 
Qiang's Research Gallery 7
Computational Materials Sciences 

Recent advances in both computational materials science and
information technology during the last two decade have led to a
paradigm shift for materials development towards the materials
by computational design approach which promises to not only save
cost but also accelerate the insertion of new materials to
applications.

A critical component in the materials by
computational design framework is the computational prediction of
material microstructures under different processing conditions,
i.e., compositional and structural inhomogeneities, which
essentially control the physical and mechanical properties of a
material.
Recently, we have been designing fast, robust and adaptive algorithms for the solution of a variety of applications problems in materials sciences. Our efforts include the study of: 
At Penn State, we have been working with a number of
colleagues in materials sciences on the
multiscale materials simulation and design, which is
the theme of our fiveyear $2.9million NSF sponsored ITR
project MATCASE,
and also our research within the NSFIUCRC PennState/GaTech
research
Center for Computational Materials
Design.

Diffuse interface/phase field method is very popular in computational materials science. The idea goes back to van de Walls more than 100 years ago. 
Much of our works have followed from the pioneering works of Cahn and Hilliard for phase transition problems. A smooth order parameter is used to define the material interface/defects implicitly which has a thin (but finite) transition layer across the interface. The approach enjoys the same spirit as the GinzburgLandau formalism for the mesoscopic modeling of superconductivity and quantized vortices. 
Nucleation is an important problem in materials sciences.
We recently developed a diffuse interface method for predicting the critical
nuclei morphology in solid state transformations. For the first time, we
were able to reveal the dependence of possible critical nuclei on the elastic
energy contributions in anisotropic elastic solids. Twodimensional
energy diagram is shown in a recent PRL paper. 
The critical nuclei can be predicted without a priori information
via the computation of saddle point and
minimum energy path. 
In 3d, there are two other possible nuclei branches with lower
symmetry, but
the plate shape often has lower formation energy.

Phase field simulation of microstructure evolution is an
important part of the our multiscale materials simulation
process. To improve its performance,
we combine the moving mesh idea with the high resolution and
Fast FFTbased implementation of spectral methods into an
adaptive spectral methods for the phase field models. 
A map is used between the computational and physical domain so that the grids still remain uniform in the computational domain,
but the physical mesh becomes clustered near the interfacial regions
and thus provide better resolution. 
To minimize the overhead, the moving mesh PDEs are solved in a similar manner as the original phase field models via semiimplict integration with time splitting. 
The performance of numerical scheme is much improved with the moving mesh Fourie spectral method when the microstrucure has concentrated interfacial regions. 
Algorithms are developed to compute the correct phase diagram by automatically identifying the presence of miscibility gap. 
Some references:
Contact Qiang Du 20080501