (6)Na3—O1i2.74 (9)
TI4—O3vii1.78 (6)Na3—O1ii2.74 (9)
TI4—O12.18 (8)Na3—O4xvii3.03 (9)
TI4—O1viii2.18 (8)Na3—O4xviii3.03 (9)
TI4—O1ix2.18 (8)Na3—O4xix3.03 (9)
TI5—O41.97 (7)Na3—O3viii3.10 (1)
TI5—O4iv1.97 (7)Na3—O3vi3.10 (1)
TI5—O4iii1.97 (7)Na3—O3xx3.10 (1)
TI5—O3x2.01 (5)Na4—O4xiii2.337 (9)
TI5—O3xi2.01 (5)Na4—O4ii2.337 (9)
TI5—O3xii2.01 (5)Na4—O4iii2.337 (9)
Na1—O12.14 (7)Na4—O3xxi2.49 (9)
Na1—O1ix2.14 (7)Na4—O3xxii2.49 (9)
Na1—O1viii2.14 (7)Na4—O3xi2.49 (9)
Na1—O2ix2.32 (3)Na4—O4ix2.998 (7)
Na1—O2viii2.32 (3)Na4—O4viii2.998 (7)
Na1—O22.32 (3)Na4—O42.998 (7)
O1ii—Ti1—O1i97.65 (7)O1—Na2—O2ix70.81 (8)
O1—Ti1—O1i97.65 (8)O3—Na2—O3xiv68.76 (9)
O1i—Ti1—O2i87.01 (6)O3vi—Na2—O3xiv68.76 (6)
O1—Ti1—O2i167.06 (7)O3xiv—Na2—O1ii61.05 (1)
O1ii—Ti1—O2i93.66 (9)O3xiv—Na2—O1xv106.53 (5)
O1—Ti1—O1ii97.65 (7)O3xiv—Na2—O1ix126.60 (3)
O1i—Ti1—O2ii167.06 (7)O3xiv—Na2—O2ii108.82 (2)
O1—Ti1—O2ii93.66 (5)O3xiv—Na2—O2xv128.54 (7)
O1ii—Ti1—O2ii87.01 (8)O3xiv—Na2—O2ix161.44 (4)
O1i—Ti1—O293.66 (9)O3vi—Na2—O368.76 (10)
O1—Ti1—O287.01 (10)O3—Na2—O1ii126.60 (5)
O1ii—Ti1—O2167.06 (9)O3—Na2—O1xv61.05 (7)
O2—Ti1—O2i80.63 (10)O3—Na2—O1ix106.53 (5)
O2ii—Ti1—O2i80.63 (5)O3—Na2—O2ii161.44 (8)
O2ii—Ti1—O280.63 (9)O3—Na2—O2xv108.82 (16)
O4i—Ti2—O497.70 (5)O3—Na2—O2ix128.54 (10)
O4ii—Ti2—O497.70 (5)O3vi—Na2—O1ii106.53 (4)
O4i—Ti2—O2150.19 (9)O3vi—Na2—O1xv126.60 (5)
O4—Ti2—O284.10 (7)O3vi—Na2—O1ix61.05 (4)
O4ii—Ti2—O2111.60 (6)O3vi—Na2—O2ii128.54 (9)
O4ii—Ti2—O4i97.70 (4)O3vi—Na2—O2xv161.44 (7)
O4i—Ti2—O2i84.10 (7)O3vi—Na2—O2ix108.82 (12)
O4—Ti2—O2i111.60 (6)O1xv—Na2—O1ii117.02 (4)
O4ii—Ti2—O2i150.19 (8)O1ix—Na2—O1ii117.02 (3)
O4i—Ti2—O2ii111.60 (8)O1ii—Na2—O2ii47.77 (2)
O4—Ti2—O2ii150.19 (5)O1ii—Na2—O2xv89.76 (6)
O4ii—Ti2—O2ii84.10 (5)O1ii—Na2—O2ix103.92 (3)
O2—Ti2—O2i67.85 (12)O1ix—Na2—O1xv117.02 (4)
O2ii—Ti2—O2i67.85 (6)O1xv—Na2—O2ii103.92 (6)
O2ii—Ti2—O267.85 (11)O1xv—Na2—O2xv47.77 (6)
O2iii—TI3—O2100.58 (6)O1xv—Na2—O2ix89.76 (6)
O2iv—TI3—O2100.58 (8)O1ix—Na2—O2ii89.76 (4)
O2iii—TI3—O4147.63 (8)O1ix—Na2—O2xv103.92 (4)
O2—TI3—O478.93 (8)O1ix—Na2—O2ix47.77 (4)
O2iv—TI3—O4111.39 (9)O2xv—Na2—O2ii57.34 (10)
O2iv—TI3—O2iii100.58 (4)O2ix—Na2—O2ii57.34 (6)
O2iii—TI3—O4iii78.93 (6)O2ix—Na2—O2xv57.34 (11)
O2—TI3—O4iii111.39 (5)O3vii—Na3—O3xiv117.88 (6)
