Crystal growth and crystal structures of the layered ionic conductors–sodium lithium titanium oxides

International Journal of Inorganic Materials 2 (2000) 443–449

Crystal growth and crystal structures of the layered ionic conductors– sodium lithium titanium oxides a b, b a G.V. Shilov , V.B. Nalbandyan *, V.A. Volochaev , L.O. Atovmyan a

Institute of Problems of Chemical Physics, Russian Academy of Sciences, Chernogolovka, Moscow Region, 142432, Russia b Rostov State University, 7 ul. Zorge, Rostov-na-Donu, 344090, Russia Accepted 11 May 2000

Abstract Single crystals of four structure types have been grown from melts of the Na 2 O–Li 2 O–TiO 2 system. Structures of two of them have been determined by the single-crystal X-ray diffraction. The both structures comprise brucite-like octahedral (Ti,Li)O 2 layers with random Li / Ti distribution. One of them, (Na 0.73 Li 0.24 )(Li 0.32 Ti 0.68 )O 2 , is rhombohedral (a-NaFeO 2 type), whereas the other, Na 0.66 (Li 0.22 Ti 0.78 )O 2 , hexagonal containing sodium ions in trigonal prisms of two kinds with occupancies 0.36(1) and 0.29(3), respectively. One more crystal, (Na,Li) 3 (LiTi 2 )O 6 , is a superlattice of the a-NaFeO 2 type due to Li / Ti ordering. Relationships between the cation–cation repulsion, cationic disorder, relative stability of the structure types and their cation transport properties have been discussed.  2000 Elsevier Science Ltd. All rights reserved. Keywords: A. oxides; B. crystal growth; C. X-ray diffraction; D. crystal structure; D. ionic conductivity

1. Introduction The A 1 x (M, M9)O 2 mixed-oxide family, based upon the brucite-like octahedral (M,M9)O 6 / 3 layers, has been well known for its cation transport properties. Some of the compounds, e.g. A x CoO 2 bronzes, contain a mixed-valence metal and exhibit both ionic and electronic conduction. These may serve as electrode materials [1–5]. Phases containing M and M9 in their stable oxidation states, e.g. K 0.72 In 0.72 Sn 0.28 O 2 [6], Na 0.6 Cr 0.6 Ti 0.4 O 2 [7] and related compounds [6–13], are high-conductivity solid electrolytes with negligible electronic contribution. The brucite-like layers may be stacked in various ways, giving rise to a variety of structure types [1–3,14,15]. Those most common for alkali compounds are: O3 — the rhombohedral triple-layered structure having the A1 cation in an octahedral environment (the aNaFeO 2 -type); P2 — the hexagonal primitive double-layered structure having the A1 cation in a trigonal–prismatic environment.

*Corresponding author. E-mail address: [email protected] (V.B. Nalbandyan).

The latter is especially favourable for fast cation transport due to a wider bottleneck in the interlayer. However, all these conclusions have been based mainly on the powder diffraction data [1–17]. Single-crystal structure determinations were only performed for mixedvalence A x CoO 2 [18] and Nax TiO 2 [19], and also for nominally stoichiometric RbScO 2 [20,21] and LiCoO 2 [22]. No single-crystal study of a P2 or O3 solid electrolyte has been reported. The only structural investigation of the P2-type cation conductor (K 0.72 In 0.72 Sn 0.28 O 2 ) was made using the powder film technique [16]. Even the space group for the P2 type has been a subject of contradiction: P-6 m2 [16,20], P63 22 [18] and P63 /mmc [17,21] have been reported. Furthermore, the superlattice effects have been found (but not interpreted) for the P2-type cobalt bronzes [18]. That is why we decided to prepare P2- and O3-type solid electrolytes in a single-crystal form to determine their crystal structures and cation transport properties. Sodium lithium titanium oxide system, (Na 12y Li y ) x (Li x / 3 Ti 12x / 3 )O 2 [13] has been chosen as the most suitable model since it contains both the P2 and O3 phases with relatively high ionic conductivities (e.g. 3.5 S / m at 3008C for Na 0.66 Li 0.22 Ti 0.78 O 2 ceramics) and

1466-6049 / 00 / $ – see front matter  2000 Elsevier Science Ltd. All rights reserved. PII: S1466-6049( 00 )00050-7

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G.V. Shilov et al. / International Journal of Inorganic Materials 2 (2000) 443 – 449

Fig. 1. A portion of the composition triangle Na 2 O–Li 2 O–TiO 2 . Dots 1–6 represent starting melt compositions, and crosses show compositions of grown crystals according to the X-ray data.

relatively low melting temperatures. Moreover, superlattice M / M9 order, if any, was expected to be most pronounced in that system due to large differences in charge, size and scattering power between Li 1 and Ti 41 ions.

