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The room-temperature structure of the B-site-ordered complex perovskite dicalcium magnesium tungstate, Ca2MgWO6, has been determined by simultaneous Rietveld refinement of neutron and X-ray powder diffraction patterns. Ca2MgWO6 is characterized by B-site ordering and an a-a-c+-type BO6 octahedral tilt mechanism.
Supporting information
The single-phase powder sample of Ca2MgWO6 was synthesized by a conventional solid-state reaction, using CaCO3, MgO and WO3 as starting materials. To avoid sublimation of WO3, the precursor powder of MgWO4 was prepared by calcination of a wet milled mixture of MgO and WO3 in stoichiometric proportions at 1073 K for 10 h in air. The precursor was ground and mixed with a stoichiometric quantity of CaCO3, and this mixture was milled and heated in air at 1573 K for 10 h.
X-ray powder diffraction pattern was collected at room temperature using Cu Kα radiation. The neutron powder diffraction pattern was collected at room temperature with a high-resolution powder diffractometer (HRPD) (λ=1.8339 Å) at the HANARO reactor, Korea Atomic Energy Research Institute (KAERI). Neutrons from the ST2 channel of the reactor were monochromated by a vertically focusing composite Ge monochromator at 90° take-off position. Cell parameters were obtained from the WinPLOTR (Roisnel & Rodríguez-Carvajal, 2001) program using the neutron diffraction profile. Analysis of the systematic absences indicated space group P21/n. The Rietveld method was used to refine the crystal structure. The X-ray and neutron profiles were simultaneously fitted by the Fullprof 2000 program (Rodríguez-Carvajal, 2001). The initial parameters for the refinement were taken from the data for the isostructural compound Sr2YbNbO6. Atomic displacement parameters were assumed to be isotropic.
For both compounds, program(s) used to refine structure: Fullprof 2000; molecular graphics: Xtaldraw.
Crystal data top
Ca2MgWO6 | V = 231.97 (1) Å3 |
Mr = 384.3 | Z = 2 |
Monoclinic, P21/n | Dx = 5.5 Mg m−3 |
Hall symbol: -P 2yn | Cu Kα1, Cu Kα2 radiation, λ = 1.54056, 1.54439 Å |
a = 5.4199 (1) Å | T = 293 K |
b = 5.5479 (1) Å | Particle morphology: irregular |
c = 7.7147 (2) Å | white |
β = 90.092 (2)° | flat sheet, 25 × 25 mm |
Data collection top
Rigaku Rotaflex diffractometer | Data collection mode: reflection |
Graphite monochromator | Scan method: step |
Specimen mounting: packed powder sheet | 2θmin = 10.3°, 2θmax = 129.95°, 2θstep = 0.05° |
Refinement top
Refinement on Inet | Excluded region(s): none |
Least-squares matrix: full with fixed elements per cycle | Profile function: pseudo-Voigt |
Rp = 0.070 | 36 parameters |
Rwp = 0.105 | Weighting scheme based on measured s.u.'s |
Rexp = 0.084 | (Δ/σ)max = 0.01 |
χ2 = 2.403 | Background function: polynomial |
2394 data points | |
Crystal data top
Ca2MgWO6 | β = 90.092 (2)° |
Mr = 384.3 | V = 231.97 (1) Å3 |
Monoclinic, P21/n | Z = 2 |
a = 5.4199 (1) Å | Cu Kα1, Cu Kα2 radiation, λ = 1.54056, 1.54439 Å |
b = 5.5479 (1) Å | T = 293 K |
c = 7.7147 (2) Å | flat sheet, 25 × 25 mm |
Data collection top
Rigaku Rotaflex diffractometer | Scan method: step |
Specimen mounting: packed powder sheet | 2θmin = 10.3°, 2θmax = 129.95°, 2θstep = 0.05° |
Data collection mode: reflection | |
Refinement top
Rp = 0.070 | χ2 = 2.403 |
Rwp = 0.105 | 2394 data points |
Rexp = 0.084 | 36 parameters |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | |
Ca | 0.0108 (5) | 0.0469 (3) | 0.2480 (6) | 0.094 (4)* | |
