Phase equilibria of long-period stacking ordered phase in the ternary Mg-Y-Al alloys

•The 18R and 10H have been confirmed as the thermodynamically stable phases in Mg-Y-Al system.•The phase transformation of 18R→10H have been well determined.•The coexistence of 18R and 10H are observed by the atomic-scale resolution identification.•Three isothermal sections focusing on the LPSO phases was constructed by the experimental data.