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Singlecrystal Xray diffraction and specific heat studies establish that strontium hexavanadium undecaoxide, SrV_{6}O_{11}, undergoes a P6_{3}/mmc to inversion twinned P6_{3}mc structural transition as the temperature is lowered through 322 K. The P6_{3}/mmc and P6_{3}mc structures have been determined at 353 K and at room temperature, respectively. For the roomtemperature structure, seven of the ten unique atoms lie on special positions, and for the 353 K structure all of the seven unique atoms sit on special positions. The P6_{3}/mmc to P6_{3}mc structural phase transition, accompanied by a magnetic transition, is a common characteristic of AV_{6}O_{11} compounds, independent of the identity of the A cations.
Supporting information
Sr_{2}V_{2}O_{7} and V_{2}O_{3} were mixed in a 1:5 molar ratio. The mixture was
sealed in a platinum capsule and heated at 1073 K for 1 d and 1473 K for 2
weeks, successively. Crystals of SrV_{6}O_{11} were hexagonal plates with
principal faces {001}. Sizes were typically 0.2 mm across the plate and 0.1 mm
in thickness.
Data collection at 353 K was achieved by blowing hot nitrogen gas onto the
specimen. The temperature was calibrated by an chromelalumel thermocouple
with a waterice standard. The specific heat of singlecrystal SrV_{6}O_{11} was
measured using a Quantum Design Physical Property Measurement System (PPMS).
The temperature range of the measurements was from 2.4 to 350 K.
Structural parameters including one singledomain model or two twin models,
scale factors and one free parameter for extinction correction were refined
with SHELXL97 (Sheldrick, 2008).
For both compounds, data collection: CAD4 (Enraf–Nonius, 1981); cell refinement: CAD4 (Enraf–Nonius, 1981); data reduction: SDP (Frenz, B. A. & Associates, Inc., 1985); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008). Molecular graphics: VESTA (K. Momma et al., 2008) for I_353K; ATOMS (Dowty, 2003) for I_RT. For both compounds, software used to prepare material for publication: SHELXL97 (Sheldrick, 2008).
(I_353K) strontium haxavanadium undecaoxide
top
Crystal data top
SrV_{6}O_{11}  D_{x} = 5.016 Mg m^{−}^{3} 
M_{r} = 569.26  Mo Kα radiation, λ = 0.71073 Å 
Hexagonal, P6_{3}/mmc  Cell parameters from 22 reflections 
Hall symbol: P6c2c  θ = 43.0–44.5° 
a = 5.7773 (1) Å  µ = 14.15 mm^{−}^{1} 
c = 13.0852 (3) Å  T = 353 K 
V = 378.23 (1) Å^{3}  Plate, black 
Z = 2  0.31 × 0.14 × 0.08 mm 
F(000) = 528  
Data collection top
Enraf–Nonius CAD4 diffractometer  447 reflections with I > 1.5σ(I) 
Radiation source: finefocus sealed tube  R_{int} = 0.016 
Graphite monochromator  θ_{max} = 45.0°, θ_{min} = 3.1° 
ω/2θ–scan  h = −5→5 
Absorption correction: gaussian (SDP; Frenz, B. A. & Associates, Inc., 1985)  k = −9→9 
T_{min} = 0.413, T_{max} = 0.532  l = −26→26 
1290 measured reflections  3 standard reflections every 240 min 
645 independent reflections  intensity decay: 0.7% 
Refinement top
Refinement on F^{2}  Primary atom site location: isomorphous structure methods 
Leastsquares matrix: full  Secondary atom site location: difference Fourier map 
R[F^{2} > 2σ(F^{2})] = 0.021  w = 1/[σ^{2}(F_{o}^{2}) + (0.0218P)^{2} + 0.2463P] where P = (F_{o}^{2} + 2F_{c}^{2})/3 
wR(F^{2}) = 0.054  (Δ/σ)_{max} < 0.001 
S = 1.37  Δρ_{max} = 0.84 e Å^{−}^{3} 
447 reflections  Δρ_{min} = −0.81 e Å^{−}^{3} 
