Refinements were performed using the GSAS suite of programs.  

Structural model of parent K-L used for refinement was taken from ref: Barrer, R.M. and Villiger, H. Z. Kristallogr., 128, 352-370 (1969) - Inorganic Crystal Structure Database identifier: ICSD 18099

The partially exchanged Cs-LTL and Li-LTL refinements were then modelled using the final refined structure of the parent K-L.
Occupancies of sites A-D were refined (A, the d6r, vacant in all cases) along with the fradctional coordinates of site D. 

Merlinoite is a competing phase during synthesis and was included as a second phase in the refinement. 

The final refined structures were exported from GSAS to CIF files, the atomic positions of which were labelled as follows: Site letter (B-D) followed by cation identity (Cs, Li, K). E.g. K-L site D is labelled 'KD' followed by its coordinates x,y,z. 

XRD measurements were performed at the ISIS Neutron and Muon Source in the Materials characterisation lab using their two high resolution X-ray diffractometres which are equipped with rotating copper anodes. Experiments were run over night simultaneously to maximise scan time and peak resolution. 

The parent K-L was run on a diffractometer with no monochromator, whereas the Li-L and Cs-L were run on a diffractometers equipped with a monochromator. 
When refinements were perfomed in GSAS the inst_xry.prm instrument parameter file was modified accordingly:
the beta and alpha radiation as 1.540500 and 1.544300 for K-L (no monochromator) and 1.540500 for Cs-L and Li-L (monochromator).