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Upon cooling from its hexagonal high-temperature modification, AlPO4 (aluminium phosphate) tridymite successively transforms to several displacively distorted forms, including a normal structure–incommensurate–lock-in phase transition sequence. The space-group symmetries in this series are P1121, P1121(αβ0) and P212121, respectively. The distortion pattern of the intermediate P1121 phase can be described as alternate shifts of adjacent layers of tetrahedra coupled with tilting of the tetrahedra. The symmetry and direction of the shifts are different from the analogous SiO2 tridymite modification. The atomic displacement parameters of the O atoms are strongly anisotropic due to thermal motions of the rigid tetrahedra. Condensation of a lattice vibration mode results in the formation of an incommensurate structural modulation below 473 K. The 3+1 superspace-group symmetry of the modulated phase is P1121(αβ0).
Supporting information
AlPO4 tridymite was prepared by annealing non-crystalline AlPO4 (Merck No.
1.01098.1000) at 1223 K for 1 d. The sample was transformed to hexagonal high
tridymite by heating to 593 K with a hot-air jet directed perpendicular to the
capillary and then cooled to the desired temperatures. A gradual phase
transition from hexagonal to monoclinic symmetry was observed near 573 K.
Below 473 K the appearance of weak satellite reflections indicated the
formation of an incommensurate modulation. Two powder data sets were collected
at 473 (10) and 463 (10) K in order to refine the crystal structure of the
normal phase and the average structure of the incommensurate phase,
respectively. The sample contained about 4 wt% corundum which was refined
together with the tridymite phase.
The crystal structure was refined according to the Rietveld method (Rietveld,
1969) using the GSAS program package (Larson & von Dreele, 1984).
Initially, only lattice parameters, six peak-shape parameters of the
pseudo-Voigt function, 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 2θ
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 extra reflections were found in the temperature range from 573 to 473 K with
respect to hexagonal AlPO4 tridymite, however, except for 00 l, all
reflections were broadened or split, indicating a monoclinic deformation of
the unit cell (see Fig. 2a). The extinctions are compatible with space groups
P1121 (No. 4) and P1121/m (No. 11). The latter was rejected since
P1121/m is not a subgroup of P63mc (No. 186) which is the symmetry of the
hexagonal high temperature form and since a mirror plane perpendicular to the
pseudo-hexagonal c axis is incompatible with an ordered arrangement of
the Al and P atoms in the tetrahedral framework. The atomic coordinates of the
hexagonal high-temperature phase at 593 K (Graetsch, 2001a) were used
as starting parameters. The z parameter of Al was fixed in order to
define the origin.
The wavevector of the modulated phase was refined to q = 0.0068 (1)a* +
0.006 (1)b* at 463 K with the program JANA2000 (Petricek & Dusek, 2000). The
average structure of the incommensurate phase was refined with GSAS
neglecting the weak satellite reflections.
Soft constraints were set on the interatomic distances, keeping the sizes of
the tetrahedra close to those of AlPO4 quartz: Al—O = 1.73, O—O = 2.83,
P—O = 1.52 and O—O = 2.49 Å (Muraoka & Kihara, 1997), but refined to
smaller values. The change from individual isotropic to anisotropic
displacement parameters reduced the R(F2) value from 0.084 to 0.040
for the basic structure at 473 K and from 0.098 to 0.038 for the average
structure of the incommensurate phase at 463 K, at an increase from 47 to 77
refined parameters. Corrections for absorption and extinction were found to be
unnecessary. Preferred orientation was not observed. The obtained s.u.'s of
the atomic coordinates and displacement parameters were multiplied with a
factor of three in order to account for possible serial correlations leading
to artificially low standard deviations (cf. Hill & Flack, 1987;
Baerlocher & McCusker, 1994).
For both compounds, data collection: DIFFRAC-AT V3.0 (Reference ?); 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) for (I); ORTEP-3 (Farrugia, 1997), WATOMS (Dowty, 1994) for (II). For both compounds, software used to prepare material for publication: WINWORD 97.