26 parameters  Extinction correction: SHELXL, Fc^{*}=kFc[1+0.001xFc^{2}λ^{3}/sin(2θ)]^{1/4} 
0 restraints  Extinction coefficient: 0.061 (3) 
Crystal data top
SrV_{6}O_{11}  Z = 2 
M_{r} = 569.26  Mo Kα radiation 
Hexagonal, P6_{3}/mmc  µ = 14.15 mm^{−}^{1} 
a = 5.7773 (1) Å  T = 353 K 
c = 13.0852 (3) Å  0.31 × 0.14 × 0.08 mm 
V = 378.23 (1) Å^{3}  
Data collection top
Enraf–Nonius CAD4 diffractometer  447 reflections with I > 1.5σ(I) 
Absorption correction: gaussian (SDP; Frenz, B. A. & Associates, Inc., 1985)  R_{int} = 0.016 
T_{min} = 0.413, T_{max} = 0.532  3 standard reflections every 240 min 
1290 measured reflections  intensity decay: 0.7% 
645 independent reflections  
Refinement top
R[F^{2} > 2σ(F^{2})] = 0.021  26 parameters 
wR(F^{2}) = 0.054  0 restraints 
S = 1.37  Δρ_{max} = 0.84 e Å^{−}^{3} 
447 reflections  Δρ_{min} = −0.81 e Å^{−}^{3} 
Special details top
Experimental. Data collection was carried out at 353 K by blowing hot nitrogen gas onto the
specimen. The temperature was calibrated by an chromel  alumel thermocouple
with a waterice standard. 
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 F^{2} against ALL reflections. The weighted Rfactor
wR and goodness of fit S are based on F^{2}, conventional
Rfactors R are based on F, with F set to zero for
negative F^{2}. The threshold expression of F^{2} >
σ(F^{2}) is used only for calculating Rfactors(gt) etc.
and is not relevant to the choice of reflections for refinement.
Rfactors based on F^{2} are statistically about twice as large
as those based on F, and R factors based on ALL data will be
even larger. 
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å^{2}) top  x  y  z  U_{iso}*/U_{eq}  
Sr1  0.3333  0.6667  0.2500  0.01058 (13)  
V1  0.5000  0.5000  0.5000  0.00609 (9)  
V2  0.0000  0.0000  0.35381 (4)  0.00490 (9)  
V3  0.3333  0.6667  0.7500  0.00656 (13)  
O1  0.17350 (14)  0.3470 (3)  0.41844 (9)  0.0069 (2)  
O2  0.3048 (4)  0.1524 (2)  0.2500  0.0083 (3)  
O3  0.3333  0.6667  0.59029 (16)  0.0061 (4)  
Atomic displacement parameters (Å^{2}) top  U^{11}  U^{22}  U^{33}  U^{12}  U^{13}  U^{23} 
Sr1  0.01041 (16)  0.01041 (16)  0.0109 (2)  0.00521 (8)  0.000  0.000 
V1  0.00578 (12)  0.00919 (16)  0.00444 (13)  0.00459 (8)  0.00005 (9)  0.00011 (18) 
V2  0.00495 (11)  0.00495 (11)  0.00479 (15)  0.00247 (6)  0.000  0.000 
V3  0.00402 (19)  0.00402 (19)  0.0117 (3)  0.00201 (9)  0.000  0.000 
O1  0.0065 (4)  0.0066 (5)  0.0078 (4)  0.0033 (2)  0.00099 (19)  0.0020 (4) 
O2  0.0120 (7)  0.0053 (8)  0.0055 (6)  0.0026 (4)  0.000  0.000 
O3  0.0060 (5)  0.0060 (5)  0.0062 (8)  0.0030 (3)  0.000  0.000 
Geometric parameters (Å, º) top
Sr1—O1  2.7232 (13)  V2—O2  2.0423 (16) 
Sr1—O2  2.892 (2)  V3—O2^{i}  1.810 (2) 
V1—O1  1.9522 (9)  V3—O3  2.090 (2) 
V1—O3  2.0438 (12)  V1—V1^{ii}  2.8887 (1) 
V2—O1  1.9312 (14)  V2—V2^{iii}  2.7166 (9) 
   
O1—V1—O1^{iv}  90.39 (8)  O2^{i}—V3—O3  90 
O1—V1—O1^{v}  89.61 (8)  V1—O1—V1^{ii}  95.44 (6) 
O1—V1—O3^{v}  92.68 (4)  V1—O3—V1^{ii}  89.93 (7) 
O1—V1—O3  87.32 (4)  V2—O2—V2^{iii}  83.38 (8) 
O1—V2—O1^{vi}  102.26 (5)  V1—O1—V2  126.29 (4) 
O1—V2—O2  87.46 (4)  V1—O3—V3  125.31 (5) 
O2—V2—O2^{vi}  80.59 (6)  V2—O2—V3^{viii}  138.31 (4) 
O2^{i}—V3—O2^{vii}  120   
Symmetry codes: (i) x−y, x, z+1/2; (ii) −x+y, −x+1, z; (iii) x, y, −z+1/2; (iv) −y+1, x−y+1, z; (v) y, −x+y, −z+1; (vi) −x+y, −x, z; (vii) y, −x+y+1, z+1/2; (viii) y, −x+y, z−1/2. 
