Incommensurate lattice modulations in Potassium Vanadate

Potassium Vanadate (K$_{\mathrm{2}}$V$_{\mathrm{3}}$O$_{\mathrm{8}})$ is an S $=$ \textonehalf 2D square lattice antiferromagnet that shows spin reorientation indicating a strong coupling between the magnetism and its dielectric properties with a promise of rich physics that promises multiferroicity. These tangible physical properties are strongly tied through a spin-lattice coupling to the underlying lattice and superlattice behavior. It has a superlattice (SL) onsetting below T$_{\mathrm{c}}=$115 K with an approximate [3 x 3 x 2] modulation. Here we present our recent experiments at TOPAZ beamline at SNS which for the first time proves conclusively that the lattice modulations are incommensurate, with an in-plane Q of 0.315. We will also show our attempts to refine the data using JANA which requires a redefinition of the lattice, as well as the temperature and Q dependence of the superlattice modulation measured using neutrons at HFIR and synchrotron x-rays at APS. Our results are not only relevant for the ongoing search of multifunctional behavior in K$_{\mathrm{2}}$V$_{\mathrm{3}}$O$_{\mathrm{8\thinspace }}$but also generally for the superlattice modulations observed in a large family of fresnoites.