Equilibrium　phase　diagram　of　ruthenium-zirconium　oxide　(Ru-Zr-O)　was　calculated　by　a　combination　of　ab　initio　density　functional　theory　and　thermodynamic　calculations.　The　phase　diagrams　suggest　that　the　solubility　between　ruthenium　oxide　and　zirconium　oxide　is　very　low　under　normal　experimental　conditions,　in　good　agreement　with　the　prior　reports　in　literature.　Also　provided　is　the　theoretical　support　for　the　reported　phenomenon　that　doping　or　amorphization　of　Ru-Zr-O　might　suppress　phase　separation　of　the　oxide.　To　study　the　spinodal　decomposition　of　Ru-Zr-O,　we　successfully　prepared　an　amorphous　Ru048Zr0.52O2　film　of　a　solid　solution　phase　by　a　thermal　decomposition　at　a　low　temperature　(563　K).　In　situ　transmission　electron　microscopy　was　utilized　to　witness　the　spinodal　decomposition　of　the　amorphous　Ru0.48Zr0.52O2　solid　solution　by　electron-beam　annealing.　The　present　fundamental　study　of　the　phase　behavior　of　Ru-Zr-O　provides　a　guideline　for　the　phase　and　microstructure　design　of　Ru-based　mixed　oxides　for　various　important　applications.