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The structures of the β-cristobalitephases of SiO2 and AlPO4A. F. Wright a b & A. J. Leadbetter a ca School of Chemistry, University of Bristol, Bristol, BS8 1TS,Englandb Institut Laue-Langevin, B.P. No. 156, 38042, Grenoble,Francec Chemistry Department, University of Exeter, Exeter, EX44QD, England

Version of record first published: 20 Aug 2006

To cite this article: A. F. Wright & A. J. Leadbetter (1975): The structures of the β-cristobalite phases of SiO2 and AlPO4 , Philosophical Magazine, 31:6, 1391-1401

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[ 1391 3

The structures of the p-cristobalite phases of SiO, and AlPO,

By A. P. WRIGHT? and A. J. LEADBETTERS School of Chemistry, University of Bristol, Bristol BSS lTS, England

[Received 24 February 1975 and after revision 21 April 19751

ABSTRACT The crystal structures of the ' cristobalite ' phases of SiO, and AIPO, have

been determined from X-ray data collected at high temperatures. A model is suggested which gives a much better fit t,o t,he data than previously published struc- tures. I n this model, the 16 oxygen atoms of the unit cell are stat,istically distributed over the 96 positions ( I t ) of the space group Fd3m. This averaged structure is interpreted as comprising domains of ' ideal ' cristobalite (space group 142d) joined together in six different orientations as a kind of micro-twinning. In this way the structure retains a short-range order similar to low cristobalite, but loses part of the long-range order of the oxygen atoms. From the results of least-squares refinements at several temperatures, a static disordering is calculated, equal to (U,2)1/2=0.18 A for the silicon atoms. The p-cristobalite phase of AIPO, issimilarly disordered, with a short-range structure isomorphous with BPO,.

-

Q 1. INTRODUCTION The cristobalite form of silica exists in two modifications (01 and /3) separated

by a rapid displacive transition a t T - 270°C. The structure of the low-tempera- ture form is well established (Dollase 1965); it has the tetragonal space groupP4,2 with 4 SiO, groups per unit cell. The Si-0 bond lengths (1.601 and 1.608) and the Si-0-Si angles (146.8') are similar to those in low quartz and many silicates.

The structure of /3- or high-cristobalite is not yet established. Three different structures have been proposed. The first was that of Wyckoff (1925 a, b) who used powder photographs taken a t 240' and 430°C to deduce the cubic space group Fd3m with eight SiO, groups per unit cell. The silicon atoms form a diamond lattice with the oxygen atoms a t the mid-points between adjacent silicons. This gives Si-0-Si angles of 180" and perfectly tetrahedral SiO, groups. The structure is sometimes described in textbooks as 'ideal cris- tobalite ' (Clark 1972, Evans 1964). This structure cannot be correct because of the linear Xi-0-Si angles, and the Si-0 bond length of 1-54A, both of which differ markedly from the values found in other forms of silica. These difficulties were recognized by Barth (1932) who redetermined the structure using powder photographs from a sample of unspecified origin. On the basis of some extra reflections, the space group P2,3 was suggested, and the proposed structure was a slight distortion of the Wyckoff model, having Si-0 distances between 1.58 and 1.68 A. The agreement between calculated and observed intensities

t Present address: Institut Laue-Langevin, B.P. No. 156,38042 Grenoble. France. Present address: Chemistry Department, University of Exeter, Exeter EX4 4QD,

England. 4 ~ 2

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1392 A. F. Wright and A. J. Leadbetter

was poor, and the additional reflections have only been reported since in an impure specimen of cristobalite (Aumento 1966).

The third structure was proposed by Nieuwenkamp (1937) on the basis of rotation photographs of a single crystal a t 270°C. The space group was confirmed as Fd3m with the oxygen atoms occupying positions lying randomly on a circle of radius 0.4d normal to the Xi-Si axis. The agreement between the calculated and experimental intensities was improved, but the physical nature of the disorder is unclear. Nieuwenkamy suggested that the oxygen atoms might be either rotating around the circles, or might occupy point positions on the circles. The former suggestion is unacceptable due to the large vib- rational amplitudes involved but the latter is feasible provided there is strong short-range correlation so as to give satisfactory bond angles around the silicon atoms.

