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Similar to silica tridymite, AlPO4 tridymite shows a sequence of displacive phase transitions resulting in a dynamically disordered hexagonal high-temperature modification. Rietveld refinement reveals that the thermal motions of the tetrahedra can be described either by strongly anisotropic displacement parameters for oxy­gen or by split O atoms. Due to the ordered distribution of aluminium and phospho­rus over alternating tetrahedra, the space group symmetry of high-temperature AlPO4 tridymite is reduced with respect to SiO2 tridymite from P63/mmc to P63mc.

Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S0108270101005133/br1322sup1.cif
Contains datablocks alpohp, I, II

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S0108270101005133/br1322Isup2.rtv
Contains datablock I

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S0108270101005133/br1322IIsup3.rtv
Contains datablock II

Comment top

AlPO4 crystallizes in several modifications which are isotypic with the silica minerals quartz, tridymite and cristobalite (Flörke, 1965). The latter two are high-temperature forms which persist metastably at ambient conditions. AlPO4 and SiO2 tridymites show a similar sequence of displacive phase transitions upon heating and several forms with different superstructures at room temperature (Spiegel et al., 1990). The transition temperatures are shifted to lower values for AlPO4 tridymite. Whereas the crystal structures of most of the silica tridymite phases are known, merely two room temperature forms of AlPO4 tridymite have been refined so far (Graetsch, 2000). The present refinement of the hexagonal high-temperature modification of AlPO4 tridymite was carried out in the course of an investigation of the phase transitions of tridymite. For the lack of suitable single crystals a powder sample was used. The framework structure of tridymite consists of corner-sharing tetrahedra which form layers made up by six-membered rings of tetrahedra. Antiparallel layers are stacked in the direction of the hexagonal c axis forming a two layer sequence. Viewed along the c axis the vertices of the tetrahedra alternatively point up and down (Fig. 1a). All tetrahedra have the same size in silica tridymite, whereas tetrahedra occupied either by aluminium or phosphorus have different sizes in AlPO4 tridymite. The cation distribution is ordered as in all other AlPO4 polymorphs so that all up-pointing tetrahedra are exclusively occupied by either aluminium or phosphorus (depending on the point of view). This destroys the mirror plane perpendicular to the 63 screw axis and reduces the symmetry from P63/mmc (No. 194) for hexagonal SiO2 tridymite to P63mc (No.186) for AlPO4 tridymite. The structure of hexagonal AlPO4 high tridymite is dynamically disordered as can be seen by the large and strongly anisotropic thermal displacement parameters of the oxygen atoms which are small along directions connecting Al and P atoms and large in perpendicular or inclined directions (Fig. 1 b), whereas the displacement ellipsoids of the cations are almost spherical. This indicates that the thermal motions are most likely dominated by so-called rigid unit modes which leave the stiff tetrahedra almost undistorted (cf. Pryde & Dove, 1998). The average structure with all atoms on special positions yields an idealized picture: the shape of the rings of tetrahedra is perfectly hexagonal, the Al—O and P—O bonds being 1.66 (1) and 1.46 (1) Å, respectively, and the corresponding O—O edges of the tetrahedra [2.72 (1) and 2.38 (1) Å] are shorter than the room-temperature values. The intertetrahedral Al—O—P angles appear as straight (180°) instead of approximately 147° as has been found for the room-temperature forms (Graetsch, 2000).

More realistic interatomic distances and angles can be obtained by using a split atom model for the oxygen atoms in order to describe the dynamical disorder as has been shown by Kihara (1980) for high-temperature silica tridymite and by Peacor (1973) and Wright & Leadbetter (1975) for β-cristobalite. For a split atom model of AlPO4 tridymite, the two symmetrically non-equivalent oxygen atoms of the average structure were removed from the 2 b and 6c positions and distributed over four general 12 d positions of space group P63mc with occupancy 1/6 so that they are located on circles between the Al and P atoms (Fig. 1c). Rietveld refinement showed that the split atom model with one overall isotropic displacement parameter describes the diffraction pattern equally well but the Al—O and P—O distances remain close to the values of 1.72 (1) and 1.51 (1) Å, respectively, as has been found by Muraoka & Kihara (1997) for the quartz form of AlPO4 (berlinite) at room temperature. The average intertetrahedral Al—O—P angle is 150° and the radius of the circles populated by six equi-distant split oxygen atoms refined to ca 0.4 Å which is much the same as for high-temperature silica cristobalite and tridymite (Peacor, 1973; Wright & Leadbetter, 1975; Kihara, 1980).

Average structure and split atom model refined to the same wRp values for the same number of variables so that it was not possible to gain further insight into the nature of the disorder from X-ray powder refinements, i.e. to distinguish between free vibrations of the tetrahedra or dynamic micro-twins.

