Phase field model was employed to study the variations of interatomic potentials of Ni 3 Al (L1 2 phase) and Ni 3 V (DO 22 phase) as a function of temperature and concentration. The long-range order (LRO) parameter related interatomic potentials equations formulated by Khachaturyan were utilized to establish the inversion equations for L1 2 and DO 22 phases, with which interatomic potentials could be calculated. The interatomic potentials of Ni-Al and Ni-V exhibited approximately linear increases and decreases, individually, with enhanced Al concentration. Substituting the inverted interatomic potentials into the microscopic phase field equations led to three cases of precipitation sequence: the DO 22 phase preceded L1 2 phase precipitating at the interatomic potentials of Ni-V > Ni-Al; the vice cases; and two phases precipitated simultaneously at interatomic potentials of Ni-V and Ni-Al were equal.
DONG WeiPing WANG YongXin YANG Kun CHEN Zheng LU YanLi
The ferroelectric domain formation(FDF) and polarization switching(FDPS) subjected to an external electric field are simulated using the phase-field(PF) method,and the FDPS mechanism under different external electric fields is discussed.The results show that the FDF is a process of nucleation and growth in ferroelectric without applying any external stress.Four kinds of parallelogram shaped ferroelectric domains are formed at the steady state,in which the 180° anti-phase domains regularly align along the 45° direction and the 90° anti-phase domains regularly distribute like a stepladder.Steady electric fields can rotate domain polarization by 90° and 180°,and force the orientation-favorite domains and the average polarization to grow into larger ones.The greater the steady electric field,the larger the average polarization at the steady state.In ferroelectrics subject to an alternating electric field,domain polarization switches to cause a hysteresis loop and an associated butterfly loop with the alternating electric field.The coercive field and remnant field are enhanced with the increase of the electric field frequency or strength,or with the decrease of temperature.
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.
The phase-field crystal(PFC) model is employed to study the shape transition of strained islands in heteroepitaxy on vicinal substrates.The influences of both substrate vicinal angles β and the lattice mismatch ξ are discussed.The increase of substrate vicinal angles is found to be capable of significantly changing the surface nanostructures of epitaxial films.The surface morphology of films undergoes a series of transitions that include Stranski-Krastonov(SK) islands,the couple growth of islands and the step flow as well as the formation of step bunching.In addition,the larger ξ indicates an increased strained island density after coarsening,and results in the incoherent growth of strained islands with the creation of misfit dislocations.Coarsening,coalescence and faceting of strained islands are also observed.Some facets in the shape transition of strained islands are found to be stable and can be determined by β and crystal symmetry of the film.