(I_RT) strontium haxavanadium undecaoxide
top
Crystal data top
SrV_{6}O_{11}  D_{x} = 5.013 Mg m^{−}^{3} 
M_{r} = 569.26  Mo Kα radiation, λ = 0.71073 Å 
Hexagonal, P6_{3}mc  Cell parameters from 22 reflections 
Hall symbol: P6c2c  θ = 43.0–44.5° 
a = 5.7702 (1) Å  µ = 14.19 mm^{−}^{1} 
c = 13.0784 (3) Å  T = 295 K 
V = 377.11 (1) Å^{3}  Plate, black 
Z = 2  0.31 × 0.14 × 0.08 mm 
F(000) = 528  
Data collection top
Enraf–Nonius CAD4 diffractometer  1065 reflections with I > 1.5σ(I) 
Radiation source: finefocus sealed tube  R_{int} = 0.016 
Graphite monochromator  θ_{max} = 45.0°, θ_{min} = 3.1° 
ω/2θ–scan  h = −5→5 
Absorption correction: gaussian (SDP; Frenz, B. A. & Associates, Inc., 1985)  k = −8→8 
T_{min} = 0.382, T_{max} = 0.529  l = −25→25 
1284 measured reflections  3 standard reflections every 240 min 
1247 independent reflections  intensity decay: 0.4% 
Refinement top
Refinement on F^{2}  Secondary atom site location: difference Fourier map 
Leastsquares matrix: full  w = 1/[σ^{2}(F_{o}^{2}) + (0.0294P)^{2} + 0.2563P] where P = (F_{o}^{2} + 2F_{c}^{2})/3 
R[F^{2} > 2σ(F^{2})] = 0.022  (Δ/σ)_{max} < 0.001 
wR(F^{2}) = 0.055  Δρ_{max} = 0.97 e Å^{−}^{3} 
S = 1.21  Δρ_{min} = −1.27 e Å^{−}^{3} 
1065 reflections  Extinction correction: SHELXL, Fc^{*}=kFc[1+0.001xFc^{2}λ^{3}/sin(2θ)]^{1/4} 
44 parameters  Extinction coefficient: 0.052 (2) 
0 restraints  Absolute structure: refinement of absolute structure parameter (Flack, 1983) 
Primary atom site location: isomorphous structure methods  Absolute structure parameter: 0.434 (7) 
Crystal data top
SrV_{6}O_{11}  Z = 2 
M_{r} = 569.26  Mo Kα radiation 
Hexagonal, P6_{3}mc  µ = 14.19 mm^{−}^{1} 
a = 5.7702 (1) Å  T = 295 K 
c = 13.0784 (3) Å  0.31 × 0.14 × 0.08 mm 
V = 377.11 (1) Å^{3}  
Data collection top
Enraf–Nonius CAD4 diffractometer  1065 reflections with I > 1.5σ(I) 
Absorption correction: gaussian (SDP; Frenz, B. A. & Associates, Inc., 1985)  R_{int} = 0.016 
T_{min} = 0.382, T_{max} = 0.529  3 standard reflections every 240 min 
1284 measured reflections  intensity decay: 0.4% 
1247 independent reflections  
Refinement top
R[F^{2} > 2σ(F^{2})] = 0.022  0 restraints 
wR(F^{2}) = 0.055  Δρ_{max} = 0.97 e Å^{−}^{3} 
S = 1.21  Δρ_{min} = −1.27 e Å^{−}^{3} 
1065 reflections  Absolute structure: refinement of absolute structure parameter (Flack, 1983) 
44 parameters  Absolute structure parameter: 0.434 (7) 
Special details top
Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes)
are estimated using the full covariance matrix. The cell e.s.d.'s are taken
into account individually in the estimation of e.s.d.'s in distances, angles
and torsion angles; correlations between e.s.d.'s in cell parameters are only
used when they are defined by crystal symmetry. An approximate (isotropic)
treatment of cell e.s.d.'s is used for estimating e.s.d.'s involving l.s.
planes. 
