3.1.1. Ba(IO3)OH Crystal Structure
A structural model of new iodate was determined using the direct methods with SHELXS [
9]. Suggested space group C2 did not give a positive result and did not allow solving of the structure. The analysis of the reflection absence allowed three possible space groups, namely, C2/m, C2 and Cm. The centrosymmetric group C2/m was not confirmed in the structure solving and did not agree also with the SHG signal. The third acentric group, Cm, was true (
Table 1) and allowed four heavy atoms to be identified, two Ba-atoms and two I-atoms, in accordance with the composition of crystals. The remaining O sites were found from difference Fourier synthesis and then introduced into the model, which significantly reduced the R-factor. Both I-atoms were coordinated umbrella-like by O1, O2, O4 and O5 with the distances typical for the IO
3-group. The O3 atom was identified as oxygen of the hydroxyl group based on Pauling’s balance of valences because it participates only in the coordination of Ba-atoms. The resulting chemical formula is Ba(IO
3)OH, Z = 4. Absorption assessment showed the need to take this into account, which was done using numerical absorption correction based on Gaussian integration over a multifaceted crystal model [
10].
The refinement of the model in SHELXL in isotropic approximation of atomic displacement parameters gave R ~ 9%. According to the Flack parameter x = 0.33, twinning in the crystal was supposed and twin-mirror mz was suggested: it corresponded to the layered nature of the structure—cleavage at (001). Introduction of a twin by matrix 100/010/00-1 improved temperature displacement parameters, interatomic distances and lowered the R-factor to ~6%; the twin component was 0.3.
The final structural model was refined using the least squares procedure in anisotropic approximation of the atomic displacements for heavy cations and isotropic for oxygens with the refinement of the weighting scheme using SHELXL [
9]. Atomic coordinates and selected bonds are presented in
Table 2 and
Table 3. Illustrations were produced using ATOMS [
11] and CORELDRAW programs.
3.1.2. Comparison of Ba(IO3)OH and Bi(IO3)O Structures Using OD-Approach
Among Ba-iodates, two compounds are known: Ba(IO
3)
2 [
12] and Ba(IO
3)
2H
2O [
13]. Recently, (Pb,Ba)(IO
3)
2 was investigated [
14]. All the structures demonstrate chess-order distribution of large cations and isolated (IO
3) groups, which means they are fundamentally different from the new iodate. The new Ba(IO
3)OH structure is composed of two types of layers joined in a triple. The central layer contains Ba-ions and OH-groups. Its optimal description is anion-centered with the anionic OH-group coordinated tetrahedrally by four Ba-cations. The tetrahedra are connected by edges in a layer with the formula {Ba(OH)}
+. A similar layer was found in perite PbBiO
2Cl [
15] and seeligerite [
16] minerals. Isolated (IO
3)
− umbrella-like groups form their own second “layers” {(IO
3)}
− on both sides of the described first layer. Such an arrangement is typical for mica and other layered minerals; see, for example,
Figure 1a,b. It shows the perfect cleavage of crystals described above.
In accordance with the topology-symmetry analysis, every layer has its own local symmetry, which may differ from each other and from the whole structure. The central layer denoted as L0 possess tetragonal space group
P4/nmm, significantly higher than the structure space group
Cm; symmetry elements are given in
Figure 2 in
ab projection.
