DNA origami has proven useful for organizing diverse nanoscale components into patterns with 6 nm resolution. However for many applications, such as nanoelectronics, large-scale organization of origami into periodic lattices is desired. Here, we report the self-assembly of DNA origami rectangles into two-dimensional lattices based on stepwise control of surface diffusion, implemented by changing the concentrations of cations on the surface. Previous studies of DNA-mica binding identified the fractional surface density of divalent cationsñ s2 ð Þ as the parameter which best explains the behaviour of linear DNA on mica. We show that for n s2 between 0.04 and 0.1, over 90% of DNA rectangles were incorporated into lattices and that, compared with other functions of cation concentration,ñ s2 best captures the behaviour of DNA rectangles. This work shows how a physical understanding of DNA-mica binding can be used to guide studies of the higher-order assembly of DNA nanostructures, towards creating large-scale arrays of nanodevices for technology.