2. Experimental Since the liquidus data for the Na 2 TiO 3 –Li 2 TiO 3 join [23] only showed an eutectic at 9848C and 16 mole % Li 2 TiO 3 and failed to reveal the O3 phase found near 25 mole % Li 2 TiO 3 by powder X-ray analysis [13], we conclude that the crystal melts incongruently. An excess of sodium titanate is therefore necessary for growing (Na 12y Li y ) x (Li x / 3 Ti 12x / 3 )O 2 single crystals from the melt of the Li 2 O–Na 2 O–TiO 2 ternary system. To ensure this, we used melts with a fixed Na:Li ratio of 4 and variable

titania content. In Fig. 1, starting melt compositions are indicated by dots with numbers, and arrows point to approximate compositions of the grown crystals. Weighed amounts of reagent-grade sodium carbonate, lithium carbonate, and titanium dioxide (the total mass being about 50–70 g) were mixed, placed into 50 ccm platinum crucible and heated slowly to ca. 1050–11008C to achieve complete melting. Then 1 mm thick platinum wire was immersed into the melt and started rotation combined with slow pulling out, while the melt was cooled at a rate of 308C per h. After sufficient amount of crystalline material had been grown on the wire, it was removed and cooled. The resulting crystals were separated mechanically and characterised by means of a polarizing microscope, Weissenberg camera, and also by the powder X-ray method using Cu Ka radiation with a DRON-2.0 diffractometer. Crystals selected for the X-ray structure analysis were mounted on an automated diffractometer (Kuma Diffraction KM-4 model), and the data were collected using monochromated Mo Ka radiation and the v 22u scan mode. Since crystal sizes did not exceed 0.230.230.1 mm 3 , the absorption effect was neglected. The details of data collection and refinement are given in Table 1. All calculations were performed using the SHELX packages [24,25]. For the solid-state synthesis, weighed amounts of reagents were mixed thoroughly with a mortar and pestle, pressed into pellets and calcined for 3 h at 450, 800 and 9508C (i.e. just below the solidus temperature) with intermediate grindings and pressings, and finally quenched in air.

3. Results Six melt compositions were used in crystal growth experiments (see Fig. 1), and crystals of four structure types were obtained. All of them were translucent colourless or pale yellow. Run 1 yielded rhomb-shaped plates of Na 1.3 Li 0.7 Ti 3 O 7 . Its structure has been reported in a separate paper [26]. Runs 2 to 6 gave mica-like hexagonal

Table 1 Crystallographic data and details of data collection and refinement Structure type

P2

O3

O3S

Composition Crystal system Space group ˚ a, A ˚ c, A ˚ 3) V (A Z Dx , g / cm 3 m, cm 21 Number of reflections used, I . 2s (I) R

Na 0.66 Li 0.22 Ti 0.78 O 2 Hexagonal P63 /mmc (No 194) 2.9600(10) 11.127(3) 84.43(5) 2 3.39 39 227 0.0558

(Na 0.73 Li 0.24 )(Li 0.32 Ti 0.68 )O 2 Trigonal R-3 m (No 166) 2.9930(10) 16.045(5) 124.48(7) 3 3.40 35 240 0.0813

(Na 2.76 Li 0.24 )(LiTi 2 )O 6 Trigonal P31 12 (No 151) 5.18852.9953œ3 16.02 373.4 3 3.52

G.V. Shilov et al. / International Journal of Inorganic Materials 2 (2000) 443 – 449

445

Table 2 Positional parameters and B(eq) in the P2- and O3-type structures of sodium lithium titanium oxides

Table 4 ˚ and bond angles (8) in the P2- and Selected interatomic distances (A) O3-type structures of sodium lithium titanium oxides

Atom

Contact or angle

P2

O3

Ti–O36 Na(1)–O36 Na(2)–O36 Na(1)–Ti36 Na(2)–Ti32 Na(1)–Na(1)36 Na(1)–Na(2)33 Na(1)–Na(2)33 Na(2)–Na(2)36 O–O33 O–O36 O–Ti–O angles Ti–O–Ti angles