Mg | 0.0000 | 0.5000 | 0.0000 | 0.100 (5)* | |
W | 0.5000 | 0.0000 | 0.0000 | 0.048 (4)* | |
O1 | 0.2134 (5) | 0.8037 (5) | 0.0419 (5) | 0.089 (3)* | |
O2 | 0.3059 (6) | 0.2838 (5) | −0.9536 (5) | 0.096 (3)* | |
O3 | 0.4155 (3) | 0.0252 (3) | −0.2402 (5) | 0.085 (3)* | |
Geometric parameters (Å, º) top
Ca—O1i | 2.358 (5) | Ca—O2ix | 2.725 (5) |
Ca—O2ii | 2.372 (5) | Ca—O3x | 3.136 (3) |
Ca—O3iii | 2.345 (3) | Ca—O3xi | 3.217 (2) |
Ca—O3iv | 2.431 (2) | Mg—O1 | 2.069 (3) |
Ca—O1v | 2.624 (5) | Mg—O2vii | 2.077 (3) |
Ca—O1vi | 2.675 (5) | Mg—O3xii | 2.057 (4) |
Ca—O1iv | 3.396 (5) | W—O1i | 1.925 (3) |
Ca—O2vii | 2.591 (5) | W—O2vii | 1.929 (3) |
Ca—O2viii | 3.385 (5) | W—O3 | 1.913 (4) |
| | | |
O1—Mg—O2vii | 90.1 (2) | O1i—W—O2vii | 89.4 (2) |
O1—Mg—O3xii | 88.4 (2) | O1i—W—O3x | 89.4 (2) |
O2vii—Mg—O3xii | 91.6 (2) | O2vii—W—O3x | 90.6 (2) |
Symmetry codes: (i) x, y−1, z; (ii) −x+1/2, y−1/2, −z−1/2; (iii) −x, −y, −z; (iv) x−1/2, −y+1/2, z+1/2; (v) −x+1/2, y−1/2, −z+1/2; (vi) −x, −y+1, −z; (vii) x, y, z+1; (viii) −x, −y, −z−1; (ix) x−1/2, −y+1/2, z+3/2; (x) −x+1, −y, −z; (xi) x−1/2, −y−1/2, z+1/2; (xii) −x+1/2, y+1/2, −z−1/2. |
Crystal data top
Ca2MgWO6 | Z = 2 |
Mr = 384.3 | Dx = 5.5 Mg m−3 |
Monoclinic, P21/n | Neutron radiation, λ = 1.8339 Å |
Hall symbol: -P 2yn | µ = 0.11 mm−1 |
a = 5.4199 (1) Å | T = 293 K |
b = 5.5479 (1) Å | Particle morphology: irregular |
c = 7.7147 (2) Å | white |
β = 90.092 (2)° | cylinder, 50 × 10 mm |
V = 231.97 (1) Å3 | |
Data collection top
HANARO HRPD diffractometer | Data collection mode: transmission |
Ge monochromator | Scan method: step |
Specimen mounting: packed powder cylinder | 2θmin = 0°, 2θmax = 159.95°, 2θstep = 0.05° |
Refinement top
Refinement on Inet | Excluded region(s): none |
Least-squares matrix: full with fixed elements per cycle | Profile function: pseudo-Voigt |
Rp = 0.038 | 36 parameters |
Rwp = 0.050 | Weighting scheme based on measured s.u.'s |
Rexp = 0.035 | (Δ/σ)max = 0.01 |
χ2 = 4.162 | Background function: polynomial |
3200 data points | |
Crystal data top
Ca2MgWO6 | V = 231.97 (1) Å3 |
Mr = 384.3 | Z = 2 |
Monoclinic, P21/n | Neutron radiation, λ = 1.8339 Å |
a = 5.4199 (1) Å | µ = 0.11 mm−1 |
b = 5.5479 (1) Å | T = 293 K |
c = 7.7147 (2) Å | cylinder, 50 × 10 mm |
β = 90.092 (2)° | |
Data collection top
HANARO HRPD diffractometer | Scan method: step |
Specimen mounting: packed powder cylinder | 2θmin = 0°, 2θmax = 159.95°, 2θstep = 0.05° |
Data collection mode: transmission | |
Refinement top
Rp = 0.038 | χ2 = 4.162 |
Rwp = 0.050 | 3200 data points |
Rexp = 0.035 | 36 parameters |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | |
Ca | 0.0108 (5) | 0.0469 (3) | 0.2480 (6) | 0.094 (4)* | |
Mg | 0.0000 | 0.5000 | 0.0000 | 0.100 (5)* | |
W | 0.5000 | 0.0000 | 0.0000 | 0.048 (4)* | |
O1 | 0.2134 (5) | 0.8037 (5) | 0.0419 (5) | 0.089 (3)* | |
O2 | 0.3059 (6) | 0.2838 (5) | −0.9536 (5) | 0.096 (3)* | |
O3 | 0.4155 (3) | 0.0252 (3) | −0.2402 (5) | 0.085 (3)* | |
Geometric parameters (Å, º) top
Ca—O1i | 2.358 (5) | Ca—O2ix | 2.725 (5) |
Ca—O2ii | 2.372 (5) | Ca—O3x | 3.136 (3) |
Ca—O3iii | 2.345 (3) | Ca—O3xi | 3.217 (2) |
Ca—O3iv | 2.431 (2) | Mg—O1 | 2.069 (3) |
Ca—O1v | 2.624 (5) | Mg—O2vii | 2.077 (3) |
Ca—O1vi | 2.675 (5) | Mg—O3xii | 2.057 (4) |
Ca—O1iv | 3.396 (5) | W—O1i | 1.925 (3) |
Ca—O2vii | 2.591 (5) | W—O2vii | 1.929 (3) |
Ca—O2viii | 3.385 (5) | W—O3 | 1.913 (4) |
| | | |
O1—Mg—O2vii | 90.1 (2) | O1i—W—O2vii | 89.4 (2) |
O1—Mg—O3xii | 88.4 (2) | O1i—W—O3x | 89.4 (2) |