Related literature top

For related literature, see: Flörke (1965); Graetsch (2000); Hill & Flack (1987); Kihara (1978, 1980); Larson & von Dreele (1994); LeBail, Duroy & Fourquet (1988); Muraoka & Kihara (1997); Peacor (1973); Pryde & Dove (1998); Rietveld (1969); Spiegel et al. (1990); Wright & Leadbetter (1975).

Experimental top

AlPO4 tridymite was prepared by annealing non-crystalline AlPO4 (Merck No. 1.01098.1000) at 1223 K for 1 d. The sample consisted of 87 wt% triclinic, 9 wt% monoclinic tridymite and 4 wt% corundum at room temperature (cf. Graetsch, 2000). The latter was utilized as an additional internal standard for the temperature control. Above 373 K only a single incommensurate high-temperature tridymite phase showed up in the X-ray powder diagrams together with corundum. Near 573 K a gradual transition to hexagonal high temperature AlPO4 took place. The diffractogram used for Rietveld refinements was recorded at ca 593 (15) K in transmission mode using a focusing Ge(111) monochromator.

Refinement top

The crystal structure was refined according to the Rietveld method (Rietveld, 1969) using the GSAS program package (Larson & von Dreele, 1994). Initially, lattice parameters, six peak shape parameters of the pseudo-Voigt function (No.2), one asymmetry parameter and one parameter for the zero-point correction were refined without a structure model according to the LeBail method (LeBail et al., 1988). The high background at low 2 theta caused by the position sensitive detector was removed by the fixed background subtraction feature of the GSAS program package. Remaining background was fitted with six parameters using a power series function (No.6). The structure refinement was started with the atomic co-ordinates of the isotypic hexagonal high temperature silica tridymite phase at 733 K (Kihara, 1978). Unlike AlPO4 cristobalite and berlinite, no extra reflections were found for hexagonal AlPO4 tridymite with respect to its silica analog. Extinctions indicate as possible space groups: P63/mmc, P63mc, P62c, P3¯c1 and P31c, however, a framework of alternating AlO4 and PO4 tetrahedra is only compatible with P63mc and P31c. Refinements in space group P31c yielded no lower R-values than in P63mc in spite of an additional refinable positional parameter for O2. The z positional parameter of the aluminium atom was fixed in order to define the origin in the space group P63mc. Soft constraints were set on the interatomic distances so that the sizes of the tetrahedra should remain close those of AlPO4 quartz: Al—O = 1.73, O—O = 2.83, P—O = 1.52, O—O = 2.49 Å (Muraoka & Kihara, 1997) but refined to 1.66, 2.72, 1.45 and 2.38 Å, respectively, for the average structure. Change from individual isotropic to anisotropic displacement parameters reduced the wRp-value from 0.027 to 0.019 (for 34 and 41 variables, respectively) and R(F2) from 0.088 to 0.045 (for 70 reflections). Refinement of the split atom model for the oxygen atoms did not result in lower R-values but in more realistic interatomic distances which are close to those of berlinite. Corrections for absorption and extinction were found to be unnecessary. Preferred orientation was not observed. The small step size of 0.008° 2 θ most likely leads to artificially low standard deviations (cf. Hill & Flack, 1987; Baerlocher & McCusker, 1994). In order to obtain correct values only every 7t h data point was used in a final refinement cycle with fixed profile parameters. The Durban-Watson d statistic value became close to 2 (1.98). This procedure increased the estimated standard deviations by a factor of approximately 4 with respect to those obtained with the original data set.

Computing details top

For both compounds, data collection: DIFFRAC-AT (Version 3.0; Siemens, unpublished); cell refinement: GSAS (Larson & von Dreele, 1994); data reduction: GSAS; program(s) used to solve structure: GSAS; program(s) used to refine structure: GSAS; molecular graphics: ORTEP-3 (Farrugia, 1997) and WATOMS (Dowty, 1994); software used to prepare material for publication: WINWORD97.