2.003(1) 2.437(1) 2.437(1) 3.265(1) 2.7818(8) 2.960(1) 1.7090(6)a 3.418(1) 2.960(1) 2.700(1) 2.960(1) 84.73(5), 95.27(5), 180.0 95.27(5)

2.037(4) 2.352(5) – 3.184(1) – 2.993(1) – – – 2.764(1) 2.993(1) 85.5(2), 94.5(2), 180.0 94.5(2)

x

y

z

B(eq)

Occupancy

P2 Ti a O Na(1) Na(2)

0 1/3 2/3 0

0 2/3 1/3 0

1/2 0.40609(12) 1/4 1/4

1.10(2) 1.08(2) 2.1(2) 4.4(6)

0.796(11) 1 0.361(14) 0.29(3)

Ti a O Na a

0 0 1/3

0 0 2/3

O3 0 0.2661(4) 1/6

1.43(3) 1.91(7) 1.66(7)

0.71(2) 1 0.77(3)

a Here, and also in Tables 3 and 4, ‘Ti’ stands for (Ti,Li), and ‘Na’ in the O3 phase stands for (Na,Li) since Li ions were not included in refinements (see text).

This value should not be considered as a real Na 1 –Na 1 distance. This is only a separation between lattice sites which cannot be occupied simultaneously. In other words, it is a jump length for sodium ion transport. a

plates, very similar to each other in habit. The oscillation and Weissenberg photographs, however, revealed three different structure types. Crystals from runs 2 and 3 were ˚ and c¯11.1 A, ˚ which is charachexagonal with a¯3.0 A teristic of the P2 type. Crystals from the runs 4 and 5 were ˚ and c¯16.5–16.1 A, ˚ characrhombohedral with a¯3.0 A teristic of the O3 type. For the run 6 crystals, however, the respective rhombohedral cell was only a subcell, since superlattice reflections were found. These indicated a¯ ˚ and a trigonal primitive lattice rather than the œ333.0 A rhombohedral one. This structure type is labelled as O3S in Table 1. The largest crystals grown, up to 10 mm in diameter and 1 mm thick, were those of the P2 phase, since the difference in composition between the liquid and the solid was a minimum for this phase (see Fig. 1). Those crystals have been used for conductivity measurements and ion exchange experiments [27]. Single crystals for structural studies were selected from batches 2 (P2 type) and 5 (O3 type). The both structures were solved by the Patterson and Fourier methods and successfully refined anisotropically within the highest space groups allowed by systematic absences and Laue symmetry, i.e., P63 /mmc and R-3 m, respectively. The structural data are summarised in Tables 1–4 and Figs. 2 and 3. Due to a low scattering power of lithium and its random distribution, the lithium ions could not be located immediately. So refinements were carried out taking into account only Na, Ti, and O ions. Neverthe-

less, definite conclusions concerning lithium content and its position in the structures may well be drawn. First, charge balance cannot be achieved without Li 1 ions. Based on the occupancies listed in Table 2, the composition of the P2 crystal would be ‘Na 0.65 Ti 0.80 O 2 ’,

Table 3 Thermal parameters in the P2- and O3-type structures of sodium lithium titanium oxides Atom

Ti O Na(1) Na(2)

P2

O3

U11

U33

U11

U33

0.0124(2) 0.0149(4) 0.034(2) 0.058(10)

0.0169(3) 0.0112(4) 0.0087(12) 0.052(11)

0.0090(3) 0.0173(8) 0.0155(9) –

0.0364(8) 0.038(2) 0.032(2) –

Fig. 2. The crystal structure of Na 0.66 Li 0.22 Ti 0.78 O 2 , illustrating the coordination polyhedra of titanium / lithium (octahedra) and sodium (trigonal prisms).

