superprotonic transitions in the M2(HSO4)(H2PO4) family of compounds. From this it was established that the average cation to tetrahedral anion, <M-X>, distance surfaces as the best measure of a MHXO4 compound’s probability for undergoing a supeprotonic transition, agreeing with the generally observed behavior of the compounds. The <X-X>
distance was found to be much less useful as a predictive measure of a superprotonic transition, contrary to the proposed hypothesis that the main effect of increased cation size was to create larger X-X distances and thereby allow freer rotations of the tetrahedra.
Having identified M-X distances as such a critical crystal-chemical measure, the question is then what exactly does this distance do to the interactions of the atoms so as to favor the presence of superprotonic transitions. In the present study, the <M-X>
distance was modified by varying the radius of the cations, but as can be seen in the MHSO4/MHSeO4 systems, varying the size of the tetrahedra has an equal, if not greater, effect on superprotonic transitions, Table 3.1. As stated before, this anion size effect contradicts the assumption that bigger X-X distances are the critical measure for transitions, as bigger tetrahedra in an otherwise unchanged structure should cause more steric hindrances between the oxygen atoms of the tetrahedra. Instead, increasing the size of a tetrahedron, which is equivalent to increasing the <X-O> distance, seems to decrease these inhibiting interactions. For this reason, it is sensible to assume that the increased X- O distances allow for a greater degree of freedom in the oxygen’s position as a
tetrahedron rotates/librates. Similarly, a larger cation radius equates to proportionally larger <M-O> distances, creating “floppier” MOx polyhedra. An increase in the <M-X>
distance therefore causes both the XO4 tetrahedra and MOx polyhedra to loosen up, which can be seen experimentally in the increasing thermal parameters of the oxygen atoms with increasing <M-O> distances, Figure 3.14. The good match between the two parameters is particularly pleasing since this comparison includes all the compounds presented in this work, plus all the published compounds from the MH2XO4 and mixed
MHYO4-MH2XO4 family of compounds (M = alkali metals and NH4; X = P, As; Y = S, Se).
3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 1
2 3 4 5 6
NH4HSeO4
R
2= 0.68
<Biso>
Oxygen(Angstroms
2)
<M-X> (Angstroms) Compounds:
without with
Superprotonic Transitions
Figure 3.14 Average thermal parameters of the oxygen atoms versus <M-X> distances:
the two parameters generally scale with each other. The dashed lines denotes the cutoff between the with and without transition regions of the graph. It appears that either <M- X> distances larger than ~ 4.1 Å and/or <Biso>Oxygen parameters greater than ~ 3.0 Å2 in a room temperature compound are likely to produce a superprotonic transition. Note that one might not predict the NH4HSeO4 compound to transform from these criterion, but its transition is probably facilitated by the presence of the highly directional ammonium ions. Crystallographic data was taken from various sources.
The <M-X> distance is then a measure of the overall mobility of the oxygen atoms, an increase in which should lower any barriers to tetrahedral reorientations.
Specifically, the oxygen atoms would have more flexibility to avoid close contact with the electrons of the cations by bending their respective M-O and X-O bonds. With respect to the cation size effect, this flexibility in the M-O bonds could be restated in terms of the higher polarizability of the cations as their radius increases, Figure 3.15. In this case, it would be the electrons of the cations that are adjusting their positions, resulting in the oxygen atoms having access to positions not available to them with smaller cations. Such a phenomenon also explains the observed increase in room temperature protonic
conduction of the M2(HSO4)(H2PO4) compounds as the cation radius is enlarged (section 3.3.3), bigger movements of the oxygen atoms facilitating the formation and migration of defects. Larger M-X distances then assist both room temperature conduction and
superprotonic transitions by enhancing the mobility of the oxygen atoms and thereby reducing barriers to structural rearrangements.
1.3 1.4 1.5 1.6 1.7 1.8
0.0 0.5 1.0 1.5 2.0 2.5 3.0
3.5 Cs
Rb K
Na
R2 = 0.97
Electric Dipole Polarizabilities (Angstroms3 )
<Rcation> (Angstroms)
Figure 3.15 Cation radius versus polarizablity shows a nearly linear relationship between the two parameters. Larger cations therefore lead to “floppier” MOx polyhedra.
Polarization data taken from calculated electric dipole polarizabilities of M+1 cations126. This reduction of the barriers to tetrahedral reorientations can be visualized energetically by considering that longer M-X distances will lead to weaker M-O and X-O bonds. The potential wells in which the oxygen atoms reside will therefore become increasingly shallow as M-X distances are lengthened. For such potentials, oxygen atoms will have a larger range of motion and smaller transition energies when compared to the deeper potential wells associated with smaller M-X distances, Figure 3.16. The
transitions under consideration here are distortions from the optimal arrangement of the oxygen atoms due to the formation of defects and/or XO4 reorientations. This energetic explanation of the cation/anion size effect then further illuminates the correlation between the magnitude of a room temperature phase’s protonic conductivity and its probability of having a superprotonic transition.
b) a)
D
1> D
2r
1> r
2∆
E
1<
∆E
2∆E2
∆E1
r2 r1
x
x
D2 D1
Energy
Distance
Figure 3.16 Schematic representation of the potential wells for oxygen atoms with a) longer and b) shorter M-O/X-O distances. A shallow potential well associated with a long M-X distance results in a large range of motion for an oxygen atom, but small transition energy necessary to reach a distance outside of this range. In contrast, a shorter M-X distance will result in the oxygen atom residing in a deeper well with a smaller range of motion and bigger transition energy.
As all the above interpretations of the cation/anion size effect are quite general in nature, larger M-X distances should facilitate tetrahedral reorientations, and thereby superprotonic transitions, in a similarly general manner. However, this effect will be most evident for superprotonic transitions in which almost freely rotating tetrahedra are
required. For the superprotonic transitions of the MHXO4 compounds, the <M-X>
distance is then a good chemical-crystal measure with which to predict the presence of
superprotonic transitions, the known superprotonic phases for this family of compounds having highly disordered tetrahedra. For other compounds, the anion/cation size effect should still apply, but may not be the determining factor in the presence or absence of a transition, other structural effects having a more dominant role (i.e., the M3H(XO4) family of compounds). Even in such compounds, the results of these studies should help reveal exactly what is the critical parameter, as any cation/anion size effects can be examined in the manner shown here and removed from consideration if they are found not to fully describe the situation. Moreover, as the stoichiometry of a compound can often be used to guess its possible superprotonic structure (which in turn governs how the tetrahedra will reorient), the search for new superprotonic conducting solid acids can be narrowed to those most likely to have a transformation using the criteria described in this chapter. This focused attention will hopefully speed up the process of synthesizing novel solid acids with properties ideal for application.