Refinement. The specimen was twinned about (001). The refinement was carried out on the
basis of the twin model. 
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å^{2}) top  x  y  z  U_{iso}*/U_{eq}  
Sr1  0.3333  0.6667  0.25372 (12)  0.00913 (12)  
V1  0.50511 (3)  0.49489 (3)  0.5  0.00503 (6)  
V21  0.0000  0.0000  0.14466 (15)  0.0053 (3)  
V22  0.0000  0.0000  0.35226 (14)  0.0031 (2)  
V3  0.3333  0.6667  0.74409 (12)  0.00449 (14)  
O11  0.17369 (16)  0.3474 (3)  0.0836 (2)  0.0064 (2)  
O12  0.17370 (17)  0.3474 (3)  0.4203 (2)  0.0057 (2)  
O2  0.3057 (3)  0.15287 (15)  0.2507 (2)  0.0076 (2)  
O31  0.3333  0.6667  0.5882 (3)  0.0062 (4)  
O32  0.6667  0.3333  0.4074 (3)  0.0057 (4)  
Atomic displacement parameters (Å^{2}) top  U^{11}  U^{22}  U^{33}  U^{12}  U^{13}  U^{23} 
Sr1  0.00883 (11)  0.00883 (11)  0.0097 (3)  0.00441 (5)  0.000  0.000 
V1  0.00483 (8)  0.00483 (8)  0.00376 (9)  0.00115 (7)  0.00005 (10)  −0.00005 (10) 
V21  0.0073 (4)  0.0073 (4)  0.0012 (4)  0.00366 (19)  0.000  0.000 
V22  0.0015 (3)  0.0015 (3)  0.0064 (6)  0.00074 (14)  0.000  0.000 
V3  0.00384 (13)  0.00384 (13)  0.0058 (4)  0.00192 (7)  0.000  0.000 
O11  0.0066 (4)  0.0066 (4)  0.0061 (4)  0.0036 (5)  0.0008 (2)  −0.0008 (2) 
O12  0.0054 (4)  0.0054 (4)  0.0059 (5)  0.0025 (5)  −0.0007 (2)  0.0007 (2) 
O2  0.0113 (4)  0.0113 (4)  0.0046 (4)  0.0091 (5)  0.0002 (3)  −0.0002 (3) 
O31  0.0060 (6)  0.0060 (6)  0.0064 (8)  0.0030 (3)  0.000  0.000 
O32  0.0038 (6)  0.0038 (6)  0.0096 (10)  0.0019 (3)  0.000  0.000 
Geometric parameters (Å, º) top
Sr1—O11  2.738 (2)  V22—O12  1.951 (2) 
Sr1—O12  2.700 (2)  V22—O2  2.025 (3) 
Sr1—O2  2.8887 (9)  V3—O2^{ii}  1.8057 (15) 
V1—O11^{i}  1.9422 (18)  V3—O31  2.038 (4) 
V1—O12  1.9598 (16)  V3—O32^{ii}  2.136 (3) 
V1—O31  2.069 (2)  V1—V1^{iii}  2.7966 (6) 
V1—O32  2.018 (2)  V1—V1^{iv}  2.9736 (6) 
V21—O11  1.911 (2)  V21—V22  2.7151 (8) 
V21—O2  2.063 (3)   
   
O11^{i}—V1—O11^{v}  90.71 (13)  O2^{ii}—V3—O31  92.74 (9) 
O12—V1—O12^{vi}  89.66 (12)  O2^{ii}—V3—O32^{ii}  87.26 (9) 
O11^{i}—V1—O12  89.72 (6)  V1^{ix}—O11—V1^{x}  92.10 (11) 
O11^{i}—V1—O31  92.01 (10)  V1—O12—V1^{iv}  98.69 (11) 
O12—V1—O32  93.21 (10)  V1—O31—V1^{iv}  91.91 (12) 
