Ba2CuTeO6 has garnered considerable interest as the combination of stacking sequence and Cu2+ displacements lead to a magnetic geometry that reproduce the effects of a spin ladder. Such systems are excellent models for studying quantum criticality, as they exhibit a quantum critical point from non-magnetic spin singlet dimers to Néel magnetic order as the inter-ladder exchange J$_{inter}$ is increased. We will use neutron diffraction to examine compounds where W is used to moderate these interactions in the compounds Ba2CuTe1-xWxO6. Muon spin relaxation measurements indicate that these new materials demonstrate quantum criticality. The structural insights from neutron diffraction will be invaluable in interpreting the low temperature states near the quantum critical point.