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
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.
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.
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.
(I) aluminium phosphate
top
Crystal data top
AlPO4 | Dx = 2.157 (1) Mg m−3 |
Mr = 121.95 | Cu Kα1 radiation, λ = 1.540562 Å |
Hexagonal, P63mc | µ = 8.0 mm−1 |
Hall symbol: P 6c -2c | T = 593 K |
a = 5.0976 (3) Å | Particle morphology: plate-like |
c = 8.3441 (4) Å | white |
V = 187.77 (2) Å3 | cylinder, 10 × 0.5 mm |
Z = 2 | Specimen preparation: Prepared at 1223 K |
F(000) = 120 | |
Data collection top
Siemens D5000 diffractometer | Data collection mode: transmission |
Radiation source: sealed X-ray tube | Scan method: step |
Primary Ge(111) monochromator | 2θmin = 15°, 2θmax = 90°, 2θstep = 0.008° |
Specimen mounting: packed in 0.5 mm glass capillary | |
Refinement top
Refinement on Inet | Profile function: pseudo-Voigt |
Least-squares matrix: full with fixed elements per cycle | 41 parameters |
Rp = 0.013 | 22 constraints |
Rwp = 0.019 | |
Rexp = 0.010 | (Δ/σ)max = 0.01 |
χ2 = 3.802 | Background function: power series in Q**2n/n! and n!/Q**2n |
9652 data points | Preferred orientation correction: none |
Excluded region(s): none | |
Crystal data top
AlPO4 | Z = 2 |
Mr = 121.95 | Cu Kα1 radiation, λ = 1.540562 Å |
Hexagonal, P63mc | µ = 8.0 mm−1 |
a = 5.0976 (3) Å | T = 593 K |
c = 8.3441 (4) Å | cylinder, 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 capillary | 2θmin = 15°, 2θmax = 90°, 2θstep = 0.008° |
Data collection mode: transmission | |
Refinement top
Rp = 0.013 | χ2 = 3.802 |
Rwp = 0.019 | 9652 data points |
Rexp = 0.010 | 41 parameters |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | |
Al | 0.33333 | 0.66667 | 0.06250 | 0.07 (1) | |
P | 0.33333 | 0.66667 | 0.4365 (4) | 0.05 (1) | |
O1 | 0.33333 | 0.66667 | 0.2616 (5) | 0.12 (1) | |
O2 | 0.5109 (3) | 0.4891 (3) | −0.0046 (6) | 0.14 (1) | |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
Al | 0.069 (5) | 0.069 (5) | 0.065 (8) | 0.035 (3) | 0 | 0 |
P | 0.047 (3) | 0.047 (3) | 0.048 (6) | 0.024 (2) | 0 | 0 |
O1 | 0.163 (5) | 0.163 (5) | 0.036 (5) | 0.081 (3) | 0 | 0 |
O2 | 0.165 (4) | 0.165 (4) | 0.136 (5) | 0.129 (4) | 0.021 (2) | −0.021 (2) |
Geometric parameters (Å, º) top
Al—O1 | 1.662 (5) | P—O2iv | 1.461 (3) |
Al—O2i | 1.665 (3) | P—O2v | 1.461 (3) |
Al—O2 | 1.665 (3) | O1—O2iii | 2.387 (6) |
Al—O2ii | 1.665 (3) | O1—O2iv | 2.387 (6) |
O1—O2i | 2.719 (6) | O1—O2v | 2.387 (6) |
O1—O2 | 2.719 (6) | O2—O2vi | 2.382 (2) |
O1—O2ii | 2.719 (6) | O2—O2vii | 2.382 (2) |
O2—O2i | 2.715 (2) | Al—P | 3.121 (4) |
O2—O2ii | 2.715 (2) | Al—Pviii | 3.125 (2) |
P—O1 | 1.459 (6) | Al—Pix | 3.125 (2) |
P—O2iii | 1.461 (3) | Al—Px | 3.125 (2) |
| | | |
O1—Al—O2i | 109.6 (2) | O1—P—O2iv | 109.7 (3 |
O1—Al—O2 | 109.6 (2) | O1—P—O2v | 109.7 (3 |
O1—Al—O2ii | 109.6 (2) | O2iii—P—O2iv | 109.3 (2) |
O2i—Al—O2 | 109.3 (2) | O2iii—P—O2v | 109.3 (2) |
O2i—Al—O2ii | 109.3 (2) | O2iv—P—O2v | 109.3 (2) |
O2—Al—O2ii | 109.3 (2) | P—O1—Al | 180.0 (4) |
O1—P—O2iii | 109.7 (3 | Pix—O2—Al | 180.0 (5) |
Symmetry codes: (i) y−x, −x+1, z; (ii) −y+1, x−y+1, z; (iii) x−y, x, z+1/2; (iv) −x+1, −y+1, z+1/2; (v) y, y−x+1, z+1/2; (vi) −y+1, x−y, z; (vii) y−x+1, −x+1, z; (viii) x−y, x, z−1/2; (ix) x−y+1, x, z−1/2; (x) x−y+1, x+1, z−1/2. |
(II) aluminium phosphate
top
Crystal data top
AlPO4 | Dx = 2.157 (1) Mg m−3 |
Mr = 121.95 | Cu Kα1 radiation, λ = 1.540562 Å |
Hexagonal, P63mc | µ = 8.0 mm−1 |
Hall symbol: P 6c -2c | T = 593 K |
a = 5.0976 (3) Å | Particle morphology: plate-like |