O2iv—TI3—O4iii147.63 (6)O3xvi—Na3—O3xiv117.88 (3)
O2iii—TI3—O4iv111.39 (7)O3xiv—Na3—O1i130.74 (3)
O2—TI3—O4iv147.63 (4)O3xiv—Na3—O191.77 (4)
O2iv—TI3—O4iv78.93 (4)O3xiv—Na3—O1ii71.14 (4)
O4—TI3—O4iii71.47 (7)O3xiv—Na3—O4xvii74.32 (2)
O4iv—TI3—O4iii71.47 (5)O3xiv—Na3—O4xviii60.63 (2)
O4iv—TI3—O471.47 (7)O3xix—Na3—O4xiv112.81 (3)
O3vii—TI4—O3v88.20 (8)O3viii—Na3—O3xiv163.65 (6)
O3vi—TI4—O3v88.20 (7)O3xx—Na3—O3xiv52.30 (4)
O3vi—TI4—O1viii172.26 (6)O3vi—Na3—O3xiv66.69 (2)
O3v—TI4—O1ix98.85 (5)O3xvi—Na3—O3vii117.88 (7)
O3—TI4—O1v95.19 (2)O3vii—Na3—O1i91.77 (10)
O3vi—TI4—O3vii88.20 (11)O3vii—Na3—O171.14 (7)
O3ix—TI4—O1vii95.19 (11)O3vii—Na3—O1ii130.74 (6)
O3v—TI4—O1172.26 (9)O3xvii—Na3—O4vii112.81 (7)
O3vi—TI4—O198.85 (11)O3vii—Na3—O4xviii74.32 (8)
O3v—TI4—O1ix98.85 (11)O3vii—Na3—O4xix60.63 (8)
O3viii—TI4—O1vi95.19 (7)O3viii—Na3—O3vii66.69 (6)
O3v—TI4—O1172.26 (7)O3xx—Na3—O3vii163.65 (6)
O1viii—TI4—O1ix77.43 (10)O3vi—Na3—O3vii52.30 (6)
O1—TI4—O1ix77.43 (8)O3xvi—Na3—O1i71.14 (5)
O1—TI4—O1viii77.43 (5)O3xvi—Na3—O1130.74 (7)
O4iv—TI5—O484.42 (6)O3xvi—Na3—O1ii91.77 (6)
O4iii—TI5—O484.42 (6)O3xvi—Na3—O4xvii60.63 (7)
O4—TI5—O3xi87.67 (9)O3xviii—Na3—O4xvi112.81 (5)
O4—TI5—O3xii170.18 (6)O3xvi—Na3—O4xix74.32 (5)
O4—TI5—O3x89.03 (3)O3viii—Na3—O3xvi52.30 (3)
O4iii—TI5—O4iv84.42 (4)O3xx—Na3—O3xvi66.69 (6)
O4iv—TI5—O3xi170.18 (9)O3vi—Na3—O3xvi163.65 (5)
O4iv—TI5—O3xii89.03 (5)O1—Na3—O1i59.92 (13)
O4—TI5—O3xi87.67 (2)O1ii—Na3—O1i59.92 (8)
O4iii—TI5—O3xi89.03 (8)O1i—Na3—O4xvii131.65 (7)
O4iii—TI5—O3xii87.67 (7)O1i—Na3—O4xviii165.86 (5)
O4iii—TI5—O3x170.18 (5)O1i—Na3—O4xix116.04 (11)
O3xii—TI5—O3xi98.03 (7)O1i—Na3—O3viii62.05 (2)
O3x—TI5—O3xi98.03 (6)O1i—Na3—O3xx104.41 (7)
O3x—TI5—O3xii98.03 (6)O1i—Na3—O3vi118.98 (4)
O1ix—Na1—O179.40 (9)O1ii—Na3—O159.92 (11)
O1viii—Na1—O179.40 (8)O1—Na3—O4xvii165.86 (9)
O1ix—Na1—O2149.28 (6)O1—Na3—O4xviii116.04 (14)
O1viii—Na1—O296.31 (7)O1—Na3—O4xix131.65 (11)
O1—Na1—O269.93 (7)O1—Na3—O3viii104.41 (4)
O1—Na1—O2xiii130.00 (7)O1—Na3—O3xx118.98 (6)
O1ii—Na1—O256.68 (5)O1—Na3—O3vi62.05 (6)
O1—Na1—O2iii111.02 (6)O1ii—Na3—O4xvii116.04 (7)
O1viii—Na1—O1ix79.40 (5)O1ii—Na3—O4xviii131.65 (3)
O1ix—Na1—O2ix69.93 (4)O1ii—Na3—O4xix165.86 (6)
O1viii—Na1—O2ix149.28 (7)O1ii—Na3—O3viii118.98 (4)
O1—Na1—O2ix96.31 (4)O1ii—Na3—O3xx62.05 (5)