Figures top
[Figure 1] Fig. 1. (a) Polyhedral representation of hexagonal high-temperature AlPO4 viewed along the c axis (the AlO4 tetrahedra are white and the PO4 tetrahedra are shaded), (b) ORTEP-3 (Farrugia, 1997) plot of the average structure with 50% probability displacement ellipsoids, and (c) representation of the split atom model perpendicular to the c axis.
[Figure 2] Fig. 2. Comparison of observed (crosses) and calculated (solid line) powder-diffraction patterns of high-temperature AlPO4 tridymite (average structure) and corundum (ca 4 wt%) at ca 593 K. The difference pattern is shown below. The short bars indicate the positions of the reflections.
(I) aluminium phosphate top
Crystal data top
AlPO4Dx = 2.157 (1) Mg m3
Mr = 121.95Cu Kα1 radiation, λ = 1.540562 Å
Hexagonal, P63mcµ = 8.0 mm1
Hall symbol: P 6c -2cT = 593 K
a = 5.0976 (3) ÅParticle morphology: plate-like
c = 8.3441 (4) Åwhite
V = 187.77 (2) Å3cylinder, 10 × 0.5 mm
Z = 2Specimen preparation: Prepared at 1223 K
F(000) = 120
Data collection top
Siemens D5000
diffractometer
Data collection mode: transmission
Radiation source: sealed X-ray tubeScan method: step
Primary Ge(111) monochromator2θmin = 15°, 2θmax = 90°, 2θstep = 0.008°
Specimen mounting: packed in 0.5 mm glass capillary
Refinement top
Refinement on InetProfile function: pseudo-Voigt
Least-squares matrix: full with fixed elements per cycle41 parameters
Rp = 0.01322 constraints
Rwp = 0.019
Rexp = 0.010(Δ/σ)max = 0.01
χ2 = 3.802Background function: power series in Q**2n/n! and n!/Q**2n
9652 data pointsPreferred orientation correction: none
Excluded region(s): none
Crystal data top
AlPO4Z = 2
Mr = 121.95Cu Kα1 radiation, λ = 1.540562 Å
Hexagonal, P63mcµ = 8.0 mm1
a = 5.0976 (3) ÅT = 593 K
c = 8.3441 (4) Åcylinder, 10 × 0.5 mm
V = 187.77 (2) Å3
Data collection top
Siemens D5000
diffractometer
Scan method: step
Specimen mounting: packed in 0.5 mm glass capillary2θmin = 15°, 2θmax = 90°, 2θstep = 0.008°
Data collection mode: transmission
Refinement top
Rp = 0.013χ2 = 3.802
Rwp = 0.0199652 data points
Rexp = 0.01041 parameters
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Al0.333330.666670.062500.07 (1)
P0.333330.666670.4365 (4)0.05 (1)
O10.333330.666670.2616 (5)0.12 (1)
O20.5109 (3)0.4891 (3)0.0046 (6)0.14 (1)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Al0.069 (5)0.069 (5)0.065 (8)0.035 (3)00
P0.047 (3)0.047 (3)0.048 (6)0.024 (2)00
O10.163 (5)0.163 (5)0.036 (5)0.081 (3)00
O20.165 (4)0.165 (4)0.136 (5)0.129 (4)0.021 (2)0.021 (2)
Geometric parameters (Å, º) top
Al—O11.662 (5)P—O2iv1.461 (3)
Al—O2i1.665 (3)P—O2v1.461 (3)
Al—O21.665 (3)O1—O2iii2.387 (6)
Al—O2ii1.665 (3)O1—O2iv2.387 (6)
O1—O2i2.719 (6)O1—O2v2.387 (6)
O1—O22.719 (6)O2—O2vi2.382 (2)
O1—O2ii2.719 (6)O2—O2vii2.382 (2)
O2—O2i2.715 (2)Al—P3.121 (4)
O2—O2ii2.715 (2)Al—Pviii3.125 (2)
P—O11.459 (6)Al—Pix3.125 (2)
P—O2iii1.461 (3)Al—Px3.125 (2)
O1—Al—O2i109.6 (2)O1—P—O2iv109.7 (3
O1—Al—O2109.6 (2)O1—P—O2v109.7 (3
O1—Al—O2ii109.6 (2)O2iii—P—O2iv109.3 (2)
O2i—Al—O2109.3 (2)O2iii—P—O2v109.3 (2)
O2i—Al—O2ii109.3 (2)O2iv—P—O2v109.3 (2)
O2—Al—O2ii109.3 (2)P—O1—Al180.0 (4)
O1—P—O2iii109.7 (3Pix—O2—Al180.0 (5)
Symmetry codes: (i) yx, x+1, z; (ii) y+1, xy+1, z; (iii) xy, x, z+1/2; (iv) x+1, y+1, z+1/2; (v) y, yx+1, z+1/2; (vi) y+1, xy, z; (vii) yx+1, x+1, z; (viii) xy, x, z1/2; (ix) xy+1, x, z1/2; (x) xy+1, x+1, z1/2.
(II) aluminium phosphate top
Crystal data top
AlPO4Dx = 2.157 (1) Mg m3
Mr = 121.95Cu Kα1 radiation, λ = 1.540562 Å
Hexagonal, P63mcµ = 8.0 mm1
Hall symbol: P 6c -2cT = 593 K
a = 5.0976 (3) ÅParticle morphology: plate-like
c = 8.3441 (4) Åwhite
V = 187.77 (2) Å3cylinder, 10 × 0.5 mm
Z = 2Specimen preparation: Prepared at 1223 K
F(000) = 120
Data collection top
Siemens D5000
diffractometer
Data collection mode: transmission
Radiation source: sealed X-ray tubeScan method: step
Primary Ge(111) monochromator2θmin = 15°, 2θmax = 90°, 2θstep = 0.008°
Specimen mounting: packed in 0.5 mm glass capillary
Refinement top
Refinement on InetProfile function: pseudo-Voigt
Least-squares matrix: full with fixed elements per cycle41 parameters
Rp = 0.01366 constraints
Rwp = 0.019
Rexp = 0.010(Δ/σ)max = 0.01
χ2 = 4.622Background function: power series in Q**2n/n! and n!/Q**2n
9652 data pointsPreferred orientation correction: none
Excluded region(s): none
Crystal data top
AlPO4Z = 2
Mr = 121.95Cu Kα1 radiation, λ = 1.540562 Å
Hexagonal, P63mcµ = 8.0 mm1
a = 5.0976 (3) ÅT = 593 K
c = 8.3441 (4) Åcylinder, 10 × 0.5 mm
V = 187.77 (2) Å3
Data collection top
Siemens D5000
diffractometer
Scan method: step
Specimen mounting: packed in 0.5 mm glass capillary2θmin = 15°, 2θmax = 90°, 2θstep = 0.008°
Data collection mode: transmission
Refinement top
Rp = 0.013χ2 = 4.622
Rwp = 0.0199652 data points
Rexp = 0.01041 parameters
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
Al0.333330.666670.062500.0530 (6)*
P0.333330.666670.4376 (4)0.0530 (6)*
O10.2524 (9)0.5859 (9)0.2631 (4)0.0530 (6)*.16667
O20.5417 (8)0.5445 (8)0.0438 (7)0.0530 (6)*.16667
O30.4285 (7)0.4033 (7)0.0018 (8)0.0530 (6)*.16667
O40.4837 (8)0.4317 (8)0.0382 (7)0.0530 (6)*.16667
Geometric parameters (Å, º) top
Al—O11.724 (4)O1—O1vi0.714 (6)
Al—O21.722 (4)O1—O1vii0.825 (6)
Al—O31.725 (4)O2—O2vii0.440 (8)
Al—O41.727 (3)O2—O3vii0.426 (8)
P—O11.514 (5)O2—O30.747 (8)
P—O2i1.508 (4)O2—O4vii0.726 (8)
P—O3ii1.513 (4)O2—O40.846 (8)
P—O4ii1.514 (5)Al—P3.130 (4)
O1—O1iii0.411 (6)Al—Pviii3.122 (2)
O1—O1iv0.414 (6)Al—Pix3.122 (2)
O1—O1v0.714 (6)Al—Px3.122 (2)
P—O1—Al150.4 (3)Pix—O3—Al149.1 (2)
Pix—O2—Al150.3 (4)Pix—O4—Al148.8 (4)
Symmetry codes: (i) xy, y+1, z+1/2; (ii) xy, x, z+1/2; (iii) x, xy+1, z; (iv) yx, y, z; (v) yx, x+1, z; (vi) y+1, xy+1, z; (vii) y+1, x+1, z; (viii) xy, x, z1/2; (ix) xy+1, x, z1/2; (x) xy+1, x+1, z1/2.