(I) aluminium phosphate
top
Crystal data top
AlPO4 | F(000) = 120 |
Mr = 121.95 | Dx = 2.177 (1) Mg m−3 |
Monoclinic, P1121 | Cu Kα radiation, λ = 1.54056 Å |
Hall symbol: P 1 1 2c | µ = 7.9 mm−1 |
a = 5.0800 (2) Å | T = 473 K |
b = 5.0748 (2) Å | Particle morphology: plate-like |
c = 8.3009 (3) Å | white |
β = 90° | cylinder, 40 × 0.5 mm |
V = 186.03 (1) Å3 | Specimen preparation: Prepared at 1223 K |
Z = 2 | |
Data collection top
Siemens D5000 diffractometer | Data collection mode: transmission |
Radiation source: sealed X-ray tube | Scan method: step |
Primary focussing Ge(111) monochromator | 2θmin = 15°, 2θmax = 90°, 2θstep = 0.008° |
Specimen mounting: powder filled into a 0.5 mm glass capillary | |
Refinement top
Refinement on Inet | Profile function: pseudo-Voigt |
Least-squares matrix: full with fixed elements per cycle | 77 parameters |
Rp = 0.011 | 24 constraints |
Rwp = 0.015 | w = 1/[y(obs)]1/2 |
Rexp = 0.011 | (Δ/σ)max = 0.01 |
χ2 = 1.850 | 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 | V = 186.03 (1) Å3 |
Mr = 121.95 | Z = 2 |
Monoclinic, P1121 | Cu Kα radiation, λ = 1.54056 Å |
a = 5.0800 (2) Å | µ = 7.9 mm−1 |
b = 5.0748 (2) Å | T = 473 K |
c = 8.3009 (3) Å | cylinder, 40 × 0.5 mm |
β = 90° | |
Data collection top
Siemens D5000 diffractometer | Scan method: step |
Specimen mounting: powder filled into a 0.5 mm glass capillary | 2θmin = 15°, 2θmax = 90°, 2θstep = 0.008° |
Data collection mode: transmission | |
Refinement top
Rp = 0.011 | χ2 = 1.850 |
Rwp = 0.015 | 9652 data points |
Rexp = 0.011 | 77 parameters |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | |
Al | 0.3539 (16) | 0.6361 (15) | 0.06250 | 0.06 (1) | |
P | 0.3137 (17) | 0.6982 (16) | 0.4371 (4) | 0.05 (1) | |
O1 | 0.3346 (17) | 0.6673 (18) | 0.2621 (4) | 0.11 (1) | |
O2 | 0.545 (4) | −0.022 (2) | −0.0226 (11) | 0.12 (1) | |
O3 | 0.007 (3) | 0.451 (4) | −0.0163 (12) | 0.14 (1) | |
O4 | 0.535 (4) | 0.441 (4) | 0.0247 (8) | 0.11 (1) | |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
Al | 0.057 (6) | 0.056 (6) | 0.060 (5) | 0.032 (5) | −0.022 (7) | −0.030 (7) |
P | 0.053 (5) | 0.049 (5) | 0.044 (4) | 0.024 (4) | 0.003 (8) | 0.007 (8) |
O1 | 0.16 (2) | 0.14 (2) | 0.034 (4) | 0.080 (8) | 0.04 (3) | 0.02 (3) |
O2 | 0.23 (3) | 0.10 (3) | 0.07 (2) | 0.09 (2) | 0.04 (3) | 0.01 (2) |
O3 | 0.024 (11) | 0.14 (2) | 0.18 (3) | 0.016 (11) | −0.05 (2) | −0.03 (3) |
O4 | 0.18 (2) | 0.12 (2) | 0.11 (2) | 0.12 (2) | −0.01 (3) | −0.04 (3) |
Geometric parameters (Å, º) top
Al—O1 | 1.672 (4) | P—O3iv | 1.469 (11) |
Al—O2i | 1.669 (11) | P—O4iii | 1.468 (13) |
Al—O3 | 1.667 (12) | O1—O2iii | 2.39 (2) |
Al—O4 | 1.681 (13) | O1—O3iv | 2.39 (2) |
O1—O2i | 2.75 (2) | O1—O4iii | 2.42 (2) |
O1—O3 | 2.74 (2) | O2—O3v | 2.39 (2) |
O1—O4 | 2.72 (2) | O2—O4 | 2.41 (2) |
O2—O3ii | 2.72 (2) | O3—O4vi | 2.40 (2) |
O2—O4ii | 2.73 (2) | Al—P | 3.142 (4) |
O3—O4 | 2.73 (2) | Al—Pvii | 3.127 (7) |
P—O1 | 1.471 (5) | Al—Pviii | 3.106 (7) |
P—O2iii | 1.470 (12) | Al—Pix | 3.116 (10) |
| | | |