O1xiii—Na1—O2ix56.68 (5)O1ii—Na3—O3vi104.41 (5)
O1ix—Na1—O2ii111.02 (4)O4xviii—Na3—O4xvii55.02 (7)
O1ix—Na1—O2iii130.00 (4)O4xix—Na3—O4xvii55.02 (8)
O1viii—Na1—O2ix149.28 (7)O4xvii—Na3—O3viii89.40 (2)
O1viii—Na1—O2viii69.93 (3)O4xvii—Na3—O3xx54.15 (5)
O1viii—Na1—O296.31 (7)O4xvii—Na3—O3vi108.78 (5)
O1viii—Na1—O2xiii111.02 (5)O4xix—Na3—O4xviii55.02 (6)
O1viii—Na1—O2ii130.00 (2)O4xviii—Na3—O3viii108.78 (2)
O1iii—Na1—O2viii56.68 (5)O4xviii—Na3—O3xx89.40 (7)
O2viii—Na1—O2ix110.89 (5)O4xviii—Na3—O3vi54.15 (4)
O2—Na1—O2ix110.89 (6)O4xix—Na3—O3viii54.15 (4)
O2xiii—Na1—O2ix49.56 (5)O4xix—Na3—O3xx108.78 (6)
O2ii—Na1—O2ix66.06 (4)O4xix—Na3—O3vi89.40 (4)
O2iii—Na1—O2ix147.92 (3)O3xx—Na3—O3viii118.85 (4)
O2—Na1—O2viii110.89 (5)O3vi—Na3—O3viii118.85 (2)
O2xiii—Na1—O2viii66.06 (4)O3vi—Na3—O3xx118.85 (5)
O2ii—Na1—O2viii147.92 (2)O4ii—Na4—O4xiii119.34 (3)
O2iii—Na1—O2viii49.56 (3)O4iii—Na4—O4xiii119.34 (4)
O2xiii—Na1—O2147.92 (6)O4xiii—Na4—O3xxii84.92 (5)
O2ii—Na1—O249.56 (5)O4xiii—Na4—O3xxi70.53 (4)
O2iii—Na1—O266.06 (5)O4xiii—Na4—O3xi128.51 (2)
O2ii—Na1—O2xiii115.17 (3)O4xiii—Na4—O4171.43 (2)
O2iii—Na1—O2xiii115.17 (4)O4ix—Na4—O4xiii61.78 (2)
O2iii—Na1—O2ii115.17 (3)O4xiii—Na4—O4viii57.88 (3)
O1xiv—Na2—O1vi115.02 (3)O4iii—Na4—O4ii119.34 (5)
O1—Na2—O1vi115.02 (5)O4xiii—Na4—O3xi128.51 (6)
O1vi—Na2—O3xiv73.29 (4)O4iii—Na4—O3xxi84.92 (8)
O1vi—Na2—O391.24 (6)O4iii—Na4—O3xi70.53 (3)
O1vi—Na2—O3vi141.38 (5)O4xiii—Na4—O4viii57.88 (2)
O1ii—Na2—O1vi58.68 (4)O4iii—Na4—O4ix171.43 (3)
O1xv—Na2—O1vi58.78 (4)O4—Na4—O4ii61.78 (4)
O1ix—Na2—O1vi156.85 (4)O4iii—Na4—O3xi70.53 (7)
O1vi—Na2—O2ii70.81 (5)O4iii—Na4—O3xxii128.51 (4)
O1xv—Na2—O2vi55.25 (5)O4iii—Na4—O3xxi84.92 (6)
O1vi—Na2—O2ix109.42 (5)O4viii—Na4—O4iii61.78 (3)
O1—Na2—O1xiv115.02 (6)O4iii—Na4—O457.88 (4)
O1xiv—Na2—O3xiv141.38 (2)O4ii—Na4—O4viii171.43 (3)
O1xiv—Na2—O373.29 (5)O3xxii—Na4—O3xi59.77 (17)
O1xiv—Na2—O3vi91.24 (4)O3xxi—Na4—O3xi59.77 (13)
O1ii—Na2—O1xiv156.85 (2)O3xxii—Na4—O4103.10 (5)
O1xv—Na2—O1xiv58.68 (5)O3xxi—Na4—O4viii59.41 (5)
O1ix—Na2—O1xiv58.78 (3)O3xxii—Na4—O4viii116.02 (6)
O1xiv—Na2—O2ii109.42 (2)O3xxi—Na4—O3xxii59.77 (11)
O1xiv—Na2—O2xv70.81 (7)O3xi—Na4—O4ix116.02 (4)
O1ix—Na2—O2xiv55.25 (3)O3xi—Na4—O4viii103.10 (6)
O1—Na2—O3xiv91.24 (8)O3xxii—Na4—O4ix59.41 (3)
O1—Na2—O3141.38 (8)O3xi—Na4—O459.41 (1)
