Observation　regarding　the　SEM　and　TEM　images　of　the　precipitation　and　growth　morphology　of　topologically　close-packed　(TCP)　phase　indicates　that　the　orientation　relationships　between　the　TCP　phase　with　different　morphologies　and　the　matrix　are　not　that　similar.　Concerning　with　this　phenomenon,　via　DFT　calculations,　the　possible　interface　structures　between　the　σ　phase　and　the　matrix　γ,　as　well　as　the　μ　phase　and　the　matrix　γ　have　been　established　and　discussed　under　different　orientation　relationships.　The　experimental　characterizations　and　simulated　calculations　reveal　that　the　orientation　relationships　between　TCP　phase　and　the　matrix　determine　interplanar　spacing　mismatches　and　the　interface　energy　of　the　low　index　dense　arrangement　interfaces　of　the　two　phases,　while　the　two　parameters　exert　influence　on　the　growth　and　morphology　of　TCP　phase.　The　interface　energy　of　the　σ/γ　interface　with　(111)γ//(001)σ　orientation　is　small　while　its　interplanar　spacing　mismatch　is　large,　so　the　TCP　phase　under　this　orientation　relationship　tend　to　take　planar　expansion　along　interface　instead　of　growing　layer　by　layer　parallel　to　the　plane,　giving　rise　to　plate-like　morphology.　However,　those　of　the　σ/γ　with　(110)γ//(1–10)σ　and　the　μ/γ　with　(110)γ//(111)μ　are　just　the　opposite,　so　the　TCP　phases　under　these　orientations　tend　to　grow　layer　by　layer　instead　of　expand　along　plane,　forming　needle-like　or　rod-like　morphology　eventually.　©　2021　Elsevier　Inc.