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The Raman spectrum and analysis of phonon modes in sodalite

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1981 J. Phys. C: Solid State Phys. 14 1193

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J. Phys. C: Solid State Phys., 14 (1981) 1193-1202. Printed in Great Britain.

The Raman spectrum and analysis of phonon modes in sodalite

J Ariai and S R P Smith Department of Physics, University of Essex, Colchester, CO4 3SQ, UK

Received 5 October 1980

Abstract. Polarised Raman spectra of chloro- and bromo-sodalite [Na,Al,(SiO,),Br], single crystals have been recorded, and 28 of the predicted 32 Raman-active phonon modes observed. A full group-theoretical analysis of the zone-centre phonons is given. The internal modes are assigned using as a basis the normal mode frequencies of the XO, complex(X = Si or AI). A ‘super-lattice’ approximation has enabled qualitative predictions to be made about the intensities of the Raman and infrared modes, leading to a consistent model for the inter- pretation of the Raman spectrum and the infrared spectrum of Henderson and Taylor.

1. Introduction

Sodalite, [Na,Al,(SiO,),Cl],, is the archetypal member of the sodalite group of minerals. These minerals, which can be grown synthetically, are of particular technological import- ance because of the photochromic and cathodochromic properties associated with F- centres lying at halide vacancy sites. The purpose of this investigation of the Raman scattering spectrum of sodalite is to attempt to measure and classify all the Raman- active phonon modes in sodalite, so as to provide a basis for the understanding of Raman and infrared measurements in such materials.

Various authors have studied the IR spectra of sodalite in an attempt to assign the IR bands to the vibrational modes (Milkey 1960, Vierne and Brunel 1969, Taylor et a1 1971, Henderson and Taylor 1977 and Stroud et al1979). Raman scattering measurements on parts of the spectrum have been reported by Angel1 (1973) (unpolarised measurements) and briefly by Golubova and Belitskii (1975) (both Raman and IR). Badrinarayan et a1 (1980) have measured the Raman spectra of different phases of sodalite in order to identify the electron donor sites responsible for the release of the electron which is trapped at the halide vacancy to form the F-centre. So far, however, there has been no complete and thorough work on lattice vibrations in sodalite, and the need for such an effort is obvious. Our aim has been to measure as many Raman-active modes as possible, and to correlate them with the group-theoretical predictions for the normal modes of sodalite.

We have calculated the number and symmetries of the zone-centre phonon modes in sodalite. Details are given in 5 3. The result agrees with that of Golubova and Belitskii (1974), but not with that of Stroud et al (1979). In order to make correlations between these modes and particular atomic vibrations, we have used certain approximate

0022-3719/81/081193 + 10 $01.50 @ 1981 The Institute of Physics 1193

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1194 9 Ariai and S R P Smith

symmetry properties ofthe sodalite lattice to construct a ’sapzr- latiicz‘of higher symmetry than the original lattice. Applying group theory to the modes of this super-lattice enables us to classify the Raman-active modes in sodalite as either ‘strong’ or ‘weak’ scatterers. This procedure is modestly successful in exp!aining qualitatively the observed relative intensities of the Raman-active modes and their frequencies. It enabies us to assign all of the 13 observed ‘internal’ vibrations (in the frequency range 350-1100~m-’) to the normal modes of the XO, complex (where X = Si or Al). We have observed 13 (out of the 14 possible) ‘external’ modes (from 50-300 ci-n-’) where the mode intensities are again in agreement with our qualitative predictions. The Raman spectrum and theoretical predictions are also in agreement with the IR data (Henderson and Taylor 1977) for the internal mode region.

The experimental results axe given in $2, the grouptheoretical analysis in $3, and the ccmparison between theory and experiment (Raman and IR) in $4.

2. Experimental results

The Raman spectra have been measured using the 514.5 nm and 488 nm lines of an argon ion laser, operating at -0.5 W. The spectra were recorded ia 90” scattering geometry, using a computer-controlled Spex 1401 double monochromator (resolution 1.1 cm- I).