O11^{i}—V1—O32  90.07 (6)  V1—O32—V1^{iii}  87.71 (13) 
O12—V1—O31  84.69 (5)  V21—O2—V22  83.23 (6) 
O11—V21—O11^{vii}  103.77 (13)  V1^{ix}—O11—V21  127.16 (7) 
O11—V21—O2  86.82 (6)  V1—O12—V22  125.26 (5) 
O2—V21—O2^{vii}  79.77 (13)  V1—O31—V3  123.91 (8) 
O12—V22—O12^{vii}  100.84 (11)  V1—O32—V3^{xi}  126.87 (9) 
O12—V22—O2  87.90 (4)  V21—O2—V3^{xi}  135.03 (16) 
O2—V22—O2^{vii}  81.62 (11)  V22—O2—V3^{xi}  141.73 (15) 
O2^{ii}—V3—O2^{viii}  119.774 (16)   
Symmetry codes: (i) y, −x+y, z+1/2; (ii) x−y, x, z+1/2; (iii) −y+1, x−y, z; (iv) −x+y, −x+1, z; (v) −x+1, −y+1, z+1/2; (vi) −y+1, x−y+1, z; (vii) −y, x−y, z; (viii) y, −x+y+1, z+1/2; (ix) x−y, x, z−1/2; (x) −x+1, −y+1, z−1/2; (xi) y, −x+y, z−1/2. 
Experimental details
 (I_353K)  (I_RT) 
Crystal data 
Chemical formula  SrV_{6}O_{11}  SrV_{6}O_{11} 
M_{r}  569.26  569.26 
Crystal system, space group  Hexagonal, P6_{3}/mmc  Hexagonal, P6_{3}mc 
Temperature (K)  353  295 
a, c (Å)  5.7773 (1), 13.0852 (3)  5.7702 (1), 13.0784 (3) 
V (Å^{3})  378.23 (1)  377.11 (1) 
Z  2  2 
Radiation type  Mo Kα  Mo Kα 
µ (mm^{−}^{1})  14.15  14.19 
Crystal size (mm)  0.31 × 0.14 × 0.08  0.31 × 0.14 × 0.08 

Data collection 
Diffractometer  Enraf–Nonius CAD4 diffractometer  Enraf–Nonius CAD4 diffractometer 
Absorption correction  Gaussian (SDP; Frenz, B. A. & Associates, Inc., 1985)  Gaussian (SDP; Frenz, B. A. & Associates, Inc., 1985) 
T_{min}, T_{max}  0.413, 0.532  0.382, 0.529 
No. of measured, independent and observed [I > 1.5σ(I)] reflections  1290, 645, 447  1284, 1247, 1065 
R_{int}  0.016  0.016 
(sin θ/λ)_{max} (Å^{−}^{1})  0.995  0.995 

Refinement 
R[F^{2} > 2σ(F^{2})], wR(F^{2}), S  0.021, 0.054, 1.37  0.022, 0.055, 1.21 
No. of reflections  447  1065 
No. of parameters  26  44 
Δρ_{max}, Δρ_{min} (e Å^{−}^{3})  0.84, −0.81  0.97, −1.27 
Absolute structure  ?  Refinement of absolute structure parameter (Flack, 1983) 
Absolute structure parameter  ?  0.434 (7) 
Selected bond lengths (Å) for (I_353K) topSr1—O1  2.7232 (13)  V2—O2  2.0423 (16) 
Sr1—O2  2.892 (2)  V3—O2^{i}  1.810 (2) 
V1—O1  1.9522 (9)  V3—O3  2.090 (2) 
V1—O3  2.0438 (12)  V1—V1^{ii}  2.8887 (1) 
V2—O1  1.9312 (14)  V2—V2^{iii}  2.7166 (9) 
Symmetry codes: (i) x−y, x, z+1/2; (ii) −x+y, −x+1, z; (iii) x, y, −z+1/2. 