O1—Al—O2i | 110.6 (6) | O1—P—O4iii | 110.8 (6) |
O1—Al—O3 | 110.3 (5) | O2iii—P—O3iv | 108.7 (9) |
O1—Al—O4 | 108.4 (4) | O2iii—P—O4iii | 110.0 (9) |
O2i—Al—O3 | 109.2 (8) | O3iv—P—O4iii | 109.4 (8) |
O2i—Al—O4 | 109.1 (8) | Al—O1—P | 178.7 (5) |
O3—Al—O4 | 109.2 (8) | Alii—O2—Pviii | 166.0 (8) |
O1—P—O2iii | 108.8 (6) | Al—O3—Pvii | 171.1 (8) |
O1—P—O3iv | 108.9 (6) | Al—O4—Pviii | 160.9 (7) |
Symmetry codes: (i) x, y+1, z; (ii) x, y−1, z; (iii) −x+1, −y+1, z+1/2; (iv) −x, −y+1, z+1/2; (v) x+1, y, z; (vi) x−1, y, z; (vii) −x, −y+1, z−1/2; (viii) −x+1, −y+1, z−1/2; (ix) −x+1, −y+2, z−1/2. |
(II) aluminium phosphate
top
Crystal data top
AlPO4 | F(000) = 120 |
Mr = 121.95 | Dx = 2.179 (1) Mg m−3 |
Monoclinic, P1121 | Cu Kα radiation, λ = 1.54056 Å |
Hall symbol: P 1 1 2c | µ = 7.9 mm−1 |
a = 5.0803 (2) Å | T = 463 K |
b = 5.0703 (2) Å | Particle morphology: plate-like |
c = 8.2992 (3) Å | white |
β = 90° | cylinder, 40 × 0.5 mm |
V = 185.87 (1) Å3 | Specimen preparation: Prepared at 1223 K |
Z = 2 | |
Data collection top
Siemens D5000 diffractometer | Data collection mode: transmission |
Radiation source: sealed X-ray tube | Scan method: step |
Focussing primary Ge(111) monochromator | 2θmin = 15°, 2θmax = 90°, 2θstep = 0.008° |
Specimen mounting: filled into a 0.5 mm glass capillary | |
Refinement top
Refinement on Inet | Profile function: pseudo-Voigt |
Least-squares matrix: full with fixed elements per cycle | 77 parameters |
Rp = 0.011 | 24 constraints |
Rwp = 0.015 | w = 1/[y(obs)]1/2 |
Rexp = 0.011 | (Δ/σ)max = 0.01 |
χ2 = 1.904 | 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 | V = 185.87 (1) Å3 |
Mr = 121.95 | Z = 2 |
Monoclinic, P1121 | Cu Kα radiation, λ = 1.54056 Å |
a = 5.0803 (2) Å | µ = 7.9 mm−1 |
b = 5.0703 (2) Å | T = 463 K |
c = 8.2992 (3) Å | cylinder, 40 × 0.5 mm |
β = 90° | |
Data collection top
Siemens D5000 diffractometer | Scan method: step |
Specimen mounting: filled into a 0.5 mm glass capillary | 2θmin = 15°, 2θmax = 90°, 2θstep = 0.008° |
Data collection mode: transmission | |
Refinement top
Rp = 0.011 | χ2 = 1.904 |
Rwp = 0.015 | 9652 data points |
Rexp = 0.011 | 77 parameters |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | |
Al | 0.3515 (13) | 0.6324 (11) | 0.06250 | 0.04 (1) | |
P | 0.3152 (12) | 0.7015 (11) | 0.4368 (4) | 0.04 (1) | |
O1 | 0.3347 (16) | 0.6661 (18) | 0.2616 (5) | 0.10 (1) | |
O2 | 0.537 (3) | −0.027 (2) | −0.0237 (11) | 0.09 (1) | |
O3 | 0.005 (2) | 0.443 (3) | −0.0149 (13) | 0.13 (1) | |
O4 | 0.536 (3) | 0.441 (3) | 0.0247 (9) | 0.11 (1) | |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
Al | 0.039 (5) | 0.040 (5) | 0.051 (4) | 0.012 (7) | −0.022 (7) | −0.016 (8) |
P | 0.042 (4) | 0.038 (4) | 0.033 (4) | 0.020 (3) | 0.007 (6) | 0.002 (6) |
O1 | 0.13 (1) | 0.15 (2) | 0.014 (4) | 0.070 (7) | 0.03 (2) | −0.00 (2) |
O2 | 0.18 (2) | 0.06 (2) | 0.05 (2) | 0.06 (2) | 0.03 (2) | 0.02 (1) |
O3 | 0.03 (1) | 0.12 (2) | 0.17 (2) | 0.02 (1) | −0.05 (1) | −0.04 (2) |
O4 | 0.16 (2) | 0.13 (2) | 0.12 (2) | 0.13 (2) | 0.01 (2) | −0.02 (2) |