The hydrothermally grown bromo-sodalite single crystal was kindly provided by Dr D J Marshall (RSRE, Baldock), whilst the chloro-sodalite single crystal was grown by Bye and White (I 970) and lent to us by Dr A Hassib (University of Khartoum, Sudan). The crystals were initially cut with faces normal to the fourfold axis (x, y and z) of the tetragonal T, sodalite lattice, but in order to distinguish between A, and E scattering, the crystals were again cut with one face normal to the two-fold ax& (Oll), designated the z’ axis. The orthogonal two-fold axis, (Oli), is designated the y’ axis. Raman scattering was usually measured with the incident beam along x and the scattered beam along z’. Hayes and Loudon (1978) give the scattering tensors for the Raman-active modes A,, E and T, in T, symmetry.

Figure l(a) shows the complete Raman spectrum of bromo-sodalite recorded at room temperature (294 Ti), using 514.5 nm excitation. The upper trace shows the spectrum in (y’y‘) polarisation, in which all three types of mode A,, E and T, appear with scattering intensities a’, b2 and d2 respectively (see Hayes and Loudon 1978). The lower trace shows the specrrum in the sum of (z‘x) and (z’y’) scattering geometries, where the A, modes vanish and the E and T, modes have intensities 3b2 and d 2 respectively. From these and similar spectra, we have constructed the stick plots of figures l(b), (c) and (d), which show the positions and peak heights of the A,. E and T, modes respectively. Note the different intensity scales of these diagrams.

In the sodalite lattice, the T, modes are both Raman- and infrared-active, and can therefore be split into LO and TO components. This splitting has been resolved in the case of four of the high-frequency T, modes (the largest splitting occurs for the highest LO-TO pair, at 1068 and 985 cm-l), and is presumably too small to be resolved for the remaining 11 T, modes. which include all the external modes, and the lowest internal mode. It should be mentioned that these splittings might perhaps be dependent upon the morphology of our samples, as has been pointed out by Moenke (1974), due to the presence of electric dipole centres (Van der Brom et a1 1974) associated with the coloura- tion properties.

The phonon modes all have roughly similar linewidths, except for the very narrow

Phonon modes in sodalite 1195

Frequency s i l l i t i c m - I

Figure 1. Raman spectrum of bronio-sodalite (A = 514.5 nm, T = 294K). (a) upper curve: x(y'y') z' scattering. (a) lower curve: ~ ( z ' x ) z' + x(z'y)z' scattering. (b), (c), (d) indicate the positions and intensities of the A, , E and T, modes respectively.

T, mode at 32 cm-'. No important changes occur on cooling to liquid nitrogen and helium temperatures, except that the lines become narrower, and some undergo the usual shifts of a few cm-I to higher frequencies. There is a broad structure between 521 and 588 cm-' observable in (y'y') polarisation which becomes more easily seen at low temperatures as the neighbouring modes become narrower. This is probably due to second-order Raman scattering.

The actual Raman frequencies of bromo-sodalite together with the mode assign- ments are given in table 4 of44. W-e have observed 28 modes in all: 4 A, modes, 9 E modes and 15 T, modes. We have in addition made measurements on chloro-sodalite crystals, but there are no obvious differences in either frequency or intensity between the spectra of chloro- and bromo-sodalite.

3. Group theory analysis of k = 0 modes

The commonly accepted structure for sodalite is T;(Pq3n), with two Na,(AlSiO,),Cl formula units per unit cell. The lattice spacing a, = 8.91 A. Table 1 gives the site sym- metries and positions of each atomic species (see Wyckoff 1964), the number N ; of irreducible representations r of T, spanned by the set of site coordinates for each atomic species, and the resulting number iV; of vibrational modes at k = 0. The latter quantity is obtained from the direct product of the displacement representation (r = T,) with the site representations N ; for each atomic species.

1196 J Ariui und S R P Smith

Table 1. Number of site and displacement representations for each atomic species in sodalite.

N ; (sites) N; (vibrations) Atom Site Wyckoff

symmetry position A, A, E T, T, A, A, E T, T,

C1 T (23) 2a 1 1 0 0 0 0 0 0 1 1 AI s, (3) 6c 1 0 1 1 0 0 1 1 2 3 Si s, (5) 6d 1 0 1 1 0 0 1 1 2 3 Na c, (3) 8e 1 1 0 1 1 1 1 2 3 3 0 C , (1) 24i 1 1 2 3 3 3 3 6 9 9

Totalphononmodes 4 6 10 17 19

The total number of k = 0 modes is

4A, + 6A, + 10E + 17T, + 19T,

which agrees with the analysis of Golubova and Belitskii (1974). Of these modes, only the A,, E and T, modes are Raman-active. One T, mode represents the acoustic phonon branch, which leaves the number of Raman-active optic phonons as

4A, + 10E + 18T,.