Selected bond lengths (Å) for (I_RT) topSr1—O11  2.738 (2)  V22—O12  1.951 (2) 
Sr1—O12  2.700 (2)  V22—O2  2.025 (3) 
Sr1—O2  2.8887 (9)  V3—O2^{ii}  1.8057 (15) 
V1—O11^{i}  1.9422 (18)  V3—O31  2.038 (4) 
V1—O12  1.9598 (16)  V3—O32^{ii}  2.136 (3) 
V1—O31  2.069 (2)  V1—V1^{iii}  2.7966 (6) 
V1—O32  2.018 (2)  V1—V1^{iv}  2.9736 (6) 
V21—O11  1.911 (2)  V21—V22  2.7151 (8) 
V21—O2  2.063 (3)   
Symmetry codes: (i) y, −x+y, z+1/2; (ii) x−y, x, z+1/2; (iii) −y+1, x−y, z; (iv) −x+y, −x+1, z. 
Table 1. Results for refinement of different models for SrV_{6}O_{11} at room
temperature. topSpace Group  Model  N_{r}  N_{P}  R_{1}  wR_{2} 
P6_{3}/mmc  Unique^{a}  1093  26  0.0574  0.1111 
P6_{3}mc  (x, y, z)^{b}  1093  43  0.0459  0.1002 
P6_{3}mc  (x, y, z)^{b}  1093  43  0.0390  0.0832 
P6_{3}mc  (x, y, z)+(x, y, z)^{c}  1093  44  0.0231  0.0515 
P62c  (x, y, z)^{d}  1093  32  0.0571  0.1110 
P62c  (x, y, z)^{d}  1093  32  0.0571  0.1110 
P62c  (x, y, z)+(x, y, z)^{e,f}  1093  33  0.0558  0.1100 
Notes: (a) displacement parameters of V1 are negative; (b) displacement
parameters of O2 are negative; (c) the volume fraction
(x, y, z):(x, y, z) =
0.428:0.572 (8); (d) displacement parameters of V1 and O2 are negative;
(e) displacement parameters of V1, O1 and O2 are negative; (f) the volume
fraction (x, y, z):(x, y, z) =
0.519:0.481 (72). 
Table 2. Selected bond lengths (Å) for SrV_{6}O_{11} at 353 K. topSr1—O1  2.7232 (13)  V2—O2  2.0423 (16) 
Sr1—O2  2.892 (2)  V3—O2^{i}  1.810 (2) 
V1—O1  1.9522 (9)  V3—O3  2.090 (2) 
V1—O3  2.0438 (12)  V1—V1^{ii}  2.88870 (10) 
V2—O1  1.9312 (14)  V2—V2^{iii}  2.7166 (9) 
Symmetry codes: (i) xy, x, z+1/2;
(ii) x+y, 1x, z;
(iii) x, y, z+1/2. 
Table 3. Selected bond lengths (Å) for SrV_{6}O_{11} at room temperature. topSr1—O11  2.738 (2)  V22—O12  1.951 (2) 
Sr1—O12  2.700 (2)  V22—O2  2.025 (3) 
Sr1—O2  2.8887 (9)  V3—O2^{ii}  1.8057 (15) 
V1—O11^{i}  1.9422 (18)  V3—O31  2.038 (4) 
V1—O12  1.9598 (16)  V3—O32^{ii}  2.136 (3) 
V1—O31  2.069 (2)  V1—V1^{iii}  2.7966 (6) 
V1—O32  2.018 (2)  V1—V1^{iv}  2.9736 (6) 
V21—O11  1.911 (2)  V21—V22  2.7151 (8) 
V21—O2  2.063 (3)   
Symmetry codes: (i) y, x+y, 1/2+z;
(ii) xy, x, 1/2+z;
(iii) 1y, 1+xy, z;
(iv) 1x+y, 1x, z. 
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A series of AV_{6}O_{11} compounds (A = Na, K, Sr, Ba, Pb; de Roy et al., 1987; Kanke, 1999; Kanke et al., 1991; Friese et al., 2006; Mentre et al., 1996) have generated interest because of their structural phase transitions, magnetic and transport properties (Kanke et al., 1990, 1994; Uchida et al., 1991, 2001; Mentre et al., 2001). Their crystal structures consist of hexagonal closepacked layers of the A and O atoms, and three types of V atoms (Fig. 1). The V1O_{6} octahedra form a Kagomé lattice by edge sharing. The V2O_{6} octahedra form facesharing dimers between the layers of the Kagomé lattice. The coordination of V3O_{5} is a trigonal bipyramid.