Sosman (1964) has suggested that all three structures might be correct, but in this unlikely eventuality there can only be one true equilibrium structure. However, there is indeed some difficulty concerning the samples of cristobalite. Material prepared from quartz or vitreous silica a t T N 1700°C gives sharp diffraction lines and the highest a-/3 transformation temperature (273"C), whereas material prepared a t lower temperatures gives broadened diffraction peaks which are much decreased in intensity at high angles, and transformation temperatures as low as 220°C. It is clear that the latter material is less well ordered, and the nature of this disorder has been discussed by Florke (1955) and Hill and Roy (1958) in terms of deviations from the ideal stacking of tetra- hedra. It is, however, well established that material prepared a t 1700°C is the best quality cristobalite and this has been used in the present work.

AlPO, is isomorphous with silica, and exists in the various quartz, tridymite and cristobalite forms, with transformations a t similar temperatures (Beck 1949). The structure of the a-cristobalite form has been determined by Mooney (1956) who has shown it to be similar to the corresponding silica structure with A1 and P atoms alternately replacing X i atoms. The structure of the /3-cristobalite modification has not previously been investigated.

In the present study the structure of /3-cristobalite has been refined as a function of temperature between 300" and 1200°C. The structure is indeed disordered and a detailed description is given of the nature of this disorder and of the short -range correlations in the structure. A brief preliminary report of this work has already been published (Leadbetter, Smith and Wright 1973).

It too is disordered and is shown to resemble both SiO, and BPO,.

The structure of the AlPO, analogue has also been determined a t 300°C.

0 2. EXPERIMENTAL 2.1. sio,

Several samples of cristobalite were prepared from pure vitreous silica or pure crushed quartz by heating for various times a t temperatures from 1200" to 1700°C. All samples gave the same reflections on the diffraction pattern, but only those prepared at 1690"-1700"C gave very sharp diffraction lines. The sample used in this work was prepared from vitreous silica by heating a t 1690°C for 5 hours. The extra reflections observed by Barth (1932) were

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T h e structures of the /3-cristobulite phases of XiO, and AIPO, 1393

not observed even in materials prepared a t low temperatures with the aid of a flux, e.g. NaC1. The primitive space group P2,3 was therefore discounted and from the 22 reflections observed, the space group was confirmed to be Fd3m. This implies that the structure is disordered.

2.2. AIPO, Good quality cristobalite-type AlPO, was prepared by heating precipitated

anhydrous AlPO, (purchased from British Drug Houses) a t 1300°C for 90 hours. The heating conditions represent a compromise since the crystalline quality increases with higher temperatures of preparation, but above 1300°C some decomposition occurs giving A1,0, and P,O,. At 1300°C some AIPO, of tridymite structure is formed, but this gradually transforms to the cristobalite form on prolonged heating.

The sample used in this work contained a negligible amount of the tridymite form and 2% A1,0,, estimated from the diffraction pattern. Although the crystalline quality appeared a little worse than for the silica analogue, 20 reflections were observed including the 200 and 420 reflections not observed with silica. The cubic face-centred space group F73m was selected for the refinement of the structure.

2.3. Dutu collection Using finely milled material, Bragg positions and intensities were measured

a t temperatures up to 1200°C on a Philips powder diffractometer fitted with a high-temperature attachment (Rigaku Denki). The furnace of the attachment caused some attenuation of the X-ray beam. This was determined experi- mentally and corrections to the X-ray intensities were made accordingly. The instrument was aligned a t each temperature in order to reduce the effects of expansion on the sample position. Bragg intensities were measured over the range 20= 18O to 140°, and line positions in the range 100" to 140" 20 were used for lattice parameter determinations. A very precise diffraction trace was obtained using nickel-filtered CuK, radiation from a stabilized X-ray generator and a very slow scan speed of 0.02O (20) per minute. The integrated intensities were determined from the areas of the peaks (K,,+K,,). The absorption correction was small, but was calculated according to the formula of Milberg (1958).

$ 3 . RESULTS AND DISCUSSION

3.1. SiO, Table 1 lists the observed structure

factors for each reflection a t 300"C, the temperature used for the primary structure analysis. Also given are the calculated structure factors for the proposed model and for those of Wyckoff (1925a, b) and Nieuwenkamp (1937). Table 2 gives the results for the analyses a t temperatures up to 1200OC: the lattice constant ( f 0.0007 A), the structural parameter x, and the thermal parameters for oxygen and silicon. Also given are the derived results : the Si-0 bond lengths and Si-0-Si bond angles.