It is helpful for assignment purposes to divide the optic phonon modes into 'internal' and 'external' modes. This classification depends on the fact that the light 0,- ions are strongly bonded covalently, so that those phonon modes which consist mainly of motions of the 02- ions will have higher frequencies than the remaining modes. The procedure is justified by the phonon spectrum, which divides clearly into external modes, from 0 to 300 cm-l, and internal modes, from 300 cm-' to 1100 cm- ',

The crystal structure consists of distorted tetrahedra of (0, -)4 groups surrounding each Si site (or, equivalently, each Al site). The normal mode frequencies of an SiO, group (symmetry TJ are of symmetries A,, E, T, and T, with frequencies designated conventionally as v l , v2, v j and v4 respectively. The number of phonon modes of each symmetry in the sodalite lattice corresponding to each SiO, vibrational frequency can be obtained from the direct products of these representations with the site representations N: for Si. The resulting number of modes obtained is shown in table 2. The number of

Table 2, Number of internal modes in sodalite corresponding to each XO, normal mode.

Frequencies (cm- l) of 'free SiO,' modes

XO, Modes Number of sodalite modes N,

Mode Symmetry A, A, E Tl T,

"1 A, 1 0 1 1 0 770 "2 E 1 1 2 1 1 350 v3 T, 0 1 1 2 3 1150 "4 T, 0 1 1 2 3 510

Phonon modes in sodalite 1197

Raman-active internal modes obtained by this procedure is 2A1 + 5E + 7T2. The frequencies of the ‘free’ SiO, modes, as given by Vierne and Brunel(1969), are also listed in table 2: v1 and v 3 are ‘stretching’ modes, and v2 and v4 ‘bending’ modes. In the free radical, v, also involves motion of the central Si atom. This type of classification has been used by Griffiths (1969), who lists the modes in a wide range of minerals.

However, because each oxygen in an SiO, group is also part of a different A10, group, this classification scheme must be treated with reservation. In particular, the SiO, group is certainly not free to rotate as a group, and A1-0-Si vibrations seem likely also to lie in the internal mode range above 300 cm- ’. An alternative approach to classi- fication is that used by, for example, Henderson and Taylor (1977), and Stroud et a1 (1979), who consider that the total framework of the oxygens is responsible for the higher- frequency modes, The exact correspondence between the two approaches does not seem to be properly established.

Because of the linkages between the SiO, and A10, groups, and because the v, vibrations include a motion of the central ion, it is likely that vibrations in which the Si and A1 atoms move in anti-phase will also have frequencies in the internal mode fre- quency range. This comprises half the sum of the A1 and Si modes in table 1, i.e. the con- tribution of one of them separately: we denote these modes as anti-phasc (AP) modes. We therefore adopt the view that the internal modes (i.e. those above 300 cm-l) may be classified as v l , v2, v3, v, or AP, giving the total division of optic phonon modes as:

internal modes: 2A, + 4A2 + 6E + 8Tl + 10T2 external modes: 2A, + 2A2 + 4E + 9T1 + 8T2.

The justification for this scheme at present lies principally in the fact that it enables us to make a straightforward classification of the experimentally observed phonons, which, with a few reservations, is successful in accounting for the Raman and IR measure- ments on sodalite. We emphasise that the division of internal modes according to the frequencies v i of the SiO, complex is not intended to imply that the AI atoms have no part in these vibrations, but that empirically it appears to provide a convenient basis for the interpretation of the experimental data.

Thus far, the group-theoretical analysis has merely given information about the mode symmetries, but not their intensities. Of course, a full calculation of the intensities is very complicated, and we are in no position to do this, but it is interesting to demon- strate how the nature of the sodalite lattice enables us to make some qualitative predic- tions about the relative intensities of certain of the modes. We now describe a procedure for doing this.