While the AV_{6}O_{11} compounds show common characteristics in their paramagnetic states, they exhibit individual ones for their magnetically ordered states. In the paramagnetic states, each AV_{6}O_{11} shows one phase transition at a characteristic temperature, T_{t}. Above T_{t}, the compounds crystallize in the centrosymmetric hexagonal group P6_{3}/mmc, and show Curie–Weiss paramagnetism. Below T_{t}, the compounds lose the centre of symmetry and show secondorder transitions to hexagonal P6_{3}mc (Kanke et al., 1994). The V1O_{6} octahedron forms a regular Kagomé lattice above T_{t}. It distorts to form a V1O_{6} trimer with a regular triangular shape below T_{t}. Two V2O_{6} octahedra forming a facesharing dimer are crystallographically equivalent above T_{t}. Below T_{t}, they become inequivalent. V3 is no longer at the centre of the V3O_{5} polyhedron below T_{t}. In the P6_{3}mc form of AV_{6}O_{11}, V1 exhibits a spin gap behaviour with a spinsinglet ground state, while V2 and V3 possess magnetic moments (Uchida et al., 2001). T_{t} values for KV_{6}O_{11} (Kanke, 1999), BaV_{6}O_{11} (Friese et al., 2006) and PbV_{6}O_{11} (Kato et al., 2001) are 190, 250 and 560 K, respectively.
As first reported, the roomtemperature structure of SrV_{6}O_{11} was assigned to P6_{3}/mmc with a relatively high R factor (Kanke et al., 1992). The T_{t} = 320 K of SrV_{6}O_{11} exceeds room temperature, which suggests an incorrect assignment of the space group. We have pointed out briefly the existence of the P6_{3}/mmc–P6_{3}mc transition at 320 K (Hata et al., 1999). Kato et al. studied the transition by Xray powder diffraction. They refined the structures at 100 K in P6_{3}mc and at 623 K in P6_{3}/mmc (Kato et al., 2001). However, we considered a singlecrystal diffraction study to be indispensable for an accurate structural characterization of the acentric phase. In the present study, the crystal structure of SrV_{6}O_{11} was determined in detail both above T_{t} (353 K) and below T_{t} (room temperature) by singlecrystal Xray diffraction. The transition temperature was determined precisely by a specific heat study.
At both room temperature and 353 K, diffraction data showed hexagonal symmetry and an extinction rule, l ≠ 2n absent for hhl, indicating possible space groups P6_{3}/mmc, P62c and P6_{3}mc. P6_{3}/mmc is centrosymmetric and gives a unique structural model. But the other two are acentric, and each gives a pair of single domain models, (x, y, z) and (x, y, z), and one twin model, [(x, y, z) + (x, y, z)].
To examine the possible models, reflections with h ≥ 0, k ≥ 0, l ≥ 0, h ≤ k, 2θ < 90°, and those with h ≤ 0, k ≤ 0, l ≤ 1, h ≤ k, 2θ ≤ 90° were collected at both temperatures using a fourcircle diffractometer (Enraf–Nonius CAD4) with Mo Kα radiation. As the diffractometer is equipped with a scintillation counter, too weak reflections were regarded as unobserved. Thus, 185 of a total of 1284 reflections for room temperature, and 349 of 1290 reflections for 353 K were assigned as unobserved. The refinements did not use the unobserved data. The data, however, are of high resolution, 0.5 Å, and have what we consider sufficient completeness; for 2θ < 50°, the completeness is 97.4% for room temperature and 92.9% for 353 K, even without the unobserved data. As a result, the model examinations give clear results as follows.
The models for room temperature were examined using 1093 Friedelunaveraged reflections with I > 1.5σ (I), applying the common weighting scheme of 1/σ(I). As shown in Table 1, the twin P6_{3}mc model gave troublefree convergence and low enough R factors (R_{1 }= 0.0231, wR_{2 }= 0.0515, 44 parameters). However, all of the remaining models resulted in nonpositive definite temperature factor(s) and significantly higher R factors. Consequently, the twinned P6_{3}mc model was selected. This clear differentiation of the results for the different models also indicates high enough quality of the specimen and high enough resolution of the diffraction data.
The models for 353 K were examined using 919 unaveraged reflections with I > 1.5σ (I), applying the common weighting scheme of 1/σ (I). All seven models gave troublefree convergence and low enough R factors (R_{1 }= 0.0236–0.0242, wR_{2 }= 0.0511–0.0526, 26–44 parameters). Consequently, there is no reason to choose any of the acentric space groups, and the P6_{3}/mmc model, with the highest symmetry, is selected.