These are presented in tables 1 and 2.

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1394 A. F. Wright and A. J. Leadbetter

0

3.85

Table 1. Si0,: observed and calculated structure factors (F) at 300°C.

parameter x

0.0792 (0.0013)

hkl

111 220 31 1 222 400 33 1 422

511 j 440 53 1 442 620 533 622 444 551 -[ 711 642

731 J 800 733 660 1 822

333 1

553 1

7-1315

7-1371 7.1412 7.1437 7.1461 7-1471 7-1473 7.1487 7-1487

Observed

3.56

3-60 3.75 3.90 4.07 4-05 4.13 4.28 4.84

192.5 92.7 25 *4 80.7 35.2 84 *4 81.6

101.7 79 .O 56.8 12-5 62.3 26.4 8.5

44 .0

54.4 31 *6

48.2 24-6 13.8

43.8

32.2

3-73 4.16 4-06 4-61 4-08 4.25 4.03 4.62

Residual factor

0.0797 (0.0009) 0.0816 (0.0007) 0-0811 (0.0010) 0.0816 (0.0012) 0.0812 (O*OOlO) 0.0813 (0.0009) 0.0807 (0.0006) 0.0814 (0.0014)

Wyekoff (1925 a, b)

B (0) =4-9 A2, IF! B (Si) =2-5 di

180.1 11143 21.5 94.3 11.5 90-6 72 *8

51 -2 98.4 57 *2 0.0

52 -4 23.1 22 *9 24-9

77.6 38.4

37.4 44 -4 27.1

56 *4

29.6

riieuwenkamp (1937)

B (0)=3*5 A2, B (Si) =3.0 h2,

IF1

~ = 0 * 4 A

187.6 120.0 39.6 66.7 47.5 77 *8 75.3

82.3 73.1 45.2 12.5 52.1 32.4 3.2

41 -0

59.1 36 a 5

47.8 30.7 20-5

51.6

34.2

23 -5 yo 14.9%

300

400 500 600 700 800 900

1000

( 2 3°C)

1 1200

Present work PI

B (0) -3.56 A2, B (Si) =3*85 A2, x =0.079 h2

deb ye-Waller factors ( B/A2) Coordinate

186-8 107.3 26.4 80-7 35.8 82 -3 83.1

100.4 79.5 53 6 13.1 59 -8 25.2 4 *9

38-6

53 *7 31.9

46.9 28.0 13.2

44.0

41 -0

5.4%

Table 2. Si0,: Refined results a t each temperature.

Bond lengths, angles

1.61 1

1.611 1 *607 1.609 1 -608 1 *609 1 -609 1.611 1.609

____ Si-0-Xi"

146.7

147.0 148.4 148.0 148.3 148-1 148.1 147.7 148.2

R

0.054

0.048 0.034 0.031 0.036 0.039 0.035 0.030 0.037

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The structures of the P-cristobalite phases of SiO, and AlPO, 1395

For the proposed structure, the eight silicon atoms are placed in the special positions (a ) of the space group Fd3m (International Tables for X-ray Crystallo- graphy). The 16 oxygen atoms are distributed among the 96 ( h ) positions, with an occupation number of Q. The oxygen positions are dependent upon a single variable parameter x, and for x = &, the 96 positions are reduced to the 16 positions of the Wyckoff structure with single occupancy. The scale factor and three parameters were refined : x, and isotropic Debye-Waller factors B ( f = f o exp-(B sin28)/X2) for silicon and oxygen. The proposed structure gave a good fit to the observed intensities, a marked improvement over those of Wyckoff and Nieuwenkamp. The Si-0 -distances and Si-0-Si angles compare favourably with those of low cristobalite (Dollase 1965).

It is clear that the oxygen atoms cannot be randomly situated among the 96 sites because this would imply considerable distortion of the SiO, tetrahedra which would be energetically unfavourable. The proposed interpretation of the disorder therefore retains substantial short -range correlation and a t the same time gives only slightly distorted tetrahedra.

Considering first the possibility of a completely ordered structure with the eight silicon atoms in the positions (a ) of Fd3m, and the 16 oxygen atoms on sites specially selected from the 96 (h) positions of the refined structure, the structure may be described by the space group Fdd2 having orthorhombic symmetry, but with the constraint that a,=b,=c,. (The Fdd2 space group is used here to facilitate an explanation of the disorder. The ordered structure is uniquely described by the space group 132d containing 4,530, units.)