O1—Na2—O3vi73.29 (6)O3xxi—Na4—O4116.02 (2)
O1ii—Na2—O158.78 (5)O3xxi—Na4—O4ix103.10 (4)
O1xv—Na2—O1156.85 (6)O4ix—Na4—O4viii119.60 (2)
O1ix—Na2—O158.68 (5)O4—Na4—O4viii119.60 (3)
O1ii—Na2—O255.25 (7)O4—Na4—O4ix119.60 (4)
O1—Na2—O2xv109.42 (7)
Symmetry codes: (i) x+y, x+1, z; (ii) y+1, xy+1, z; (iii) x+y1, x, z; (iv) y, xy+1, z; (v) y, xy1, z; (vi) x+y+1, x+1, z; (vii) x1, y, z; (viii) y, xy, z; (ix) x+y, x, z; (x) y, xy, z1; (xi) x1, y, z1; (xii) x+y, x+1, z1; (xiii) x, y1, z; (xiv) y+1, xy, z; (xv) x+1, y, z; (xvi) x+y+1, x+2, z; (xvii) x+y, x+1, z+1; (xviii) y+1, xy+1, z+1; (xix) x, y, z+1; (xx) x, y+1, z; (xxi) y, xy1, z1; (xxii) x+y+1, x+1, z1.

Experimental details

Crystal data
Chemical formulaNa4Ti5O12
Mr522.30
Crystal system, space groupTrigonal, P3
Temperature (K)295
a, c (Å)5.31997 (14), 9.5567 (3)
V3)234.24 (1)
Z1
Radiation typeCu Kα1, Cu Kα2, λ = 1.54056, 1.54439 Å
Specimen shape, size (mm)Flat sheet, 18 × 20
Data collection
DiffractometerRigaku D/MAX-B
diffractometer
Specimen mountingDrifted powder on off-cut glass
Data collection modeReflection
Scan methodStep
2θ values (°)2θmin = 18.0 2θmax = 120.0 2θstep = 0.02
Refinement
R factors and goodness of fitRp = 6.85, Rwp = 9.44, Rexp = 4.07, χ2 = 28.837
No. of data points5101
No. of parameters60
No. of restraints?

Computer programs: D/MAX-B (Rigaku, 1992), FULLPROF (Rodriguez-Carvajal, 1990), SHELXS97 (Sheldrick, 1997), DIAMOND (Bergerhoff et al., 1996), WINPLOTR (Roisnel & Rodruguez-Carvajal, 1999).

Selected bond lengths (Å) top
Ti1—O1i1.82 (5)TI3—O4iii2.27 (8)
Ti1—O1ii1.82 (5)TI3—O42.27 (8)
Ti1—O11.82 (5)TI3—O4iv2.27 (8)
Ti1—O2i1.90 (7)TI4—O3v1.78 (6)
Ti1—O21.90 (7)TI4—O3vi1.78 (6)
Ti1—O2ii1.90 (7)TI4—O3vii1.78 (6)
Ti2—O41.86 (5)TI4—O12.18 (8)
Ti2—O4i1.86 (5)TI4—O1viii2.18 (8)
Ti2—O4ii1.86 (5)TI4—O1ix2.18 (8)
Ti2—O2i2.20 (8)TI5—O41.97 (7)
Ti2—O22.20 (8)TI5—O4iv1.97 (7)
Ti2—O2ii2.20 (8)TI5—O4iii1.97 (7)
TI3—O22.02 (5)TI5—O3x2.01 (5)
TI3—O2iii2.02 (5)TI5—O3xi2.01 (5)
TI3—O2iv2.02 (5)TI5—O3xii2.01 (5)
Symmetry codes: (i) x+y, x+1, z; (ii) y+1, xy+1, z; (iii) x+y1, x, z; (iv) y, xy+1, z; (v) y, xy1, z; (vi) x+y+1, x+1, z; (vii) x1, y, z; (viii) y, xy, z; (ix) x+y, x, z; (x) y, xy, z1; (xi) x1, y, z1; (xii) x+y, x+1, z1.
 

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