There are various ways in which we can generate ‘super-lattices’ in sodalite which are of a higher symmetry than the original lattice. By considering the phonon modes of these super-lattices we can make qualitative predictions about the intensities of the real lattice modes. Two such super-lattices are as follows:

(a) the C1, A1 and Si atoms taken alone lie on a lattice of symmetry 0,” (Pm3n), with the atoms at the Wyckoff positions 2a, 6d and 6c respectively;

(b) the Na ions lie on a BCC lattice with symmetry. (In fact, if we assert that the distinction between Si and A1 can be ignored (Si = A1 = X), and if we ignore the differ- ence between y and z for the oxygen positions (x, y , z), we generate the super-lattice Ti (I33m) with only one formula unit to the primitive unit cell-see Alig (1974).)

We have assumed that all the modes except those due to the Na atoms may be dis- cussed in terms of the super-lattice (a). In O;, the C1 site coordinates transform like

1198 J Ariai and S R P Smith

Q C l ) = Alg + AZg under Oh, and both the Si and AI sites like P(x) = Alg + Eg + T2,!. A linear displacement transforms like TI,, IIA Oh, so the k = 0 vibration coordinates transform like the direct products T,,, x r".

+ T2g I? for Si and Al. The Raman-active modes are Alg, Eg and T2g in Oh, and ignoring for a moment the pure translational modes ( lTIU in each case), we would expect that only the Alp, Eg and T2g modes in the 0," supsr-lattice will contribute to the strong Rarnan modes in sodalite. Of the remaining modes, the A2u, E,, and TIU modes can contribute to weak Raman scattering, and the rest are forbidden. Similarly, the TI,, modes will give strong IR absorption, the T2g modes weak absorption, and the remainder will be inactive in the IR. We therefore have a scheme for distinguishing between 'strong' and 'weak' Raman scattering and IR modes. I t is not possible in this scheme to make any firm statement about the translational TI" modes, iii which all the atoms of a particular species undergo an identical translation, and so we shall consider these modes separately, denoting them by the symbol TW. They transform like r = T, in T, symmetry.

This scheme can be extended to include the oxygen contributions. We imagine that a distorted oxygen tetrahedron 0, is placed at each Si (or AI) site (whose site symmetry is D,+. in O,"), and calculate the modes which result in 0; for (i) a rotation (TIJ of the 0,; (11) vibrations vL (i = 1 to 4). The vibrations (ii) contribute to the internal modes.

The result of this super-lattice mode scheme i s shown in table 3, where the number N i of the modes in 0," are given, and the resulting number of Rainan active modes classi- fied as strong, weak or TR. The Raman modes of the Na atom are also given in table 3,

Forexamp1e,ihisgivesTlU + ?',UforC1,and2Tlu + TZU + A2g $- E + T

Table 3. Number of 0; super-lattice modes in sodalite, and intensity classification of Raman- ' i c t i \~ modes.

Number of Raman nodes in T: iv; in 0," - -_

strong weak m __ -__ - _ _ _.___

Atom species A h A 2 g E8 TI8 =2g 4 " A," E" rrl,, T," .4, E T, A, E T* T,

c1 Si AI 0 rot

v1

"2

v 3

v4 Na

0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 1 1 1 1 0 0 0 2 1 0 1 1 0 0 1 1 0 1 1 1 1 0 0 0 2 1 0 1 1 0 0 1 1 0 0 0 2 1 0 1 1 1 1 0 0 1 i l l - 1 0 1 0 0 0 0 0 0 1 3 i O O O O - - 1 0 1 0 1 1 0 1 0 1 1 1 1 0 1 0 - 0 1 1 1 1 0 0 0 2 1 0 1 1 0 0 2 - - 0 1 1 1 1 0 0 0 2 1 0 1 1 0 0 2 -

1 1 1 0 1 1 I

though these do not fit into the super-lattice scheme (a), and are treated using the super- lattice (b), in which each Na' ion is placed at the 4c site of a T," lattice. Tke k = 0 Na modes in this lattice are A, + E + T, + 2T,, which give 'strong' Raman modes A, + E + T, plus a T, TR mode. The remaining Na modes of the T: lattice (A2 + E + 2T, + T2) correspond to zone boundary modes in the T," lattice, and are therefore expected to contribute to the 'weak' classification.