O2vii—Mg—O3xii | 91.6 (2) | O2vii—W—O3x | 90.6 (2) |
Symmetry codes: (i) x, y−1, z; (ii) −x+1/2, y−1/2, −z−1/2; (iii) −x, −y, −z; (iv) x−1/2, −y+1/2, z+1/2; (v) −x+1/2, y−1/2, −z+1/2; (vi) −x, −y+1, −z; (vii) x, y, z+1; (viii) −x, −y, −z−1; (ix) x−1/2, −y+1/2, z+3/2; (x) −x+1, −y, −z; (xi) x−1/2, −y−1/2, z+1/2; (xii) −x+1/2, y+1/2, −z−1/2. |
Experimental details
| (X-ray) | (Neutron) |
Crystal data |
Chemical formula | Ca2MgWO6 | Ca2MgWO6 |
Mr | 384.3 | 384.3 |
Crystal system, space group | Monoclinic, P21/n | Monoclinic, P21/n |
Temperature (K) | 293 | 293 |
a, b, c (Å) | 5.4199 (1), 5.5479 (1), 7.7147 (2) | 5.4199 (1), 5.5479 (1), 7.7147 (2) |
β (°) | 90.092 (2) | 90.092 (2) |
V (Å3) | 231.97 (1) | 231.97 (1) |
Z | 2 | 2 |
Radiation type | Cu Kα1, Cu Kα2, λ = 1.54056, 1.54439 Å | Neutron, λ = 1.8339 Å |
µ (mm−1) | – | 0.11 |
Specimen shape, size (mm) | Flat sheet, 25 × 25 | Cylinder, 50 × 10 |
|
Data collection |
Diffractometer | Rigaku Rotaflex diffractometer | HANARO HRPD diffractometer |
Specimen mounting | Packed powder sheet | Packed powder cylinder |
Data collection mode | Reflection | Transmission |
Scan method | Step | Step |
2θ values (°) | 2θmin = 10.3 2θmax = 129.95 2θstep = 0.05 | 2θmin = 0 2θmax = 159.95 2θstep = 0.05 |
|
Refinement |
R factors and goodness of fit | Rp = 0.070, Rwp = 0.105, Rexp = 0.084, χ2 = 2.403 | Rp = 0.038, Rwp = 0.050, Rexp = 0.035, χ2 = 4.162 |
No. of data points | 2394 | 3200 |
No. of parameters | 36 | 36 |
No. of restraints | ? | ? |
Selected bond lengths (Å) for (X-ray) topCa—O1i | 2.358 (5) | Ca—O2ix | 2.725 (5) |
Ca—O2ii | 2.372 (5) | Ca—O3x | 3.136 (3) |
Ca—O3iii | 2.345 (3) | Ca—O3xi | 3.217 (2) |
Ca—O3iv | 2.431 (2) | Mg—O1 | 2.069 (3) |
Ca—O1v | 2.624 (5) | Mg—O2vii | 2.077 (3) |
Ca—O1vi | 2.675 (5) | Mg—O3xii | 2.057 (4) |
Ca—O1iv | 3.396 (5) | W—O1i | 1.925 (3) |
Ca—O2vii | 2.591 (5) | W—O2vii | 1.929 (3) |
Ca—O2viii | 3.385 (5) | W—O3 | 1.913 (4) |
Symmetry codes: (i) x, y−1, z; (ii) −x+1/2, y−1/2, −z−1/2; (iii) −x, −y, −z; (iv) x−1/2, −y+1/2, z+1/2; (v) −x+1/2, y−1/2, −z+1/2; (vi) −x, −y+1, −z; (vii) x, y, z+1; (viii) −x, −y, −z−1; (ix) x−1/2, −y+1/2, z+3/2; (x) −x+1, −y, −z; (xi) x−1/2, −y−1/2, z+1/2; (xii) −x+1/2, y+1/2, −z−1/2. |
Selected bond lengths (Å) for (Neutron) topCa—O1i | 2.358 (5) | Ca—O2ix | 2.725 (5) |
Ca—O2ii | 2.372 (5) | Ca—O3x | 3.136 (3) |
Ca—O3iii | 2.345 (3) | Ca—O3xi | 3.217 (2) |
Ca—O3iv | 2.431 (2) | Mg—O1 | 2.069 (3) |
Ca—O1v | 2.624 (5) | Mg—O2vii | 2.077 (3) |
Ca—O1vi | 2.675 (5) | Mg—O3xii | 2.057 (4) |
Ca—O1iv | 3.396 (5) | W—O1i | 1.925 (3) |
Ca—O2vii | 2.591 (5) | W—O2vii | 1.929 (3) |
Ca—O2viii | 3.385 (5) | W—O3 | 1.913 (4) |
Symmetry codes: (i) x, y−1, z; (ii) −x+1/2, y−1/2, −z−1/2; (iii) −x, −y, −z; (iv) x−1/2, −y+1/2, z+1/2; (v) −x+1/2, y−1/2, −z+1/2; (vi) −x, −y+1, −z; (vii) x, y, z+1; (viii) −x, −y, −z−1; (ix) x−1/2, −y+1/2, z+3/2; (x) −x+1, −y, −z; (xi) x−1/2, −y−1/2, z+1/2; (xii) −x+1/2, y+1/2, −z−1/2. |
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Various perovskite compounds whose B-sites are occupied by two cation species have been synthesized so far, and their crystal structures have been determined (Galasso, 1969). These compounds have the general chemical formula ABxB1 − xO3. When the differences in ionic radii or charges between two different B-site cations increase, ordering of the B-site cations may occur, giving rise to different crystal structures (Setter & Cross, 1980). The ideal structure of the B-site-ordered complex perovskite A2B'B''O6 is a centered space group (Fm3m) resulting from the alternation of B-site cations.