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G.V. Shilov et al. / International Journal of Inorganic Materials 2 (2000) 443 – 449

Fig. 3. The crystal structure of (Na 0.73 Li 0.24 )(Li 0.32 Ti 0.68 )O 2 , illustrating the coordination polyhedra of titanium / lithium (octahedra) and sodium / lithium (elongated trigonal antiprisms).

lacking 10.15, and the composition of the O3 crystal would be ‘Na 0.77 Ti 0.71 O 2 ’, lacking 10.39. To ensure 1 electroneutrality, Li must be introduced to the formulae. So the scattering matter on the Ti site should be Ti 12x / 3 Li x / 3 rather than Ti alone. Bearing in mind the scattering factor ratio f(Ti 41 ) /f(Li 1 ) of about 9, Ti site occupancies indicated in Table 2 may then be rewritten as Ti 0.77 Li 0.23 for the P2 crystal and Ti 0.68 Li 0.32 for the O3 crystal. Now, the charge deficiency for the P2 phase becomes as low as 10.04, well within one standard deviation of the Ti site occupancy (0.01), while that for the O3 phase is still 10.20, which implies the presence of additional Li 1 ions in the interlayer. Second, the Ti–O bond lengths (see Table 4) are significantly larger than those normally found for undistorted or slightly distorted TiO 6 octahedra (e.g., 1.95 and ˚ in the orthorhombic crystal from run 1 [26]). This 1.97 A also requires lithium substitution for Ti. Third, the Na–O distance in the O3 crystal is abnormally short compared with that in the P2 crystal (see Table 4) ˚ [28]) thus and also with the ionic radii sum (2.41A confirming the Li substitution for Na in the O3 phase.

Based on the ionic radii, the lithium fraction y on Na sites could be interpolated as y ¯0.22. Fourth, the above conclusions are strongly supported by the powder diffraction data on subsolidus phase relations in the Na 2 O–Li 2 O–TiO 2 system [13], where the homogeneity region for the P2 phase was found to be onedimensional and lie along the Na x Li x / 3 Ti 12x / 3 O 2 section of the triangle (see Fig. 1), while the homogeneity region for the O3 phase was found to be bidimensional and deviate from that section towards greater Li content: (Na 12y Li y ) x (Li x / 3 Ti 12x / 3 )O 2 . Lattice constants of our P2-type crystal, listed in Table 1, are in excellent agreement with the powder diffraction ˚ [13]. With data for x50.65: a52.961; c511.133 A increasing x, a increases, and c decreases so the c / a axial ratio is most composition-sensitive parameter, being 3.760 and 3.745 at the lower and upper limit of the homogeneity range, x50.65 and x50.69, respectively [13]. A c / a ratio of 3.759 observed for our crystal agrees well with that for the lower limit, which in turn coincides with the total amount of Na found, 0.3610.2950.65 (see Table 2) and is also in reasonable agreement with x / 350.23 based upon the Ti site occupancy (see above). Hence, within the experimental error (60.01), the composition Na 0.66 Li 0.22 Ti 0.78 O 2 may be adopted for the P2 crystal studied. The composition is less definite with the O3 crystal, because of a bidimensional homogeneity region and larger uncertainty in Ti content (see Table 2). Assuming the a parameter to be dependent mainly on x value, i.e. on Li fraction on the Ti site rather than on the Na site, and ˚ for x50.66 and a5 interpolating between a52.960 A ˚ 2.995 A for x51 (a subcell parameter of the O3S phase, see below), an x value for our O3 crystal may be estimated as 0.98. This is in surprisingly good agreement with the above estimate based on the Ti site occupancy. The Li content in the interlayer is not simply the difference between an x value and the Na site occupancy, since ‘Na’ in Table 1 is actually (Na 12y Li y ) x . Taking into account the 1 1 scattering factor ratio f(Na ) /f(Li ) of about 4.5 and assuming x50.98, y may be calculated as 0.28, with uncertainty of about 0.04 based upon one standard deviation in the Na site occupancy. This is consistent with the above estimate based upon the ionic radii difference. Summarising all these data, we adopt x50.9760.03 and y50.2560.05 as the most probable composition of our O3 crystal. The value for y is far beyond the previously found limit of 0.1 [13], probably owing to a higher preparation temperature used in the present work. Unfortunately, the O3S-type crystals were of poor quality, inappropriate for the structure analysis. An ideal composition for this superlattice would be Na 3 LiTi 2 O 6 . However, the X-ray powder diffraction study on the samples prepared by solid-state reaction has shown the above composition to be a mixture of the O3S phase and a solid solution based on Na 2 TiO 3 . Along the Na 2 TiO 3 –

G.V. Shilov et al. / International Journal of Inorganic Materials 2 (2000) 443 – 449

Li 2 TiO 3 join, single phase of the O3S type was only found at 3161 mole % Li 2 TiO 3 . According to the single-crystal unit-cell data, this composition must be written as (Na 0.92 Li 0.08 ) 3 (LiTi 2 )O 6 . Lattice constants were refined by the powder method with an internal standard, and the results are given in the last column of Table 1. The subcell reflections were sharp, and their intensity distribution was essentially the same as with the O3 samples. In contrast, the superlattice reflections were weak and broadened, indicating considerable disorder.