Geometric parameters (Å, º) top
Al—O1 | 1.668 (5) | P—O3iv | 1.472 (8) |
Al—O2i | 1.667 (10) | P—O4iii | 1.472 (10) |
Al—O3 | 1.662 (9) | O1—O2iii | 2.40 (2) |
Al—O4 | 1.679 (11) | O1—O3iv | 2.41 (2) |
O1—O2i | 2.74 (2) | O1—O4iii | 2.42 (2) |
O1—O3 | 2.74 (2) | O2—O3v | 2.40 (2) |
O1—O4 | 2.71 (2) | O2—O4 | 2.41 (2) |
O2—O3ii | 2.71 (2) | O3—O4vi | 2.40 (2) |
O2—O4ii | 2.73 (2) | Al—P | 3.142 (4) |
O3—O4 | 2.72 (2) | Al—Pvii | 3.124 (6) |
P—O1 | 1.474 (6) | Al—Pviii | 3.107 (6) |
P—O2iii | 1.473 (10) | Al—Pix | 3.116 (7) |
| | | |
O1—Al—O2i | 110.6 (5) | O1—P—O4iii | 110.3 (5) |
O1—Al—O3 | 110.4 (5) | O2iii—P—O3iv | 108.9 (7) |
O1—Al—O4 | 108.4 (4) | O2iii—P—O4iii | 109.8 (7) |
O2i—Al—O3 | 109.2 (6) | O3iv—P—O4iii | 109.3 (7) |
O2i—Al—O4 | 109.1 (6) | Al—O1—P | 178.2 (5) |
O3—Al—O4 | 109.2 (6) | Alii—O2—Pviii | 166.2 (7) |
O1—P—O2iii | 109.1 (6) | Al—O3—Pvii | 170.9 (8) |
O1—P—O3iv | 109.4 (6) | Al—O4—Pviii | 161.0 (6) |
Symmetry codes: (i) x, y+1, z; (ii) x, y−1, z; (iii) −x+1, −y+1, z+1/2; (iv) −x, −y+1, z+1/2; (v) x+1, y, z; (vi) x−1, y, z; (vii) −x, −y+1, z−1/2; (viii) −x+1, −y+1, z−1/2; (ix) −x+1, −y+2, z−1/2. |
Experimental details
| (I) | (II) |
Crystal data |
Chemical formula | AlPO4 | AlPO4 |
Mr | 121.95 | 121.95 |
Crystal system, space group | Monoclinic, P1121 | Monoclinic, P1121 |
Temperature (K) | 473 | 463 |
a, b, c (Å) | 5.0800 (2), 5.0748 (2), 8.3009 (3) | 5.0803 (2), 5.0703 (2), 8.2992 (3) |
γ (°) | 119.6253 (2) | 119.6037 (3) |
V (Å3) | 186.03 (1) | 185.87 (1) |
Z | 2 | 2 |
Radiation type | Cu Kα, λ = 1.54056 Å | Cu Kα, λ = 1.54056 Å |
µ (mm−1) | 7.9 | 7.9 |
Specimen shape, size (mm) | Cylinder, 40 × 0.5 | Cylinder, 40 × 0.5 |
|
Data collection |
Diffractometer | Siemens D5000 diffractometer | Siemens D5000 diffractometer |
Specimen mounting | Powder filled into a 0.5 mm glass capillary | Filled into a 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 = 0.011, Rwp = 0.015, Rexp = 0.011, χ2 = 1.850 | Rp = 0.011, Rwp = 0.015, Rexp = 0.011, χ2 = 1.904 |
No. of data points | 9652 | 9652 |
No. of parameters | 77 | 77 |
No. of restraints | ? | ? |
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Similar to silica tridymite, isotypic AlPO4 tridymite shows a cascade of several phase transitions at elevated temperatures (Spiegel et al., 1990). For SiO2, the following space-group symmetries and crystal structures of the high temperature modifications are known: P63/mmc \leftrightarrow C2221 \leftrightarrow P1121(αβ0) \leftrightarrow P212121 \leftrightarrow Cc and F1 (in order of decreasing temperature). Pryde & Dove (1998) ascribed the origin of the phase transitions to the successive condensation of different rigid unit modes. For isoelectronic AlPO4, only the crystal structure of the hexagonal high-temperature modification has been refined so far (Graetsch, 2001b). The symmetry is reduced to P63mc with respect to P63/mmc for the silica analogue due to the ordered distribution of Al and P over the tetrahedral sites.