The real perovskite structure often deviates from the ideal cubic structure, and BO6 octahedral tilting is the most common distortion mechanism. This type of distortion is typically observed when the tolerance factor (Goldschmidt, 1926) is smaller than 1, which means that the A-site cation is small for? the cubic BO6 corner-sharing octahedral network.
Octahedral tilting in perovskites was first examined by Megaw et al. (1975), and fundamental work was carried out by Glazer (1972, 1975). The latter work demonstrated that the space group can be largely determined by the pattern of in-phase (a+), anti-phase(a−) and null (ao) octahedral tilting along one of the Cartesian coordinate axes. A classification of octahedral tilting in terms of 23 alternative tilt systems was also proposed. Woodward (1997a) predicted the space groups that arise from the combination of octahedral tilting and B-site cation ordering. When the two bond distances are non-equivalent, the rigid rotation of octahedra in the interconnected B'O6 and B''O6 network can be inhibited for certain tilt systems.
Although, the crystal structures of simple prototype perovskites have been investigated thoroughly, only a few structural studies of B-site-ordered complex perovskites have been performed. In this paper, we present a detailed structure determination of Ca2MgWO6.
The title compound is an example of a B-site-ordered complex perovskite-type material. The two cations of Mg2+ (0.86 Å) and W6+ (0.74 Å) are located at alternate? B sites as result of the large difference of valence charge of cations. The simultaneous Rietveld refinement of the neutron and X-ray data (Figs. 1a and b) measured for the title compound show that the present structure (Fig. 2) is monoclinic, in space group P21/n, and is characterized by B-site cation ordering and a−a−c+-type oxygen octahedral tilting. The antiparallel shift of the A-site cation, approximately along the [010] monoclinic direction, often accompanies octahedral tilting, as observed for the CaTiO3 system (Kay & Bailey, 1957). The present structure is isostructural with Sr2YbNbO6 (Yang et al., 1999), in which the B-site cations are ordered because of a large difference of ionic size.
The average Mg—O and W—O distances for the BO6 octahedra are 2.069 and 1.922 Å, respectively. These values are in good agreement with those predicted by the ionic radii of Shannon (1976) [r(Mg2+)=0.86 Å, r(W6+)=0.74 Å and r(O2−)=1.28 Å]. However, both types of octahedra are slightly distorted from the ideal cubic case, in order to maintain the corner-sharing network (Table 2).
Thomas (1989, 1996) and Woodward (1997b) found that the A cation strongly favors remaining in the crystallographically equivalent site and, consequently, maximizing the A-cation polyhedral volume when the octahedral tilt occurs. These authors also found that the orthorhombic a−a−c+ tilt system provides the maximum number of short A—O bonds (four) when the tilt angle increases. The tolerance factor of title compound is 0.94, which is? much smaller than 1. The arrangement of oxide ions around a Ca cation (Fig. 3) shows that four of the 12 Ca—O bonds are significantly shortened. The average length of these four short Ca—O bonds is 2.377 Å, which is close to the calculated value, assuming Ca2+ ionic radii in sixfold coordination (1.00 Å). These findings agree with the prediction.