The structure of A2B2O7 (or more specifically, A2B2O6O’) pyrochlore,1–4
which adopts the space group, is closely related to the fluorite
structure, AX2 (typically X = halogen or O), shown in Figure 5.1, which
adopts the space group. A pyrochlore can be formed by the ordered
removal of 1/8th
of the O atoms from the fluorite structure, leading to two different cation sites, an eight-coordinate A site, occupied by 2+ or 3+ species such as Cd2+, Y3+, La3+ or Sc3+, and a six-coordinate B site, where smaller, 4+
or 5+ species, including Ti4+, Sn4+, Zr4+, Hf4+ or Nb5+ reside. Using the Wyckoff
notation,5,6
where A is placed at the origin (termed origin choice two), the A and B cations occupy the 16c (0, 0, 0) and 16d (1/2, 1/2, 1/2) positions, respectively, with 16 denting the number of these sites in the pyrochlore unit cell. This produces three crystallographically-unique oxygen positions, with only the 8a (1/8, 1/8, 1/8) and the 48f (x48f, 1/8, 1/8) occupied, accounting
for one and six O in the formula units, respectively, leaving the 8b (3/8, 3/8, 3/8) site vacant. The creation of the oxygen vacancy at this site allows the O48f positions to vary, moving from its position in the ideal fluorite structure
(3/8, 1/8, 1/8) towards the 8b vacancy. As shown in Figure 5.2, in the pyrochlore structure the A site cation has scalenohedral geometry, being surrounded by six O48f and two O8a anions, with O8a typically closer. The B
site cation is surrounded by six O48f anions, giving trigonal prismatic
coordination. The O occupying the 8a (O1) site, is surrounded by four A cations whereas the O occupying the 48f (O2) site is coordinated by two A and two B cations, with both O sites adopting tetrahedral coordination. In the literature the nomenclature of O1 and O2 can sometimes be reversed, such that O1 is 48f and O2 is 8a, however, in this thesis the crystallographic
Fd3m
Figure 5.1: Structure of a 2 × 2 × 2 supercell of the fluorite CaF2,7 with expansions of the Ca and F local environments also shown.
Figure 5.2: (a) Structure of a typical A2B2O7 pyrochlore, formed by the ordered removal of 1/8th of the oxygen anions from a fluorite structure, with expansions of the local environments of the 16c, 16d, 8a and 48f sites. (b) Expansions of the NNN environments for the A and B site cations.
notation used by Brisse and Knop has been followed.8 It should be noted that
in other literature, the B site is placed at the origin, in which case the Wyckoff positions of the A16c and B16d cations, and the occupied O8a and vacant O8b
sites are swapped, leading to A16d, B16c, O8b and O8a, the last being vacant.
The preferential formation of a pyrochlore structure is though to be linked to the relative ratio of the ionic radii for the A and B cations (rA/rB).4 If this ratio
lies between 1.46-1.78, a pyrochlore structure is favourable, whereas outside of this range, alternative phases are formed. If rA/rB is below 1.46 a defect
fluorite structure (see Section 5.1.2) is thought to be favoured, whereas above
1.78, the movement of the O48f anion alone can no longer compensate for the
large size discrepancy, forcing other atoms to also move. This leads to the formation of a monoclinic layered perovskite-related structure with space
group , a phase only formed for a relatively small number of materials,
including Ca2Nb2O7,9 Sr2Nb2O710 and La2Ti2O7,11,12 the latter of which has
previously been studied using solid-state NMR spectroscopy,13 and more
recently by NMR crystallography.14
5.1.2 Defect fluorites
When the rA/rB cation ratio of A2B2O7 systems falls below 1.46, the
formation of a defect fluorite structure (formally A4O7), with space group
, is favoured. This disordered structure is adopted by a series of materials, including La2Ce2O7,15 and Y2Hf2O7,16,17 as well as several zirconates,
M2Zr2O7, where M = Gd, Ho, Er or Y.18–20 The defect fluorite structure is
closely related to that of fluorite (AX2) discussed above, but with O atoms
distributed randomly on 7/8th
of the anion sites, i.e., all anion sites have a formal fractional occupancy of 0.875. This is in contrast to the pyrochlore structure, where all the vacancies are ordered on a single type of anion site. In addition, due to the similarity in size between the A and B cations (which leads to a reduction in the preference for a type of cation to have a specific O coordination, i.e., A and B cations being exclusively eight- and six-coordinate, respectively), there is also mixing of the two cations, with the average cation
P21
Figure 5.3: Structure of a typical A4O7 defect fluorite material, where 1/8th of all anion sites will be vacant. An expansion of the cation and anion coordination environments is also shown, where 1/8th of the O surrounding the cation site are vacant and where the four sites surrounding O can be occupied by either A or B.
coordination number remaining seven, as found in the pyrochlore structure.