4. Discussion The present results confirm the brucite-like motif for the both structures, P2 and O3 (see Figs. 2,3). The MO 6 octahedra 1 are slightly compressed along the triad axis, the shortest O–O edges being those shared by the octahedra (see Table 4). The obvious reason for this is M–M repulsion, which tends to increase the M–M distance. With increasing x, the repulsion becomes weaker owing to (i) a decrease in the mean cationic charge and (ii) an increase in the mean bond length, i.e. in size of an octahedron. Thus, the octahedra become somewhat more regular, as evidenced by the O–O distances and the O–Ti–O bond angles (see Table 4). In the O3-type phase (Fig. 3), the A ion is surrounded by six oxygens which form a trigonal antiprism (an elongated octahedron). In the P2-type phase, two sodium polyhedra have been found. Both of them are trigonal prisms, equal in size, but with different next nearest neighbours: A Na(1) prism sharing edges with the octahedra of brucite-like layers, and a Na(2) prism sharing two faces with the same octahedra (Fig. 2), the both prisms being underoccupied (see Table 2). The common face of the two prisms is a rectangle with a bottleneck radius (i.e. ˚ the distance between the centre and vertices) of 2.28 A, large enough for Na 1 transport. The Na 1 ion mobility in the P2-type crystal manifests itself in a high ionic conductivity [13,27] and large U11 values for the both sodium sites (see Table 3). For the O3-type crystal, the bottleneck is a triangle and, in accordance with previous indications ˚ [3,6–8,11,12,15], its radius is much smaller: 1.99 A. However, this value is in fact an average for NaO 6 and ˚ is only an LiO 6 polyhedra, just like the value 2.35 A average A–O bond length. Local distances should deviate significantly from these values. The large fraction of lithium substituted for sodium on the octahedral sites and the absence of Li on the prismatic Na sites are quite consistent with the previous results indicating a large number of the O3-type Li x MO 2 phases [3–5,22] and the absence of P2-type phases containing Li on A sites, as illustrated by the P2→O2 transformation upon Li ion exchange in the P2-type Na x CoO 2 [14] and 1

Here and further, M stands for both octahedral cations (e.g. Li and Ti, In and Sn) and A stands for interlayer cations.

447

O / P intergrowth structure of Li 0.43 Na 0.36 Co0 2 with ordered arrangement of Li on octahedral sites and Na on prismatic sites, according to the neutron diffraction data [15]. Obviously, prismatic coordination is unfavourable for the Li ion due to its small size and hence short O–O ˚ distances of about 2.6 A. The most striking result of the present single-crystal study is the absence of a long-range order in Li / Ti distribution within brucite-like layers, despite considerable ˚ [28]). differences in their ionic charges and radii (0.15 A No superlattice reflections have been found for crystals from batches 2 to 5, although a short-range order may well exist. Long-range Li / Ti order, though imperfect, was only observed for a ‘completely filled’ structure, i.e. one having no vacancies in the interlayer, x51. This O3S phase is probably isostructural with a-Li 2 SnO 3 [29]. For K 0.72 In 0.72 Sn 0.28 O 2 [16], Na 0.6 Cr 0.6 Ti 0.4 O 2 [7], and related materials, cation order was difficult to verify due to almost identical X-ray scattering factors of the M cations. Now, by analogy with Na 0.66 Li 0.22 Ti 0.78 O 2 , the absence of a long-range order in these phases is clear, because In / Sn or Cr / Ti cations are much closer to each other both in size and oxidation number as compared with Li / Ti pair. Superlattices found with A 0.5 CoO 2 bronzes (A5K, Rb, Cs) [18] should have another origin, obviously A / vacancy order. To attain local electroneutrality in an A-deficient structure, M / M9 order should be coupled with A / vacancy order. At the preparation temperature, this order is, however, destroyed due to a high mobility of A cations. Thus, heterovalent M and M9 cations are fixed in random distribution. Then, disorder in the rigid lattice prevents A / vacancy ordering on cooling for all compounds where M and M9 are different elements. In contrast, for oxide bronzes, where M and M9 are the same element (e.g. Co 41 and Co 31 or Co 21 in A x CoO 2 ), a charge ordering is attained simply by an electron transfer (Fig. 4 illustrates one possible variant, a 2a32b superlattice for KCo 2 O 4 ). This explains the structural difference between bronzes and fixed-valence compounds [30]. Similar explanation has recently been applied to the order / disorder phenomena in Li x (Ni,M)O 2 system [5]. Excepting superlattice effects, other structural data on the P2 family, both published previously and reported here, are in reasonable agreement despite the contradiction about space group. The most interesting result is the simultaneous occupation of the two types of trigonal prism, whose occupancies exhibit regular behaviour with increasing x irrespective of chemical nature of A and M cations: The A(1) site occupancy increases monotonically, whereas the A(2) occupancy goes through a maximum at x50.66, i.e. for sodium lithium titanium oxide (see Table 5). Usually, the A(2) site is less populated owing to a shorter A–M distance (cf. Table 4). Careful examination has shown that the atomic positions reported for K 0.5 CoO 2 [18] and RbScO 2 [20], though based on lower-symmetry groups, fit sites of a higher-symmetry group, P63 /mmc. For

