Phase Field Modeling Tools Working Group

Phase Field Simulations

Phase field models of solidification have proven to be an extremely potent method for simulating the microstructure which arises during a nearly limitless host of materials phenomena: solidification, electrodeposition, and grain growth are but a small sampling of the possible applications. NIST researchers, working with colleagues all over the world have applied phase field methods to the problems of alloy solidification and grain growth to great success. What follows below is some of their research over the past decade. All of the work below is published in Acta Materialia, Physica D, and Physical Review.

Phase Field Models of Alloy Solidification

The simulations below show the solidification of a binary alloy into an undercooled melt. Click on the image to see a movie of the crystallization phenomena.

Four-fold symmetric dendrite array Six-fold symmetric dendrite array
Corner close-up of four-fold symmetric dendrite Dendrite sllidification with noise Ripening phenomenon, single domain
Ripening, single domain with core Ripening, several domains

Phase Field Models of Grain Boundary Formation

Over the past six years, in collaboration with Ryo Kobayashi (Hiroshima University) and W. Craig Carter (MIT), NIST researchers have studied solidification of pure melts, and the coupling of this phenomena with grain boundary formation via impingement of crystals, and subsequent coarsening of the grains. Below are 3 simulations of early research in this area.

Isotropic Growth, Many Seeds

Isotropic growth, many seeds

4 Fold Anisotropic Surface Energy/Kinetics, Many Seeds

4 fold anisotropic growth, many seeds

4 Fold Anisotropic Surface Energy/2 Fold Kinetics, Many Seeds,

Dendritic Growth, 3 seeds

Dendritic growth, 3 seeds

Phase Field Models of Grain Boundary Formation II

An updated model allows for the grains to evolve after impingement. This work was a collaboration between Ryo Kobayashi, Craig Carter, Jim Warren and Alex Lobkovsky. All of the following movies are embedded Quicktime.

Solidification and Impingement, Boundary Migration Dominant

Solidification and Impingement, Rotation Dominant

These Movies can be compared with the research of Professor Wolfgang Losert and graduate Student Kyu Lee,, who have done some nice confocal microscopic studies of grain systems, such as this succinonitrile-laser dye system

Experiments of Lee and Losert:

Phase Field Models of Grain Boundary Formation III

Over the last few years Dr. Laszlo Granasy and colleagues of the Research Institute of Solid State Physics and Optics in Budapest have extended the above model, and working in collaboration with Dr. James A. Warren and Dr. Jack Douglas, developed a model which can account for defect entrapment in a growing solid crystal, resulting in grain boundary formation in the crystallite. This leads to "dizzy dendrites" as well as other, more exotic microstrucutres

Growth of a Dizzy Dendrite

Growth of a Spiral Dendrite