InAlN grown by plasma-assisted molecular beam epitaxy often contains a honeycomb microstructure. The honeycomb microstructure consists of 5-10 nm diameter aluminum-rich regions which are surrounded by indium-rich regions. Layers without this microstructure were previously developed for nominally lattice-matched InAlN and have been developed here for higher indium content InAlN. In this study, InAlN was grown in a nitrogen-rich environment with high indium to aluminum flux ratios at low growth temperatures. Samples were characterized by high-resolution x-ray diffraction, atomic force microscopy, high-angle annular dark-field scanning transmission electron microscopy, and atom probe tomography. Atomic force microscopy showed InAlN layers grown at temperatures below 450 degrees C under nitrogen-rich conditions were free of droplets. InAlN films with indium contents up to 81% were grown at temperatures between 410 and 440 degrees C. High-angle annular dark-field scanning transmission electron microscopy and atom probe tomography showed no evidence of honeycomb microstructure for samples with indium contents of 34% and 62%. These layers are homogeneous and follow a random alloy distribution. A growth diagram for InAlN of all indium contents is reported. (C) 2016 Published by Elsevier B.V.