c = 8.3441 (4) Å | white |
V = 187.77 (2) Å3 | cylinder, 10 × 0.5 mm |
Z = 2 | Specimen preparation: Prepared at 1223 K |
F(000) = 120 | |
Data collection top
Siemens D5000 diffractometer | Data collection mode: transmission |
Radiation source: sealed X-ray tube | Scan method: step |
Primary Ge(111) monochromator | 2θmin = 15°, 2θmax = 90°, 2θstep = 0.008° |
Specimen mounting: packed in 0.5 mm glass capillary | |
Refinement top
Refinement on Inet | Profile function: pseudo-Voigt |
Least-squares matrix: full with fixed elements per cycle | 41 parameters |
Rp = 0.013 | 66 constraints |
Rwp = 0.019 | |
Rexp = 0.010 | (Δ/σ)max = 0.01 |
χ2 = 4.622 | Background function: power series in Q**2n/n! and n!/Q**2n |
9652 data points | Preferred orientation correction: none |
Excluded region(s): none | |
Crystal data top
AlPO4 | Z = 2 |
Mr = 121.95 | Cu Kα1 radiation, λ = 1.540562 Å |
Hexagonal, P63mc | µ = 8.0 mm−1 |
a = 5.0976 (3) Å | T = 593 K |
c = 8.3441 (4) Å | cylinder, 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 capillary | 2θmin = 15°, 2θmax = 90°, 2θstep = 0.008° |
Data collection mode: transmission | |
Refinement top
Rp = 0.013 | χ2 = 4.622 |
Rwp = 0.019 | 9652 data points |
Rexp = 0.010 | 41 parameters |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | Occ. (<1) |
Al | 0.33333 | 0.66667 | 0.06250 | 0.0530 (6)* | |
P | 0.33333 | 0.66667 | 0.4376 (4) | 0.0530 (6)* | |
O1 | 0.2524 (9) | 0.5859 (9) | 0.2631 (4) | 0.0530 (6)* | .16667 |
O2 | 0.5417 (8) | 0.5445 (8) | −0.0438 (7) | 0.0530 (6)* | .16667 |
O3 | 0.4285 (7) | 0.4033 (7) | −0.0018 (8) | 0.0530 (6)* | .16667 |
O4 | 0.4837 (8) | 0.4317 (8) | 0.0382 (7) | 0.0530 (6)* | .16667 |
Geometric parameters (Å, º) top
Al—O1 | 1.724 (4) | O1—O1vi | 0.714 (6) |
Al—O2 | 1.722 (4) | O1—O1vii | 0.825 (6) |
Al—O3 | 1.725 (4) | O2—O2vii | 0.440 (8) |
Al—O4 | 1.727 (3) | O2—O3vii | 0.426 (8) |
P—O1 | 1.514 (5) | O2—O3 | 0.747 (8) |
P—O2i | 1.508 (4) | O2—O4vii | 0.726 (8) |
P—O3ii | 1.513 (4) | O2—O4 | 0.846 (8) |
P—O4ii | 1.514 (5) | Al—P | 3.130 (4) |
O1—O1iii | 0.411 (6) | Al—Pviii | 3.122 (2) |
O1—O1iv | 0.414 (6) | Al—Pix | 3.122 (2) |
O1—O1v | 0.714 (6) | Al—Px | 3.122 (2) |
| | | |
P—O1—Al | 150.4 (3) | Pix—O3—Al | 149.1 (2) |
Pix—O2—Al | 150.3 (4) | Pix—O4—Al | 148.8 (4) |
Symmetry codes: (i) x−y, −y+1, z+1/2; (ii) x−y, x, z+1/2; (iii) x, x−y+1, z; (iv) y−x, y, z; (v) y−x, −x+1, z; (vi) −y+1, x−y+1, z; (vii) −y+1, −x+1, z; (viii) x−y, x, z−1/2; (ix) x−y+1, x, z−1/2; (x) x−y+1, x+1, z−1/2. |
Experimental details
| (I) | (II) |
Crystal data |
Chemical formula | AlPO4 | AlPO4 |
Mr | 121.95 | 121.95 |
Crystal system, space group | Hexagonal, P63mc | Hexagonal, P63mc |
Temperature (K) | 593 | 593 |
a, c (Å) | 5.0976 (3), 8.3441 (4) | 5.0976 (3), 8.3441 (4) |
V (Å3) | 187.77 (2) | 187.77 (2) |
Z | 2 | 2 |
Radiation type | Cu Kα1, λ = 1.540562 Å | Cu Kα1, λ = 1.540562 Å |
µ (mm−1) | 8.0 | 8.0 |
Specimen shape, size (mm) | Cylinder, 10 × 0.5 | Cylinder, 10 × 0.5 |
|
Data collection |
Diffractometer | Siemens D5000 diffractometer | Siemens D5000 diffractometer |
Specimen mounting | Packed in 0.5 mm glass capillary | Packed in 0.5 mm glass capillary |
Data collection mode | Transmission | Transmission |
Scan method | Step | Step |
2θ values (°) | 2θmin = 15 2θmax = 90 2θstep = 0.008 | 2θmin = 15 2θmax = 90 2θstep = 0.008 |
|
Refinement |
R factors and goodness of fit | Rp = 0.013, Rwp = 0.019, Rexp = 0.010, χ2 = 3.802 | Rp = 0.013, Rwp = 0.019, Rexp = 0.010, χ2 = 4.622 |
No. of data points | 9652 | 9652 |
No. of parameters | 41 | 41 |
No. of restraints | ? | ? |
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.