The roomtemperature structure of SrV_{6}O_{11} had earlier been described by Kanke et al. (1992) using P6_{3}/mmc. They compared the P6_{3}/mmc model, two singledomain models of P62c and two singledomain models of P6_{3}mc, using 2031 unaveraged intensities. The P6_{3}/mmc model, the better P62c model and the better P6_{3}mc model gave R = 0.070 with 24 parameters, R = 0.069 with 24 parameters and R = 0.064 with 35 parameters, respectively. The difference in the R factors was concluded to be insignificant, considering the numbers of parameters. Consequently, they chose the P6_{3}/mmc model with the highest symmetry. However, the study did not examine the twin models for the two acentric space groups. None of the models was free from negative temperature factors, and anisotropic thermal parameters were not applied to O2 even in the final refinement. In the present study, in fact only the P6_{3}mc model with twinning is free of nonpositive definite displacement parameters, and this model clearly gives the best result among the seven models tested. We thus correct the previous report with this determination that SrV_{6}O_{11} crystallizes in P6_{3}mc with twinning at room temperature.
Between the two temperatures, room temperature and 353 K, the specific heat of SrV_{6}O_{11} shows only one anomaly, at 322 K. Consequently, we conclude that the structural phase transition takes place at 322 K and coincides with the magnetic transition.
The structural refinements of the P6_{3}mc forms of NaV_{6}O_{11} (Kanke et al., 1994) and PbV_{6}O_{11} (Mentre et al., 1996) converged promptly without applying twinning. Kanke (1999) suggested that this may be due to the small anomalous dispersion term for Na for Mo Kα in NaV_{6}O_{11} or may suggest that the volume fraction ratio (x, y, z) / (x, y, z) is far from 1.0 in PbV_{6}O_{11} and/or in NaV_{6}O_{11}.
The P6_{3}mc and P6_{3}/mmc forms of SrV_{6}O_{11} are illustrated in Figs. 1 and 2, respectively. In both forms, the V1 ellipsoid is elongated towards the centre of the V1 trimer. V2 is nearly isotropic in the P6_{3}/mmc form. In the P6_{3}mc form, though, V21 is oblate, compressed into (001) and V22 is prolate along [001]. V3 shows extended displacement along [001] in the P6_{3}/mmc form, but is rather isotropic in the P6_{3}mc form.
For the P6_{3}mc form, seven of the ten unique atoms lie on special positions, and for the P6_{3}/mmc form all of the seven unique atoms sit on special positions. In the centric structure, the V1O_{6} octahedra form a regular Kagomé lattice with a uniform V1···V1 distance of 2.8887 (1) Å (Table 2). In the P6_{3}mc phase, though, the Kagomé lattice distorts, with the V1O_{6} octahedra forming a trimer with a regular triangular shape; and the V1···V1 distance separates into two types, intertrimer [2.9736 (6) Å] and intratrimer [2.7966 (6) Å] (Table 3). It is noteworthy that SrV_{6}O_{11} shows a much smaller change in the V2···V2 distance with the phase transition, as compared to the other AV_{6}O_{11} compounds. In both the P6_{3}/mmc and P6_{3}mc forms, analogous V1—O distances show similar values, independent of the nature of A. On the other hand, in both forms the V2—O and the V3—O2 distances tend to be longer for divalent A cations and shorter for monovalent A.
The P6_{3}/mmc–P6_{3}mc structural phase transition, accompanied by a magnetic transition, is a common characteristic of AV_{6}O_{11} compounds, independent of the A cations. The acentric form of SrV_{6}O_{11} shows features in common with the corresponding P6_{3}mc forms of AV_{6}O_{11} (A = Na, K, Sr, Ba, Pb). Below T_{t}, the V1O_{6} octahedron no longer forms a regular Kagomé lattice, but distorts to form a V1O_{6} trimer with a regular triangular shape. A pair of the V2O_{6} octahedra forming a facesharing dimer at higher temperatures become inequivalent. V3 moves away from the centre of the V3O_{5} polyhedron. The V1 trimer formation accompanying the structural transition is considered to be the factor that suppresses the paramagnetism below T_{t}.