Simulation of the Diffuse Scattering

The average structure of Sr0.5Ba0.5Si2O2N2:Eu2+ comprises disordered metal atom positions. Although it yields a convincing fit of the observed intensities, the model offers no information about the real structure. However, the asymmetric intensity maxima excluded during refinement result from real-structure effects. The profile of these broadened maxima is typical for diffuse scattering from planar defects. For layered structures, the presence of planar defects is due to the fact that perfect two-dimensional periodicity can be combined with different kinds of polytypic modifications with identical layer distances and almost the same lattice energy.[41]

For the simulation of diffuse intensities, the triclinic unit cell was transformed into a setting with monoclinic metrics using the matrix (1 0 0, -0.24817 1 -0.00238, 0 0 1), thus the new basis vector b’ is perpendicular to the layers. The vectors a and c which are parallel to the silicate layers were kept unchanged. The absolute value of b’ corresponds to the y-component of the original b axis. The unit cell volume is thus fixed to the refined value. In order to describe the real structure, all permutations of the metal atom sets A and B (equals shifted A) combined with silicate layers, both “normal” and rotated by 180° around [010]* (due to twinning by a twofold axis), were taken into account. Additionally, two different stacking vectors 0.24817 1 0.00238 or -0.24817 1 -0.00238 were employed, they correspond to twinning by a mirror operation. This leads to a complex model with 23 = 8 different possibilities combining layers to a real structure (see Table 3).

Table 3. Characteristics of all (23 _{= 8) possible layer transitions which have been taken into account: shift,} rotation and reflection (+ = yes; - = no).

Stacking

mode shifted metal position, i.e. anti- phase boundary

180 °rotation

(around [010]*) Stacking along -0.24817 1 -0.00238, i.e. mirror operation

Probability in final model (in %) 1 - - - 50.45 2 + - - 31.00 3 - - + 8.00 4 + - + 10.00 5 + + - 0.08 6 - + - 0.03 7 + + + 0.12 8 - + + 0.32 Σ 100

With related stacking probabilities between defined layers (metal atoms combined with silicate layers) a 3D-structure can be built up. To optimize the fit of experimental data, transition probabilities (sum: 100 %) between the different types of layers were varied arbitrarily, taking care not to change Bragg intensities of the average structure. Instrumental broadening was taken into account by a pseudo-Voigt function (u = 0.15; v = -0.02; w = 0.015; σ = 0.4) to offer a reasonable fit at all diffraction angles. Whenever a rotated silicate layer follows a non-rotated one, a twin-like boundary is created. If rotated layers are stacked along the ideal stacking vector (see stacking mode 5 and 6 in Table 3) an alternative structure is built up based on pseudosymmetry. In order to simulate SAED patterns, layers corresponding to rotational twinning (in a narrower sense; see stacking mode 7 and 8 in Table 3) are important although they are not essential for powder XRD simulations as it turned out that their frequency is low and thus the intensities from rotation-twin domains

superimpose incoherently. Non-rotated layers, stacked along -0.24817 1 -0.00238, describe mirror twinning (see stacking mode 3 and 4 in Table 3). Taking into account typical rotation- twin domain sizes of about 100 nm as reported for SrSi2O2N2, the stacking probabilities were chosen in such a way (0.44 %) that rotation-twin boundaries occur roughly every hundred nm. Rotational twinning in the real structure is illustrated in Figure 7 (see stacking mode 8 in Table 3): A silicate layer with metal atoms of set A (black unit cell) is followed by an identical one (stacking vector of the idealized structure), both being part of a domain which is followed by another two (darker shading, with corresponding metal atoms gray), generated from the first layers by 180° rotation around [010]* (indicated by a gray unit cell). The unit- cell orientation is changed because of the triclinic metrics. At the twin boundary a rotated silicate layer follows a non-rotated one. Both cation sets of the average structure are shown at the rotation-twin boundary, but in the real structure only one set is present. Both atom sets yield identical models for the described boundary.

Figure 7. Side view (along [001]) on a sequence of silicate layers with corresponding metal atoms (light gray and gray spheres for set A and B, respectively); bottom: two silicate layers with set A metal atom positions (black unit cell edges); top: layers rotated by 180° around [010]* (unit cell edges gray, metal atoms gray); due to the pseudo-symmetry of the O atom positions (see Figure. 8), rotated and non-rotated layers can coordinate both cation sets in a similar way, which corresponds to the local structure of a twin boundary. Overlap of both orientations (average structure) leads to the superposition of the two sets of metal atom positions.

Within such twin domains, most layers correspond to the ideal stacking sequence, (50.45 %; see Table 3) while other layers contain the alternative metal atom set without a change of the

stacking vector (31.00 %; see Table 3). In both cases, the unit-cell orientation and also the silicate layer sequence remain unchanged, but metal atoms are either placed on “ideal” positions (set A, as in EuSi2O2N2) or, less likely, placed on alternative positions (set B). This means that small anti-phase domains (translation vector approx. 0.5 0 0.5, see Figure 8) of few nm of size are built up.

Figure 8. Top view (along [010]*) on a silicate layer of Sr0.5Ba0.5Si2O2N2 (doped with 2 mol% Eu; SiON3 polyhedra, gray; O atoms small white spheres; N atoms small black spheres) with corresponding Sr/Ba atoms (set A white spheres; set B gray spheres). The two sets of metal atom positions are shown in the upper left and lower right parts, respectively, overlapping in the central part of the figure. The silicate layer is built up of condensed zweier single chains (one of them is highlighted by darker tetrahedra) with “zig-zag” conformation (indicated by solid black arrows). Anti-phase boundaries are formed by displacing one set of metal atoms by one translation period of the single chains, corresponding to a shift from set A to set B, or vice versa (dashed arrows), this shift maps the silicate layer onto itself (translational symmetry of the silicate substructure).

Apparently, the mixed occupation of the cation position also leads to a higher degree of stacking disorder. The displacement equals one translation period of the condensed single chains building up the silicate layer. In Figure 8 this is shown by mapping set A metal positions onto set B when moving the structure by one translation period of the silicate layer. The intensity weakening of reflections in Figure 2 corresponds to approaching the B-centered structure that results in case of equal probabilities for both atom sets.

As a consequence, anti-phase boundaries seem to be energetically more favorable than twin boundaries. With this complex model, mainly containing small anti-phase domains within larger twin domains, the PXRD pattern could be reproduced very well (see Figure 9).

Figure 9. Experimental powder pattern of a sample of Sr0.5Ba0.5Si2O2N2:Eu2+ (top, manual background correction) and a simulation based on the final real-structure model (bottom). Reflections of the impurity phase α-Si3N4 are labeled by asterisks.

In general, both anti-phase boundaries as well as twin boundaries lead to diffuse intensities and Bragg intensity weakening. However, both possibilities can be clearly distinguished. As the silicate layers have no rotational symmetry along [010]*, rotation twinning leads to a change of the average structure in the case of small twin domains and thus to a significant change of Bragg intensities. Since powder methods, in general, average over the whole sample whereas X-ray methods average only over coherently scattering volumes, the averaging present in the structure model is slightly biased as not all crystallites exhibit the same diffraction patterns as shown by SAED (see below). However, the convincing fit of the experimental data indicates that the majority of the crystallites are very similar and they are well described by the model discussed above.