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4.1 Introduction

LaF3, is a trifluoride with the tysonite structure. It has been identified as a solid electrolyte exhibiting a very high fluoride ion conductivity at elevated temperatures. Other rare-earth fluorides, e.g. C eF3 and structurally related solid solutions of mixed composition, e.g. LaF3 - SrF2, have also demonstrated similar effects (Nagel and O'Keeffe, 1973). Solid electrolytes are, of course, of great potential technological importance.

Initial interest in these materials was shown over twenty years ago, but it is only in recent years that significant efforts have been made to establish consistent structural and transport data concerning which there has been much dispute. These experimental data have stimulated the defect energy calculations reported in Chapter 5 and the molecular dynamic simulations of Chapter 6.

There have been a number of studies on LaF3, but, unfortunately, they have used different labelling conventions when describing the mobile fluorine species. As shall be seen, for a material showing multi-site behaviour, where there are already differences in interpretation of experimental data, inconsistent terminology can lead to additional problems. The main contributions of this chapter are, therefore, to provide a comprehensive review of the known experimental knowledge of LaF3 to date, and, more importantly, to establish one consistent terminology.

4.2 The Structure of the Rare Earth Fluorides

The rare-earth fluorides have been the subject of several structural investigations which show that some undergo temperature dependent transitions. Dimorphism amongst the heavier trifluorides was first recognised by Zalkin and Templeton (1953). A subsequent high temperature x-ray diffraction study by Thoma and Brunton (1966) on polymorphic transitions in YF3 and the lanthanides identified three structural types: hexagonal tysonite, orthorhombic |5-YF3 (Pnma) and "hexagonal a -Y F 3". The trifluorides of Sm- Lu and YF3 all have the orthorhombic structure at low temperatures, but convert to hexagonal modifications at high temperatures. The group Sm-Ho possess the tysonite structure at high temperatures (the transitions occur over the range 800-1350K) whilst Er-Lu possess the different "hexagonal a- Y F3" structure. This latter structure has since been identified as the a - U 03

structure type (space group C3m1), Sobolev and Fedorov (1973). The early lanthanides La-Nd are not dimorphic and exist only in the tysonite structure. Since this chapter is concerned with LaF3, only the tysonite structure will be discussed further.

4.3 The Crystal Structure of LaF3

Several space groups have been proposed to describe the structure of LaF3, and indeed the question has been controversial. This section first gives a summary of those investigations and then describes in detail the unit cell parameters for two of the most favoured space groups.

Early studies by Oftedal (1929, 1931) suggested the space group P6322 and later P63/mcm where the number of formula units per unit cell (Z) was six in each case. The same group was also used in the analysis of nmr results by Afanasiev et al. (1972) and Goldman and Shen (1966), although suggestions for Z= 1 2 in P63/mcm were also raised from the nmr studies of Sher et al. (1966). Conversely, a smaller elementary cell (a'=a/V3, c'=c) of space group P63/mmc with Z= 2 was also reported by Schlyter (1952) from x-

ray diffraction work. This was, however, thought to be an incorrect assignment because of the failure to observe weak reflections, which provided evidence for the larger cell. Subsequently, much evidence has emerged for two other groups P63cm and P3c1, which both have the larger cell and Z=6.

The hexagonal structure model with space group P63cm was first proposed by de Rango et al. (1966) from x-ray and neutron measurements. This group was also used by Andersson and Proctor (1968). A recent single crystal neutron diffraction study by Gregson et al. (1983) refined data using both P63cm and P3c1 and favoured the P63cm group. P63cm is, however, non-centrosymmetric and would, therefore, be expected to show a piezoelectric effect, for which there has been no evidence to date. Gregson and co-workers, however, suggested that this effect could easily escape detection because of the room temperature conductivity shown by this material.