The coordinates of atoms in the space group Fdd2 are (at 300OC) : (0,0, 0 ; 0 1 1.1 0 1.1 1 O ) +

9 2 , 2 , 2 , 9 2 , 2, 2 ,

8 silicon (a ) 0, 0, 0 ; t , 2, 4 ; 16 oxygen ( b ) x, y, x ; 6, p, x ; $-x, )+y, $ + z ; &+x, a-y, : + z ;

x= 0.079, y = (t -x) and z = i. I n this structure the bond angles around the silicon atoms are only slightly distorted from regular tetrahedral angles. There are two 0-Si-0 angles a t 1 1 2 ~ 8 ~ and four a t 107.8'; these are very similar to those found in low cristo- halite. There are however a total of six such structures in the average structure, each having the same silicon positions but different, though equivalent, oxygen positions. The coordinates of the average structure are obtained by permu- tation of the oxygen atom coordinates x, y, z , and applying each permutation to the Fdd2 space group. Each permutation represents a different orientation of the Fdd2 unit cell, in which the silicon atoms adopt identical positions, since these have cubic symmetry. It is clear therefore that the average structure may be described as six orientations of the hypothetical ordered material superimposed to give a unit cell of cubic average symmetry. From this it is inferred that the structure in real space involves six-fold twinning in which each domain, representing any one orientation, extends to no more than a few unit cells. This is possible only if the strain energy a t the twinning boundaries is small, requiring only a slight distortion of the SiO, tetrahedra. This is indeed possible with the proposed structure.

Assuming that oxygen atoms of fig. 1 are atoms in one orientation of the ordered unit cell, the 0-Si-0 angles between atom A and atoms B, C and D

where

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1396

Position

0-Si-0 angles with respect to atom Dldegrees

A. F. Wright and A. J. Leadbetter

Fig. 1

1 2

97-1 92.4 119.3 124.8 110.3 110.3

-.

I / / / I /

Local atomic arrangement in high cristobalite. Large circles denote silicon atoms, small solid circles denote oxygen atoms in ideal positions. Small open circles represent other possible oxygen positions around one Si-Si axis. 0 =oxygen; 0 =silicon.

are 112.8, 107-8 and 107.8. Positions 1 to 5 belong to other orientations. Occupancy by D of positions 3, 4 and 5 results in very large deviations from tetrahedral angles, but occupancy of positions 1 or 2 gives only relatively small distortions :

It is likely therefore that each twinning boundary involves a simple change in orientation such as that to positions 1 or 2 where the strain energy will be small. By these single steps the disorder may propagate throughout, the crystal to give all six orientations of the average structure. With such disorder it is to be expected that the strain will be further reduced by relaxation of the atoms from ideal lattice sites. This relaxation is revealed in unusually high values of the Debye-Waller factors. Those for oxygen are complicated by the pos- itional disorder and will be discussed later, but Debye-Waller factors for silicon have a simple and instructive form. In fig. 2 the meaii square displacement Us2 of silicon atoms derived from the experimental Debye-Waller factors, are plotted as a function of temperature together with corresponding data for quartz. U Z 2 for quartz (Wright 1972, Young 1962) is proportional to the absolute temperature as expected for harmonic oscillators a t high temperature. For cristobalite u,2 is linear with temperature, with a slope identical to that of quartz, but with an intercept a t T=OK of 0.0329. [ ( ~ ) 1 ’ 2 = 0 . 1 8 ~ ] .

__

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The structures of the P-cristobalite phases of XiO, and AIYO, 1397

- 1%

OC

0 0s

Fig. 2

QUARTZ (SI /icon )

/

/ /

Mean square displacements of oxygen and silicon atoms in high cristobalite and quartz, obtained from experimental Debye-Waller factors. 0 =silicon; 0 =oxygen.

There is therefore a temperature-independent term which contributes to the Debye-Waller factor for silicon. This is interpreted as a random static disorder which is independent of the thermal disorder since the latter shows a tem- perature variation identical with that of quartz. It is concluded that the static displacements arise out of a general relaxation of the structure to relieve stress a t the twinning boundaries, by reducing the distortion of the tetrahedral angles caused by propagation of the orientation disorder. The magnitude of the observed displacement (0.1 8 A) is in accord with this idea, being less than half the separation between adjacent oxygen sites (0.42 A).