Phonon modes in sodalite 1199

As far as IR activity is concerned, we would expect that these 'T, modes labelled as weak or TP. will give strong IR absorption. and h e strong Raman T, modes will give weak IR absorption (except for the Na contributions, wherz the I& and Raman activities are the same'),

4. Discussion of results

We will attempt to reconcile our Raman scattering results (figure 1) and the IR bands measured by Henderson and Taylor (1977) with the theoretical predictions of $3. Henderson and Taylor's measurements extend down to 300cm-', and they report bands in brorno-sodalite at 985, 732, 708, 664,465, 437 a.nd 306 cin- '. In this region, the Raman T, modes are observed at (1058,98S), 9170,965, (743.5, 735), (488,462), (449,431.5) and 370 cm- (the bracketed modes are the separated LO-TO components of the same phonon). The agreement between the spectra, which are both well defined and repro- ducible, is confined to about half of the modes; for the remainder, it appears that different bands are observed by the two techniques, as is always the case in centro-symmetric materials. This fact in itself justifies our attempt at classification in terms of a super- lattice which has an inversion centre, while the real lattice T: does not.

In the internal mode region, the observed modes fall into three groups, (1) from 950 to 1100 cm- l, (11) from 600 to 750 cm.- l 3 and (111) from 300 to 500 em-'. Consider group (I) first. These modes are likely to be the best defined in terms of our internal SiO, scheme, of which v3 lies highest and v, next. Table 3 shows that v, gives one A, mode, whereas v3 gives none; in the region I there is one A, mode (at 987 cm-'), so we conclude that the group (I) spectrum arises from the stretching modes v, and vJ . The theoretical predictions from table 3 and the experimental results are summarised in table 4. For the v 3 (stretching) vibrations, the predicted strong Raman modes (RS) are OA, + 1E + lT,, indicated by (011) in column 3, and the predicted weak Raman modes (RW) are OA, + OE + 2T,. The E mode appears at 1057 cm -', and the strong T, modes at 970 cm-'. One weak T, mode (which is admittedly only weaker in this case by about a factor of 2) is the LO-TO pair at (1068, 985) cm-I, and the other weak T, mode occurs at 965 cm-'. In the IR spectrum, a very strong and broad band is seen, peaking at 985cm-', corresponding to the first of the two RW T, modes, the other expected strong IR mode (ms),(which is expected to occur at 965 cm-l, may well be obscured in this band. Similarly, we expect one weak (IRW) T, mode in the IR, which would correspond to the RS mode at 970 cm-li but this again cannot be resolved under- neath the strong 985 cm-' absorption. The v1 modes are only the RS l A , + 1E modes at 987 and 1012 cm-', and do not contribute in the IR, as detailed in table 4. Actually, the proximity of this E mode (10i2 cm'-') to the v 3 E mode at 1057 cm-' means that our distinction between them may be in doubt, and it is probably better just to refer to the group (I) modes as stretching modes, abandoning the distinction between v1 and v 3 modes. (For comparison, in table 4 the corrzsponding Raman and IR T, modes are arranged verticaily beneath each other within the same category. The final two columns of the table show the total number of modes of each type predicted and observed, where, for example, (013) means QA, + 1E + 3TJ

The region I1 (6OCL750 cm- I) contains no A, modes, and consists of Raman E and T, modes at 607 and (744,735) cm- respectively, and IR bands at 732,708 and 644 cm-l. These modes lie somewhat above the v4 frequencies for free SiO,, but the assignment of v4 to this region fits in with the mode classification reasonably well. The only difficulty

1200 J Ariai and S R P Smith

Table 4. Classification of Raman and IR phonon modes in bromo-sodalite (IR measurements from Henderson and Taylor 1977).

Classification Strengths Predicted Observed modes (cm- ' ) Total number of modes _ _ ~ ~ _ _ _ _ _ _ _ _ _ _ _ _ . _ _ _ number of -

modes A , E T2 Predicted Observed

Rs RW V3

(stretching) IRS IRK'

RS

RW

__ - __

V1 (stretching) IRS

IRW

(013)

607 (735,744) (013) (013)

708 664 732

V2' nP RS 1122) + TR 463 497 410 (462,468) (431, 449) 370 RW (01 1) (134) (124) IRS (1) 4- TR 465 406 IRW (2) 437

(248) (248) External RS (123) + 2TR 263 297 147 295 232 132 110 99 RW 11231 167 227 59 198 179 59

Totals (4,10,18) (4,9,18)

is with the T, mode at 732 cm-' in the IR, which should be IRW since it coincides with the RS mode, but which nevertheless is of comparable strength to the other IR modes, classi- fied as IRS because they do not appear in the Raman spectrum.

