We modify the anisotropic phase-field crystal model(APFC),and present a semi-implicit spectral method to numerically solve the dynamic equation of the APFC model.The process results in the acceleration of computations by orders of magnitude relative to the conventional explicit finite-difference scheme,thereby,allowing us to work on a large system and for a long time.The faceting transitions introduced by the increasing anisotropy in crystal growth are then discussed.In particular,we investigate the morphological evolution in heteroepitaxial growth of our model.A new formation mechanism of misfit dislocations caused by vacancy trapping is found.The regular array of misfit dislocations produces a small-angle grain boundary under the right conditions,and it could significantly change the growth orientation of epitaxial layers. We modify the anisotropic phase-field crystal model (APFC), and present a semi-implicit spectral method to numerically solve the dynamic equation of the APFC model. The process results in the acceleration of computations by orders of magnitude relative to the conventional explicit finite -difference scheme, thereby, allowing us to work on a large system and for a long time. The faceting transitions introduced by the increasing anisotropy in crystal growth are then discussed. In particular, we investigate the morphological evolution in heteroepitaxial growth of our model. A new formation mechanism of misfit dislocations caused by vacancy trapping is found. The regular array of misfit dislocations produces a small-angle grain boundary under the right conditions, and it could significantly change the growth orientation of epitaxial layers.