G.V. Shilov et al. / International Journal of Inorganic Materials 2 (2000) 443 – 449

448

Fig. 4. A hypothetical ordered structure of K 0.5 CoO 2 with doubled a parameter, space group P63 /mmc. Shading is used to distinguish between similar but non-equivalent polyhedra: K(1) and K(2) prisms, Co(1) and Co(2) octahedra. To attain local electroneutrality, i.e. bond-valence balance, shaded octahedra (those sharing faces with K(2) prisms) should be occupied by Co 21 , resulting in K(1)K(2)Co 21 Co 41 3 O 8 formula unit.

K 0.72 In 0.72 Sn 0.28 O 2 [16], as well as for K 0.5 CoO 2 [18], all of the observed reflections obey an extinction rule for the c glide plane. Delmas and Werner [16] initially could not refine the structure of K 0.72 In 0.72 Sn 0.28 O 2 both on P63 / mmc and on P-6 m2, and substantial drop of R (from 0.23 to 0.13) was only achieved when In / Sn site was split into two sites with different z coordinates within P-6 m2. However, analogous splitting might well be introduced within space group P63 /mmc. Therefore, space group P63 / mmc seems to be appropriate for all the P2-type compounds. But then a question arises: why was not such a site splitting observed for other P2-type compounds? There may be three variants of answer. (i) The off-centre cation displacement within the Table 5 Occupancies of two trigonal–prismatic sites, A(1) and A(2), in various P2-type A x MO 2 structures x

A

M

A(1)

A(2)

References

0.5 0.66 0.72 0.74 1

K Na K Na Rb

Co Li,Ti In,Sn Co Sc

0.25 0.35 0.49 0.51 1

0.25 0.29 0.23 0.23 0

[18] This work [16] [17] [20,21]