The region I11 (30Cb500 cm-'1 contains the remainder of what we classify as internal modes, namely v 2 and A P (see $3). The AP TR mode is included as providing both RS and IRS contributions, and is presumably the 'T, mode at (488, 462) cm-' (Raman) and 465 cm-' (IR). The weakest of the three IR modes (437 cm- ') coincides with an RS mode. One IRW mode is missing (it should occur at 370 cm-I), and one RW T, mode (406 cm- ') is not observed, as well as a RW E mode. Seven of the eight predicted modes in this region are accounted for.

In the external mode region (below 300 cm- '1, all of the predicted 2A, + 4E + 8T, Raman modes are observed, except for one E mode. There are no available IR data in this region. The classification as RS or RW is reasonably satisfactory, though the spectrum becomes confused at low frequencies, where small features at 67 and 80 cm- ' might be additional modes, and the assignment of the rather broad feature at 59 cm-' as both a T, and an E mode is perhaps a little doubtful. No LCFTO splittings are resolved in the external T, modes.

Phonon modes in sodalite 1201

5. Conclusions

Thus we have assigned all of the predicted 4A, + 10E + 18T, zone-centre modes In sodalite except for one E mode, and we have shown that the classification scheme de- scribed in § 3 is generally very successful in describing the modes. We might remark that the frequencies of the relatively rare A, modes were very helpful guides in enabling us to arrive at a satisfactory assignment scheme. For example, both the Na vibrations and the oxygen rotations provide one A, mode, and because of this it is impossible to include either of these sets of modes within the internal mode category, if we accept as one of the characteristics of an internal mode the criterion that the mode should be a well defined vibration of a particular set of atoms, all such vibrations having roughly similar frequencies. This seems to rule out the proposal by Badrinarayan et a1 (1980) that one of the high-frequency modes should be classified as a Na-0 stretching mode, a view which is in any case not supported by the observation of Henderson and Taylor that the high- frequency IR spectrum is very little changed by the substitution of K for Na. It is also interesting to note that, on the basis of an oxygen framework model, one might well expect that what we have called the oxygen rotation modes should form part of the in- ternal mode scheme, a point of view which cannot easily be reconciled with our analysis.

Many points remain unconsidered here, amongst them the origins and consequences of the L ~ T O splittings, and also the curious feature that the strongest absorptions in the IR (at 985 and 465 cm-l) are coincident with A , modes in the Raman spectrum. It must be emphasised that our classification gives only an approximate indication of the types of atomic vibrations involved in each mode, and that substantial mode mixing will always occur. In particular, without detailed calculation we cannot estimate the relative contributions of A1 and Si to the internal modes, a problem which has received some experimental consideration in the literature (Taylor et a1 1971, Henderson and Taylor 1979 and Stroud et al 1979). However, it is clear that this study of the Raman scattering spectrum together with the group-theoretical analysis has made a substantial contribu- tion to the understanding of vibrational modes in a complicated mineral.

Acknowledgments

We would like to thank Drs D J Marshall and A Hassib for the loan of crystals. One of us (JA) would like to thank the University of Kerman, Iran, for a studentship in support of this work.

References

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1975 Chem. Abstr. No. 83-96983b

1978 Spectrochim. Actu 35A 929-35

1202 J A r i d and S R P Smith

Milkey R G 1960 Am. Minerd45 990-1007 Moenke H H W 1974 ?'he I K Spectra of Mineruls ed. V C Farmer (London: Mineralogical Society) Stroud C E? Stencel J M and Todd L T Jr 1979 J . Phq'i. Chein. 83 2378-82 Taylor M J, Marshall D J and Evans H 1971 J . Phys. Chem. Solids 32 20214 Van Den Brom W E, Kerssen J and Volger j 1974 Pirjsicu 75 1-26 Vierne R and Brunel R 1969 Bull. Soc. Miner . Cristnli. 92 409-19 Wyckoff R W C 1954 Crystal Structures vol 4 (New York: Wiley-Interscience)