Iodate “layer” L1 and L1’ have symmetry corresponded to
C1m1, equal to the space group of the structure. Using principles of OD theory [
4], groupoid of symmetry is:
L0 | L1 |
{Ba(OH)}+ | {(IO3)}− |
λ PO, ρ P(4/n)mm | λ PO, τ C1m(1) |
σ PO, ρ [0, 21y 0] |
That means, every type of layer has its own chemical formula and possesses its own local λ PO described by the space group of symmetry, which is valid as a pseudo-symmetry group. A space group is used here because the sliding in symmetry elements is in the layer and as such it actually corresponds to the layer group; parenthesis display the direction of the alternation of the layers. The central layer L0 is non-polar in the direction of alternation along the
c-axis, which is denoted by λ PO, ρ. The second layer L1 possesses symmetry
C1
m1 and is polar along the
c-axis and the
a-axis too; polarity along the alternation of the layers (
c-axis) is denoted by λ PO, τ notation. Multiplication of the L1 layer around L0 to the L1′ into the triple is realized by the 2
1y axis—the axial subgroup of the
P4/nmm group, shown in
Figure 3a in side projection with the horizontal axes 4 and −4, lying in projection, thus the 2
1y axis is running perpendicular to the projection. Such configuration corresponds to category I of structures with >1 type of layers and with the non-polar multiplication of one type of polar L1 and one type of non-polar L0 layer (τ,ρ). Thus, the triple L1-L0-L1′ dipole moments of L1, L1′ layers with iodate umbrella-like groups are located above and below the central none-polar L0 and are directed in the opposite manner, practically compensating for each other. This analysis explains the weak SHG signal.
One of the best nonlinear optical crystals, BiO(IO
3) [
1], has a similar chemical formula to the new iodate, Ba(OH)(IO
3). Let us compare both of these crystal structures. Despite different formulas and especially properties, they have many common features. The central layer contains Bi and O instead of Ba and OH. It can be described as composed of anion-centered tetrahedra with four Bi-atoms around the central O atom. IO
3-umbrella-like groups are located above and below the central layer L0 forming analogues to Ba-iodate “layers”. BiO(IO
3) structure is given in
bc-projection (
Figure 3b) in accordance with the choice of axes in the X-ray experiment (
a,b,c-axes in Ba(IO
3)OH correspond to
c,a,b-axes in BiO(IO
3)). The symmetry of the central layer L0 in Bi-iodate is equal to the symmetry of the layer L0 in Ba-iodate
P4/nmm. In Bi-compound the iodate layers L1, L1′ are slightly distorted and do not have a mirror plane (only glide-plane), in contrast to the Ba-compound, but are very similar, having polarity along the layer alternation, τ and inside the layer. However, multiplication of iodate layers L1, L1′ above and below the central L0 layer in both iodates are principally different. All the dipole moments of umbrella-like groups in Bi-iodate are oriented almost identically forming a polar 2
1 axis of the structure (
Pca2
1). That means, multiplication of the L1 layer to L1′ in the triple is made by another 2
1 axis of the tetragonal group which is perpendicular to the first, being parallel to the
c-axis [
1], equal to the
a-axis in Ba-iodate. The groupoid of symmetry is principally the same but is added by new σ-PO.
If we compare both structures avoiding different settings, in Ba-iodate L1, L1′ layers multiplication happens via the 2
1 axis perpendicular to the projection, and in Bi-iodate it is parallel; both directions belong to the equal
a,b-axis of the tetragonal group of the L0 layer; thus, both may act equally in the multiplication of layers. A common groupoid can be written as
L0 | L1 |
{Ba(OH)}+ or {BiO}+ | {(IO3)}− |
λ PO, ρ P(4/n)mm λ PO, τ C1m(1) or P1a (1) |
σ PO, ρ [21y || 21x] |
Symmetry operations explain strong SHG in Bi-iodate and very small SHG in Ba-iodate, because dipole moments are oriented opposite each other (Ba-iodate) or almost identically along the polar axis (Bi-iodate) (
Figure 3a,b). Two structural variants are so-called MDO polytypes with equal layer alternations or equal σ PO.
It is possible to assume existence of such members of a family, in which a combination of layers alternation will be presented as 21y, 21x, 21y, 21x,21y, 21x… or 21y, 21y, 21x, 21y, 21y, 21x… or in another order. In the absence of a regular alternation of σ PO, disordered structures will appear.
This brings up the question: what determines polar or non-polar iodate “layer’s” L1, L1′ alternation? It is possible to assume that heavy atoms play an important role. In the case of the significantly larger Ba2+ -ion without asymmetry (absence of lone pair), we detect higher symmetry, while in the case of smaller asymmetric Bi3+ -ion with a lone pair, a more asymmetric structure is realized.