Solid solution alloying is a promising strategy to establish high performance thermoelectrics.By alloying different elements,phase structures and phase compositions may vary accompanied by appearance of variety of interesting microstructures including mass fluctuation,lattice strain,nano-scale defects and spinodal decomposition,all of which may greatly influence the electrical and specifically the thermal transport of the material.In the present study,atomic structures of Cu2S0.5Se0.5 solid solution have been examined by using atom-resolved electron microscopy in order to investigate the structure-correlated physical insights for the abnormal thermal transport in this solid solution.Then the exceptional inter-growth nanostructures were observed.The solid solution consists of two high symmetrical phases,i.e.the hexagonal and cubic phase,which alternately intergrow to form highly oriented ultra-thin lamel-lae of nano or even,unit cell scales.The compositional oscillation in Se/S atomic ratio during alloying is responsible for the phase stability and intergrowth nanostructures.The unique binary phase intergrowth nanostructures make great contribution to the ultra-low lattice thermal conductivity comparable to glass and extremely short phonon mean free path of only 1.04 (A),peculiar continuous hexagonal-to-cubic struc-tural transformation without a critical transition temperature and its corresponding abnormal changes of thermal characters with temperatures.The present study further evokes the unlimited possibilities and potentials for tailoring nanostructures by alloying for improved thermoelectric performance.