Phase Field Microelasticity (PFM) theory and model is developed for most general problem of elasticity of arbitrary anisotropic, structurally and elastically inhomogeneous systems. PFM enables us to solve a group of materials problems of engineering importance, including diffusional and displasive phase transformations with lattice misfit and/or elastic modulus misfit, dislocation dynamics in plastic deformations, crack evolution in fracture, in bulk or finite bodies with arbitrary-shaped free surfaces. PFM also allows us to investigate multi-physical problem in one simulation model owing to its unified theoretical formalisms for these apparently different processes. Not only PFM provides the theoretical method to solve most difficult problem of elasticity but also its scheme is apt to easy and optimum realization of the parallel computing technique. PFM provides efficient tools for the three-dimensional computational prototyping of a large variety of mesoscale processes in high complex systems that are either difficult or even impossible to address experimentally. The capability of PFM has been proved by a series of successful works (phase transformations, dislocations, cracks, epitaxial films, etc.). Its potential will become more and more prominent with continuing future works. Kinetics of Structural Transformations in Metal and Ceramic Systems — Phase Field Microelasticity Theory for Heterogeneous Materials — Armen G Khachaturyan, Rutgers University, DMR Award # Stress field of a plate with grooves: (a) PFM calculation, (b) photoelasticity measurement (Frocht 1948). Heterogeneous stress due to elastic modulus misfit of the neiboring grains in polycrystal.

variant 3 variant 2 variant 1 cubic (a) (b) Microstructure in bulk material. Microstructure near free surface (top surface Z=0). Kinetics of Structural Transformations in Metal and Ceramic Systems — Martensitic Microstructures near Free Surface — Armen G Khachaturyan, Rutgers University, DMR Award #  Y.U. Wang, Y.M. Jin and A.G. Khachaturyan, “The Effects of Free Surfaces on Martensite Microstructures: 3D Phase Field Microelasticity Simulation Study,” Acta Mater. (submitted, 2003). Shape memory alloys have important engineering applications as actuators and sensors. Their properties are determined by the microstrcture patterns produced by martensitic transformation (MT). MT produces several orientation variants with strain misfit. The elastic stress accommodation between the domains of different variants and parent phase is the mechanism for the formation of domain microstructure. The domain morphology in bulk materials have been studied extensively, but the effect of free surface on it is an unsolved long-standing problem. The proposed PFM model is applicable to MT near free surface. The first simulation study is performed. The cubic to tetragonal transformation in FeNi and cubic to trigonal transformation in AuCd shape memory polycrystalline alloys are studied. The results give a quantitative understanding on how the free surface affects the morphology of the microstructures for different MT systems, and also provide the information unavailable from experiments.

Kinetics of Structural Transformations in Metal and Ceramic Systems — Surface Instability of Heteroepitaxial Thin Films — Armen G Khachaturyan, Rutgers University, DMR Award # Simulated evolution of surface morphology driven by epitaxy stress relaxation during annealing. Stress fields before and after formation of islands.  Y.U. Wang, Y.M. Jin and A.G. Khachaturyan, “Phase Field Microelasticity Modeling of Surface Instability of Heteroepitaxial Thin Films,” Acta Mater. (in press). Defect-free crystalline epitaxial films are highly demanded in semiconductor and electro-optical device industry. But the existence of internal stress generated by the crystal lattice mismatch makes epitaxial films susceptible to the formation of defects, mainly surface roughening and dislocations. The computational modeling is one effective way to study the defect forming mechanisms and evolution of defects, which are critical to develop new generation of high performance materials and improve the performance of existing ones. PFM simulations on surface instability are performed. The simulation results provide us critical information on the mechanism controlling instability. It also discloses detailed temporal evolutions of the surface morphology finally leading to the formation of equilibrium array of islands. Although surface roughening should be avoided in flat surface devices, it provides a promising means to fabricate nano-size islands (quantum dots).

Kinetics of Structural Transformations in Metal and Ceramic Systems — Dislocation Dynamics in Heteroepitaxial Thin Films — Armen G Khachaturyan, Rutgers University, DMR Award # film substrate free surface 1234 b 0 Education: 1 graduate student (Yongmei M. Jin) and 1 postdoctoral research associate (Yu U. Wang) in theoretical and computational materials modeling have participated in this research. (a) Stress field of a screw dislocation near free surface. (b) Quantitative comparison between PFM calculation and analytical solution. The simulated sequence of dislocation configurations (indicated by 0 to 4) in the (111) slip plane of a 3D epitaxial film on thick substrate. The internal stress in the epitaxial film drives a threading dislocation to move, depositing a misfit dislocation at the film/substrate interface. (a) (b)  Y.U. Wang, Y.M. Jin and A.G. Khachaturyan, “Phase Field Microelasticity Modeling of Dislocation Dynamics near Free Surface and in Heteroepitaxial Thin Films,” Acta Mater., 51, , Dislocations degrade the properties of the film and can lead to its failure. Due to the presence of free surface and film/substrate interface the dislocation behavior is different in epitaxial film from that in bulk materials. PFM solves exactly the elastic interaction among individual dislocations, free surfaces and interfaces. The model allows dislocations to self-multiply and self- organize without a priori constraint on dislocation evolution. PFM simulation enables us to obtain the detailed information of dislocation activity, which is critical in understanding mechanisms controlling the dislocation behavior in film and also in designing the epitaxial film devise.