X-ray powder diffraction revealed the sequence of displacive transitions as being P63mc \leftrightarrow P1121 \leftrightarrow P1121(αβ0) \leftrightarrow P212121 \leftrightarrow Pc and F1 for AlPO4 tridymite. The present communication reports results of Rietveld refinements of the crystal structures of the intermediate P1121 phase (which replaces the C2221 phase of SiO2 tridymite) and the average structure of the incommensurate P1121(αβ0) phase in order to work out the structural differences to the silica counterparts.
The crystal structure of hexagonal high-temperature AlPO4 tridymite is made up by alternating corner-sharing AlO4 and PO4 tetrahedra which form six-membered rings of tetrahedra (Fig. 1a). Viewed along the hexagonal c axis, the rings are in eclipsed positions for hexagonal tridymite, whereas in monoclinic high-temperature tridymite (P1121) below 573 K, whole neighboring layers are shifted with respect to each other (Figs. 1 b and 1c). The stiff tetrahedra are tilted simultaneously. The hexagonal–monoclinic transition is gradual. Shift and tilting become larger with decreasing temperature.
The situation is similar in the orthorhombic silica analogue (C2221), however, the shift direction is different from that of monoclinic AlPO4 tridymite (Figs. 1 b and 1c). The magnitude of the shift is almost alike in both cases: 0.47 Å for SiO2 at 493 K and 0.45 Å for AlPO4 at 473 K. The thermal displacement parameters of the O atoms are strongly anisotropic, whereas those of Al and P at the centers of the tetrahedra are almost spherical (Fig. 2). This indicates that the structure of monoclinic AlPO4 tridymite is dynamically disordered like hexagonal AlPO4 tridymite and that the thermal motions are probably dominated by rigid unit modes of the tetrahedra (cf. Pryde & Dove, 1998). Elastic diffraction can yield only a time-averaged picture of the structure. As a result, the sizes of the tetrahedra appear as too small and the intertetrahedral Al—O—P angles as too large. However, due to reduced thermal vibrations in the monoclinic phase, the latter are no longer straight as for the average structure of hexagonal AlPO4 tridymite. The T—O—T angle parallel to the c axis is larger (179°) than those in perpendicular direction (166, 171 and 161°).
The appearance of very weak satellite reflections around the main reflections below 473 K (Fig. 3) indicates the formation of an incommensurate modulation. A similar form of silica tridymite exists in the temperature range between about 493 and 423 K. The temperature-dependent modulation consists of wavy tilting and rotations of the tetrahedra (Nukui et al., 1979; Graetsch, 2001a).
The 3 + 1 superspace group is P1121(αβ0) for both AlPO4 and SiO2 incommensurate tridymites. The normal–incommensurate transition is gradual in both cases but involves a change of symmetry for the average structure of SiO2 tridymite [C2221 \leftrightarrow P1121(αβ0)] which is not observed for AlPO4 tridymite [P1121 \leftrightarrow P1121(αβ0)]. The atomic displacement parameters of the O atoms in the average structure of incommensurate AlPO4 tridymite are highly anisotropic (Fig. 3) as for the modifications at higher temperatures. However, it represents both static and dynamic contributions. The static component increases as the thermal motions are reduced in the temperature range from 473 to 373 K, leading to an increase in intensity of the satellite reflections.