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The non-equilibrium molecular dynamics method is adapted to calculate the phonon thermal conductivity of alphazirconium. By exchanging velocities of atoms in different regions, the stable heat flux and the temperature gradient are established to calculate the thermal conductivity. The phonon thermal conductivities under different conditions, such as different heat exchange frequencies, different temperatures, different crystallographic orientations, and crossing grain boundary (GB), are studied in detail with considering the finite size effect. It turns out that the phonon thermal conductivity decreases with the increase of temperature, and displays anisotropies along different crystallographic orientations. The phonon thermal conductivity in [0001] direction (close-packed plane) is largest, while the values in other two directions of [2......0] and [01...0] are relatively close. In the region near GB, there is a sharp temperature drop, and the phonon thermal conductivity is about one-tenth of that of the single crystal at 550 K, suggesting that the GB may act as a thermal barrier in the crystal. [ABSTRACT FROM AUTHOR]