Monoclinic AlPO₄ tridymite at 473 and 463 K from X-ray powder data

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).

S1. Comment

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.

S2. Experimental

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.

S3. Refinement

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).

Computing details

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.

Figures

	Fig. 1. Polyhedral representations of tridymite at various temperatures viewed along the c axis. (a) Hexagonal AlPO4 tridymite at 593 K, (b) monoclinic AlPO4 tridymite at 473 K and (c) orthorhombic SiO2 tridymite at 573 K (after Kihara et al., 1986). Shaded: AlO4, white: PO4 and gray: SiO4 tetrahedra. The shapes of the unit cells are shown by dotted lines. The small arrows indicate the direction of the shift of the layers of tetrahedra in (b) and (c).
	Fig. 2. ORTEP-3 (Farrugia, 1997) plot of AlPO4 tridymite viewed normal to (100) and shown with 50% probability displacement ellipsoids. The AlO4 group is surrounded by four PO4 groups and is shown as (a) the hexagonal phase at 593 K, (b) the monoclinic basic structure at 473 K and (c) the average structure of the incommensurate phase at 463 K.
	Fig. 3. Comparison of the observed (crosses) and calculated (solid line) powder diffraction patterns of high-temperature AlPO4 tridymite (a) at 473 K and (b) at 463 K. The arrows in (b) point to weak satellite reflections. The difference patterns are shown below. The short bars indicate the positions of the reflections of corundum (first row) and tridymite (second row).

(I) aluminium phosphate

Crystal data

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) Å^3	Specimen preparation: Prepared at 1223 K
Z = 2

Data collection

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

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
χ^2 = 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

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	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 (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
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)

Al—O1	1.672 (4)	P—O3^iv	1.469 (11)
Al—O2^i	1.669 (11)	P—O4^iii	1.468 (13)
Al—O3	1.667 (12)	O1—O2^iii	2.39 (2)
Al—O4	1.681 (13)	O1—O3^iv	2.39 (2)
O1—O2^i	2.75 (2)	O1—O4^iii	2.42 (2)
O1—O3	2.74 (2)	O2—O3^v	2.39 (2)
O1—O4	2.72 (2)	O2—O4	2.41 (2)
O2—O3^ii	2.72 (2)	O3—O4^vi	2.40 (2)
O2—O4^ii	2.73 (2)	Al—P	3.142 (4)
O3—O4	2.73 (2)	Al—P^vii	3.127 (7)
P—O1	1.471 (5)	Al—P^viii	3.106 (7)
P—O2^iii	1.470 (12)	Al—P^ix	3.116 (10)
O1—Al—O2^i	110.6 (6)	O1—P—O4^iii	110.8 (6)
O1—Al—O3	110.3 (5)	O2^iii—P—O3^iv	108.7 (9)
O1—Al—O4	108.4 (4)	O2^iii—P—O4^iii	110.0 (9)
O2^i—Al—O3	109.2 (8)	O3^iv—P—O4^iii	109.4 (8)
O2^i—Al—O4	109.1 (8)	Al—O1—P	178.7 (5)
O3—Al—O4	109.2 (8)	Al^ii—O2—P^viii	166.0 (8)
O1—P—O2^iii	108.8 (6)	Al—O3—P^vii	171.1 (8)
O1—P—O3^iv	108.9 (6)	Al—O4—P^viii	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

Crystal data

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) Å^3	Specimen preparation: Prepared at 1223 K
Z = 2

Data collection

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

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
χ^2 = 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

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	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 (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
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)

Al—O1	1.668 (5)	P—O3^iv	1.472 (8)
Al—O2^i	1.667 (10)	P—O4^iii	1.472 (10)
Al—O3	1.662 (9)	O1—O2^iii	2.40 (2)
Al—O4	1.679 (11)	O1—O3^iv	2.41 (2)
O1—O2^i	2.74 (2)	O1—O4^iii	2.42 (2)
O1—O3	2.74 (2)	O2—O3^v	2.40 (2)
O1—O4	2.71 (2)	O2—O4	2.41 (2)
O2—O3^ii	2.71 (2)	O3—O4^vi	2.40 (2)
O2—O4^ii	2.73 (2)	Al—P	3.142 (4)
O3—O4	2.72 (2)	Al—P^vii	3.124 (6)
P—O1	1.474 (6)	Al—P^viii	3.107 (6)
P—O2^iii	1.473 (10)	Al—P^ix	3.116 (7)
O1—Al—O2^i	110.6 (5)	O1—P—O4^iii	110.3 (5)
O1—Al—O3	110.4 (5)	O2^iii—P—O3^iv	108.9 (7)
O1—Al—O4	108.4 (4)	O2^iii—P—O4^iii	109.8 (7)
O2^i—Al—O3	109.2 (6)	O3^iv—P—O4^iii	109.3 (7)
O2^i—Al—O4	109.1 (6)	Al—O1—P	178.2 (5)
O3—Al—O4	109.2 (6)	Al^ii—O2—P^viii	166.2 (7)
O1—P—O2^iii	109.1 (6)	Al—O3—P^vii	170.9 (8)
O1—P—O3^iv	109.4 (6)	Al—O4—P^viii	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.