“…The superspace group (SSG) was taken from a study of comparable n = 4 materials (e.g., Sr 2 Nb 2 O 7 ) where there is a similar modulation observed in the a axis. [1,2] Although these n = 4 analogs have a modulation vector of q ≈ (0.5, 0, 0) and is similar to the doubling of the a axis in BaMnF 4 (A2 1 am space group setting), reported by Hidaka; [21] it is important to note that due to the alternate space group setting the incommensuration in BaMnF 4 lies along the polar axis, but in the n = 4 oxides the incommensuration is orthogonal to the polarization. Given the similarities between the reported modulations in A 2 B 2 O 7 ferroelectrics and the candidate modulation vectors determined from TEM here, a modulation vector of approximately q = (0.5, 0, 0) was used as an initial value in refinements of data at 483 K. This resulted in a final value of q = (0.456, 0, 0) for LaTaO 4 at 483 K. Refining the PND data using the Cmc2 1 (α00)0s0 SSG, with a maximum satellite index of 3, gave a satisfactory fit of all reflections, with an overall χ 2 = 2.57 (R wp = 5.6%) across two HRPD detector banks ( Figure 5).…”