The interpretation of the disorder therefore satisfies all the usual require- ments of bonding and geometry for a silica structure, whilst the average structure adequately fits the diffraction data. An idealized hypothetical short-range structure is proposed, from which there are small departures and displacements which must be cooperative, leading to a long-range disorder in the structure. The short-range order in the structure should lead to some structure in the diffuse scattering, but this was not observed in the powder experiment, and single crystals were not available. The hypothetical ordered unit cell of ,!3-cristobalite has so far been described by the Fdd2 space group. This has

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1398 A. F. Wright and A. J. Leadbetter

advantages for comparison with the average structure since both contain eight SiO, units. The true unit cell of the ordered structure contains four units according to the tetragonal space group 142d, with coordinates.

(0, 0, 0 ; 3, $9 Q)+ 4 Si (a ) 0, 0, 0 ; 0, 3, t ;

s o ( d ) 11.5 B 1 B 9 4, 8 2 9 4, 8 ; 4, x, 8 ; 4, 5, f .

The structure is shown in fig. 3 : ao= 5.042 b, co= 7-131 A, a t 270°, c ia= l / 2 . The smaller tetragonal cell allows direct comparison with that of low cristobalite (Dollase 1965) from which it may be seen that the a+ transformation is accom- plished by a small shift of oxygen and silicon atoms to positions of higher sym- metry. Further studies of the a-/3 transformation will be published at a later date.

Fig. 3

C axis projection of the local structure of high cristobalite based on the tetragonal space group 1&2d. a,=5.042 8; c,=7-131 A at 270°C.

The values of u,2 for the oxygen atoms, calculated from the observed Debye-JTTaller factors, are plotted in fig. 2 with the corresponding values for quartz. At high temperatures those for quartz are much higher than those for cristobalite, even though a contribution from static disorder is expected for the latter. Also u,2 for cristobalite does not show the expected temperature variation. Clearly u,2 obtained in this way is not a true measure of the mean square displacements of individual atoms. This arises because of overlap of the oxygen distribution of neighbouring sites around each Si-Si axis in the average structure, and the mean square displacements of individual atoms cannot be determined. With increasing temperature, as the vibrational amplitudes of the oxygen atoms increase, so the overlap increases and the oxygen distribution around the Si-Si axis approaches the toroidal distribution proposed by Nieuwenkamp. Hence, although the six positions around each Si-Si axis remain distinct, the disorder is not adequately described in terms of an occupation

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The structures of the P-cristobalite phases of XiO, and AIPO, 1399

- factor of 8 and an isotropic Debye-Waller factor. does not increase with T as rapidly as that of quartz.

The result is that U Z 2 ( T )

3.2. AlPO, The structure of AlPO, was refined using the space group FZ3m with the 16

oxygen atoms statistically distributed over the 96 general positions (i) and A1 and P atoms with coordinates :

4 ~ l ( ~ ) 0 ,0 , 0 ; 0 1 1.1 0 1.1 1 0 . , 2 , 2 , 2 , 9 2 , 2 , 2 , 2

1 1 1 . 1 3 3.5 1 3 . 3 3 1. 4 p ( c ) Y, 4, 4 , 4, 49 4 9 4, 4, 4 ) 4, 4, 4

Three coordinate parameters x, y, z were determined for the oxygen atoms, but refinementx converged with x=y= 0.1073 and z = 0-1883, equivalent to the 48 positions ( h ) of FZ3m with 6 oxygen atom on each position rather than & as with SiO,. The comparison of observed and calculated structure factors is given in table 3 ; the R-factor was 4.5%.

Table 3 AlPO,: observed and calculated structure factors (P) at 300°C.

hkl

111 200 220 311 222 400 331 420 422 333

440 531 620 335 444 551 1 711/ 642

731 J 733 660 1 822 J

511)

5531

190.8 27-8 99.7 27 *1 81.9 36.6 82.7 14.2 80.8

96-6 75.1 49.5 52 -7 25.1 39.8

50.1 31-1

43.2 16.9

41 *8

13'1 (calculated)

188.9 27 *0

107.9 26-0 80.1 31.9 80 *2 9.3

79.9

100.7 73 -4 49.1 54.7 25.1 40.4

53 *8 28.2

41 -7 10.9

40.5

The bond lengths are in good agreement with those in other AlPO, structures. a-quartz AlPO,, a-cristobalite AlPO,, A1-0 = 1.70A, P-0 = 1-56A (Mooney 1956). P-cristobalite AlPO,, A1-0 = 1-74A, P-0 = 1.52A (this work).