Experimental details

(I)(II)
Crystal data
Chemical formulaAlPO4AlPO4
Mr121.95121.95
Crystal system, space groupHexagonal, P63mcHexagonal, P63mc
Temperature (K)593593
a, c (Å)5.0976 (3), 8.3441 (4)5.0976 (3), 8.3441 (4)
V3)187.77 (2)187.77 (2)
Z22
Radiation typeCu Kα1, λ = 1.540562 ÅCu Kα1, λ = 1.540562 Å
µ (mm1)8.08.0
Specimen shape, size (mm)Cylinder, 10 × 0.5Cylinder, 10 × 0.5
Data collection
DiffractometerSiemens D5000
diffractometer
Siemens D5000
diffractometer
Specimen mountingPacked in 0.5 mm glass capillaryPacked in 0.5 mm glass capillary
Data collection modeTransmissionTransmission
Scan methodStepStep
2θ values (°)2θmin = 15 2θmax = 90 2θstep = 0.0082θmin = 15 2θmax = 90 2θstep = 0.008
Refinement
R factors and goodness of fitRp = 0.013, Rwp = 0.019, Rexp = 0.010, χ2 = 3.802Rp = 0.013, Rwp = 0.019, Rexp = 0.010, χ2 = 4.622
No. of data points96529652
No. of parameters4141
No. of restraints??

Computer programs: DIFFRAC-AT (Version 3.0; Siemens, unpublished), GSAS (Larson & von Dreele, 1994), GSAS, ORTEP-3 (Farrugia, 1997) and WATOMS (Dowty, 1994), WINWORD97.

 

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