Single crystal x-ray diffraction studies of Mansmann (1965) and Zalkin et al. (1966) were interpreted using the trigonal space group P3c1, a result supported by the Raman measurements of Bauman and Porto (1967). Structure refinements of neutron powder data by Cheetham et al. (1976) favoured the centrosymmetric P3c1 over rival group P63cm on the grounds that fewer parameters were required to gain a comparable fit. Their decision was also swayed by the indirect evidence of the absence of pyro- and piezoelectric effects. The latest refinements by Maximov and Schulz (1985) and Zalkin and Templeton (1985) have also favoured the P3c1 structure. Both of these papers showed that LaF3 crystals have a strong tendency to twin, with c as the twin axis. They demonstrated that experiments using twinned crystals would lead to incorrect symmetry assignments, such as P6 3cm. When twinning was taken into account, however, refinements gave better fits for P3c1. As further evidence in support of their claim, Zalkin and Templeton (1985) cited the infrared spectroscopic study of Jones and Satten

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(1966). This technique, which is unaffected by twinning, gave results which could be reconciled with P3c1 site symmetries, but not with those of P63C171.

To summarise, therefore, both P63CIT1 and P3c1 are possible space groups, with the weight of recent evidence favouring the latter. Both have, therefore, been used in defect calculations reported in Chapter 5. The crystal log raphic parameters for both groups are summarised in Table 4.1.

These two structures are very similar, but there are significant differences. Each structure has the Zalkin et al. (1966) cell parameters a=7.185A, c = 7 .3 5 lA a n d 6 formula units per unit cell. A major difference, however, is the number of different types of F_ site within each cell. LaF3 was one of the first crystals identified as having inequivalent lattice sites for the fluoride ion, giving rise to multi-site defect behavioural properties. For P63cm there are 4 such inequivalent fluoride ion sites (F1, F2, F3, F4) in the ratio 2:4:6:6, whilst for P3c1 there are only 3 (F1, F2, F3) in the ratio 2:4:12.

For modelling purposes, the F3/F4 sites in P63cm are classed as the same, as would be the case for a P3c1 based system. Hence, for each unit cell, the fluorines are said to reside on three sub-lattices referred to as a, p and y in the ratio 12:4:2. The La3+ cations are crystallographically equivalent and form a layered structure with the layers in the hexagonal (a- b) plane of the crystal. These layers have regular spaces through which p and y site fluorines, both situated in channels parallel to the c axis, can move in the c direction perpendicular to the (a-b) plane. The model can be simplified further according to Goldman and Shen (1966), who suggested that p and y site fluorines could be taken as being very similar. Hence the structure reduces to two sub-lattices, A and B. A is identified with the (6+6) a site fluorines which are constrained between La3+ layers and have to move more or less transversely in the (a-b) plane, whilst B is the combined (4+2) p and y sites. Thus the ratio of sites between sub-lattices A and B is 2:1. Figure 4.1 illustrates the LaF3 structure in the light of this classification.

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Another feature of note concerning the two structures is the similarity of interatomic distances as listed in T a ble 4.2. There is, however, a difference in the coordination sphere of the lanthanum atom for each group. In P6 3cm, La3+ is surrounded by 10 fluorines whereas in P3c1 the coordination number is 11 and is referred to as a ’9+2' arrangement where 2 of the fluorines are more distant from an La3+ ion than the rest (at 3.002 A). The closest distance to this in P63cm is an F3 fluorine at 3.06 A, but this forms part of the coordination sphere of a different lanthanum atom. Figures 4.2 and 4.3 show views of the lanthanum coordination spheres for each space group.

Although certain differences have been mentioned, it is important to note, that with regard to the aims of this thesis, the two structures are very similar and any differences should not have a significant effect on the defect energetics being calculated. This assumption has been tested and is reported in Chapter 5.

4.4 The Tran sport Properties of LaF3

LaF3 is a good ionic conductor even at ambient temperatures with conductivities of approximately 10'7£2'1cnrr1 at room temperature (Sher et al., 1966) to 10_2Q ’1cnrr1 at 1000K (Jaroszkiewicz and Strange, 1980). These observations raise three main questions. The first concerns the nature of disorder creating the charge carrying defects responsible for the high conductivity noted. The second asks whether the charge transport is due to mobility on the A or B sub-lattices, or on both, and the third concerns the mechanisms for the preferred transport pathways.

19Fnmr data have shown the mobile species to be the fluoride ion. However, the major source of disorder could be either anion Frenkel pairs or Schottky quartets. The latter model has been supported by the dilatation work of Sher et al. (1966). This early work on thermal expansion measurements indicated that bulk expansion was significantly greater than

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the x-ray expansion for the unit cell. This was taken as evidence that