A1-0 = 1.739& P-0 = 1.516A (Schwarzenbach 1966).

The A1-0-P bond angle of P-cristobalite AlPO, is 145.9".

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1400 A. F. Wright and A. J. Leadbetter

As with SiO,, the disordered structure may be described in terms of super- Each hypo-

The space group is l&m2 (tetra- posit,ion of different orientations of a hypothetical ordered unit. thetical unit cell contains two AlPO, groups. gonal), the atoms having the following coordinates :

(0, 0, 0 ; $, $, it)+

2 p (c) O,Q, 4; 8 0 ( m ) x , o , z ; x , o , o , X ; o , z , z ; o , 6 , s ;

2 A1 (a) 0, 0, 0, ;

Z= 0.215,

X = 0.188, c,= 7*20& a , = c , / ~ Z .

The structure closely resembles SiO,, but the hypothetical ordered cell is iso- structural with BPO, and BAsO, (Schulze 1934). The refined structure gives distorted tetrahedra for A10, and PO,, the A10, tetrahedra being flattened and the PO, tetrahedra being elongated. It is not clear whether this is a true distostion, or whether it is an error arising from the overlap of the oxygen distribution in the average structure. Lattice parameters were determined a t temperatures up to 1100°C and are reported in table 4. Clearly the low thermal expansion properties parallel those of the SiO, isomorph.

Table 4. AlPO,: lattice parameters ( 0.0007 8)

Temperature ("C) 1 a, (A) 205 F 3" 250 300 400 500

7.1951 7.1980 7.2001 7.2044 7.2070

Temperature ("(

600 700 800 900

1 000

7.2106 7.2108 7.2109 7.2116 7-2103

$4. CONCLUSIONS P-cristobalite and the AlPO, analogue are shown to have very similar dis-

ordered structures of a kind not previously observed. The disorder is likened to a twinning of ordered units or domains on a scale comparable to unit cell dimensions. The short-range order of p-cristobalite closely resembles 01-

cristobalite with Si--0 bond lengths of 1.62A, and Xi-0-Si bond angles of 146". High-accuracy X-ray powder diffraction data give a good fit in .a least -squares refinement to a cristobalite model having six possible sites for each oxygen atom, but with each silicon site singly occupied. This interpretation is supported by high values of Debye-Waller factors, which are shown to contain a contri- bution from static disorder. It is shown that the highly-symmetrical structure often quoted in textbooks in which the Si-0-Si bond angles are linear is in error.

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T h e structures of the /3-cristobalite phases of SiO, and AlPO, 1401

/3-cristobalite-type AlPO, is also disordered, isostructural with SiO,. The short -range order closely resembles BPO, and BASO, as expected.

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DOLLASE, W. A., 1965, 2. Kristallogr., 121, 369. EVANS, R. C., 1964, An Introduction to Crystal Chemistry, 2nd ed. (Cambridge Univer-

FLORKE, 0. W., 1955, Ber. Dtsch. Keram. Ges., 32, 369. HILL, V. G., and ROY, R., 1958, Trans. Br. Ceram. SOC., 57, 496. LEADBETTER, A. J., Smm, T. W., and WRIGHT, A. F., 1973, Nature, Ph!ysical Sci.,

MILBERG, M. E., 1958, J . appl. Phys., 29, 64. MOONEY, R. C. L., 1956, Acta crystallogr., 9, 728. NIEUWENKAMP, W., 1937, 2. Kristallogr., 96, 454. SCHULZE, A., 1934, 2. phys. Chem. B,24,215. SCHWARZENBACH, VON D., 1966, 2. Kristallogr., 123, 161. SOSMAN, R. B., 1964, The Phases of Silica (Rutgers University Press). WRIGHT, A. F., 1972, Thesis, University of Bristol. WYCKOFF, R. W. G., 1925 a, Am. J . Sci., 9, 448; 1825 b, 2. Kristallogr., 62, 189. YOUNG, R. A, 1962, U.S. Air Force Office of Scientific Research Department, 2569.

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244, 125.

Dow

nloa

ded

by [

Duk

e U

nive

rsity

Lib

rari

es]

at 0

7:39

10

July

201

2