Structure Refinement of KBT End Member

The KBT crystals by contrast to the BFO crystals were not available as single phase pure crystals. It was determined by crushing a selection of these crystals into a fine powder and using powder diffraction that KBT single crystals were likely present amongst the mixed crystals and indeed seemed to be the main component of the powder, but there were also other phases present. It was important to determine that the samples chosen were actually phase pure KBT before much time was invested into measuring or analysing them, adding an additional step to the selection when compared with the BFO and BFO-KBT crystals. The first part of this was to involve the use of birefringence in the crystal selection, looking for single birefringent crystals in the clusters of crystals observed. The crystals thus obtained were extremely small, suitable for single crystal diffraction but not for experiments with a birefringence microscope.

The most likely crystals were then measured in pre-experiments on the diffractometer to determine the lattice parameters. KBT is reported as having P4mmtetragonal structure, with lattice parameters a= 3.9247(0)˚A and

c = 3.9844(3)˚A [13] or a = 3.933(3)˚A and c = 3.975(4)˚A [14], but was found in Chapter 3 to have lattice parameters ora= 3.9184(2)˚A andc= 4.0146(2)˚A , quite different from the measurements quoted above. In addition to this, KBT was found to have a mixed phase of tetragonalP4mmand monoclinicP1m1. Due to the small tetragonal and monoclinic deviation from cubic, the simplest method was to find near-cubic crystals and then observe how well they would fit with the expected KBT cell. An example of this type of crystal was found, and measured in the same way

as the BFO crystal mentioned in the prior section had been.

An Rintfactor of 5.9% confirmed that the suggested tetragonal structure was a reasonable fit with the data as far as the reduction and refinalisation processes in CRYSALIS PRO were concerned, including absorption corrections.

(a)(100) (b)(001)

Figure 5.3: Residual electron density Fourier map of a room temperature sample of unmixed KBT. It can be seen that there is a lot of residual electron density both above and below the bismuth position. The red represents a residual electron density of 4 electrons ˚A−3 _and

the blue represents a residual electron density of 8 electrons ˚A−3_{, while the green represents}

a hole of -3 electrons ˚A−3_.

Refining this output structure with SHELXL was attempted, but it was not possible to get the R1 factor <14%, which implied that the refinement would not be resolved by this method. It is hypothesised that this was because of the mixed Bi-K atoms on the A-site, which adds an inherent level of disorder to the system. Figure 5.3 shows the residual electron density of the sample in MARCHING CUBES ELD[10]. The highest residual density was found to be around 9 electrons ˚A−3, which was around the oxygen position on the [001] face and the deepest hole was found to be around -5 electrons ˚A−3 around the A-site and B-site, distributed along the z-axis.

Unlike in the BFO crystal, this disorder was not decreased significantly by reducing the temperature to 200K. This can be seen in Figure 5.4, and from Table 5.3 comparing the room temperature and low temperature refinements. In the lower temperature KBT measurement, the same scale was used as in the room temperature version, meaning that while the residual electron density map seems more complicated, the highest residual electron densities in blue are diminished with

Table 5.3: KBT end member SHELXL refinement parameters tabulated. Temperature (K) 293 200 Lattice Parameters a (˚A) 3.9213(4) 3.9288(8) c (˚A) 3.9960(8) 3.960(1) Quality Parameters Rint 6.70 8.10 R1 14.32 15.44 GoF 3.17 4.964

Highest Peak (electrons ˚A−3) 9.45 9.55 Deepest Hole (electrons ˚A−3_{) -5.79 -4.67}

Redundancy 7.1 26.5 Completeness 100% (0.8) 100% (0.8) Refined Parameters 14 14 A x=y= 0, z= -0.002(2) -0.004(2) Ueq/Beq (˚A2_{) 0.073(5) 0.043(3)} U11=U22 0.057(3) 0.035(2) U33 0.011(1) 0.060(6) U23=U13=U12 0 0 B x=y= 0, z= 0.563(3) 0.507(2) Ueq/Beq (˚A2_{) 0.017(2) 0.010(1)} U11=U22 0.015(2) 0.010(2) U33 0.020(4) 0.0122(3) U23=U13=U12 0 0 O1 x 0.5 0.5 y 0 0 z 0.59(1) 0.61(1) Ueq/Beq (˚A2_{) 0.041(8) 0.027(7)} U11 0.02(1) 0.02(1) U22 0.02(1) 0.004(9) U33 0.08(2) 0.05(2) U23=U13=U12 0 0 O2 x=y= 0.5, z= 0.14(5) 0.12(2) Ueq/Beq (˚A2_{) 1.1(3) 0.17(3)}

(a)(100) (b)(001)

Figure 5.4: Residual electron density Fourier map of a 200K sample of unmixed KBT. It can be seen that there is a lot of residual electron density both above and below the bismuth position. The red represents a residual electron density of 4 electrons ˚A−3_{and the}

blue represents a residual electron density of 8 electrons ˚A−3_{, while the green represents a}

hole of -3 electrons ˚A−3_.

lower temperature. The R-factors between the two are very similar though, as there is still very high disagreement between the observed and calculated models. In the 200K residual electron density map, there is more distribution along the x-axis and y-axis, but the majority can still be seen to be along the z-axis, with the highest residual density being in a similar position. The highest density and deepest hole were of comparable sizes to the room temperature measurement.

In summary, the refinement of the KBT crystals as a single tetragonal phase was not successful. With the model proposed in Section 3.4.1 the poorness of the simple fit was expected, as it doesn’t take account of the significant volume of monoclinic phase found to exist in the powder sample, which is likely also present in the single crystal. The tabulated data from these measurements is included in Section 5.4.