brucite-like layers is a specific feature of K 0.72 In 0.72 Sn 0.28 O 2 , not applicable to other P2-type structures studied. However, this is quite unrealistic, since off-centre displacement is even more probable for Ti 41 than for Sn 41 , being a characteristic feature of d 0 cations in oxygen octahedra [26,31]. (ii) The position splitting found for K 0.72 In 0.72 Sn 0.28 O 2 is simply an artefact due to unfavourable experimental conditions (as little as 32 structure factors measured by powder film technique [16], 18 of which being practically unobservable, and the overall temperature factor being negative). (iii) The octahedral site splitting is real. The most probable reason for it is random occupation of A(2) prisms sharing faces with the octahedra. Then, the A(2)–M repulsion drives the both cations from the centres of corresponding polyhedra along the z axis. In K 0.72 In 0.72 Sn 0.28 O 2 [16], this displacement is most evident owing to high scattering factors of In and Sn and also to their random distribution. In contrast, for Na 0.74 CoO 2 [17] and K 0.5 CoO 2 [18] no Co shift has been found, probably due to ordered arrangement where each Co 21 or Co 31 ion has two neighbouring A(2) ions (see, e.g., Fig. 4). In Na 0.66 Li 0.22 Ti 0.78 O 2 , three local Na(2) prism types can be found: prisms having two neighbouring Li 1 ions, prisms with one Li 1 and one Ti 41 as neighbours, and prisms with two adjacent Ti 41 ions. Assuming random occupation of the octahedra by 0.22Li 1 and 0.78Ti 41 , the fractions of those prisms are calculated to be 0.05, 0.34 and 0.61, respectively. The latter prisms are electrostatically least favourable for Na 1 and therefore should not be occupied. As Na(2) occupancy is 0.29, the expected amount of Ti 41 ions shifted due to Na(2) neighbourhood is as small as 0.24. Assuming an ordered sequence Na–Li–Na–Li–Na– Li . . . along z axis, even smaller fraction of displaced Ti 41 ions, 0.14, is obtained. A slight displacement of such small fraction of Ti (and Na) ions might well be accounted for by the thermal parameter. Indeed, very large U33 for the Na(2) site (see Table 3) may be a result of unbalanced repulsion, where one of the adjacent M ions is Ti 41 and another is Li 1 . However, a U33 value for Ti in the P2-type crystal is quite normal and even lower than that in the O3-type crystal. It, therefore, seems that both (ii) and (iii) explanations are true: the displacement may be real, at least for disordered structures, but small and difficult to detect. There are two more serious questions, since the very existence of the P2 structure seems to violate classical building principles for ionic compounds. The P2 structure, as compared with the O3 structure, provides the same coordination for M ion, the same coordination for O ion, the same coordination number for A ion, the same M–O and A–O bond lengths, and only differs in shorter O–O distances around A ion (a prism instead of an antiprism) resulting in greater repulsion. Then, why do the P2 structures still exist? If, furthermore, the A(2) site is

G.V. Shilov et al. / International Journal of Inorganic Materials 2 (2000) 443 – 449

electrostatically less favourable, as is conventionally assumed [15–17], why is it still occupied? The latter question has never been discussed in the literature, and the former one has received some attention. Electrostatic energy calculations [32] have shown that the energy difference between the P2 and O3 structures decreases with increasing A-cation size and / or M cation electronegativity, nevertheless the O3 structure is always more stable. It has been pointed out later [33], that the P2 structure, due to unhindered thermal motion of A1 , has greater entropy, and this may be the main reason for its stabilization during high-temperature synthesis. Indeed, for RbScO 2 [20,21] and related ‘filled’ compounds, such as CsREO 2 (RE5La–Lu) [34], the P2-type phase is a hightemperature form, the low-temperature one being of the O3 type. However, our annealing experiments failed to alter the P2 structure of Na 0.64 Ni 0.32 Ti 0.68 O 2 [11], at least for dozens of hours at 900–6508C. Moreover, electrochemical or chemical oxidation of the O3 phases, accompanied by A1 ion extraction, often results in their transformation to structures with prismatic A-ion coordination even at room temperature [2,35], where the entropic term is of little significance. Now, a unifying answer to the both above questions can be given. To demonstrate a stability of the prismatic structure with respect to the octahedral one, cation distibution between the two prism types should be accounted for. With only one type of prism occupied [32], the P2 structure is always less stable than the corresponding O3 structure. However, the electrostatic energy can be lowered by partial redistribution of the A cations to the interstitial sites, since some A–A distances then become 1.15a ˚ instead of 2.960 A, ˚ see Table 4), instead of a (e.g. 3.418 A thus decreasing A–A repulsion. This explanation is only applicable provided (i) x is substantially lower than unity, since otherwise interstice would be too close to the occupied positions; (ii) the interstitial cavities are sufficiently large, such as trigonal A(2) prisms of the P2 structure rather than tetrahedra of the O3 structure; (iii) the lattice parameter a is small enough compared with the A cation diameter, since otherwise A–A repulsion would be of little significance. In view of this, stabilisation of the prismatic structures versus octahedral ones at reduced x values (typically 0.5–0.75 [1–3,6–8,11–13,18,32,35]) and with relatively small M cations [7,32,33] becomes understandable.

Acknowledgements The work was supported by the Russian Foundation for Basic Research under the grant No. 97-03-33807a. The authors are also indebted to Doctor I.L. Shukaev for many helpful discussions.

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