Marc De Graef
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Currently, there are several active research programs in our group:

MURI: Managing the Mosaic of Microstructure [AFOSR]

The ability to digitally design materials with microstructures optimized to achieve desired properties, is one of the long term goals of the materials field. Simulation-based materials design has the potential to dramatically reduce the need for expensive down-stream characterization and testing. However, this requires reliable algorithms and methodologies that incorporate variability and uncertainty in the design process, and are validated against physics-based models and experiments. Achieving the "digital design" goal requires the creation of a number of new methodologies that rely on the expertise of several research communities outside the materials field. The team we have assembled for this MURI program has broad expertise in experimental microstructure characterization, mathematical theory of microstructure, and design and informatics, and represents a microcosm of a computationally-integrated multi-university research and development laboratory.

This MURI program is carried out with Carnegie Mellon University as the lead organization, with six external universities are partners: Purdue University, Northwestern University, Caltech, Georgia Tech, University of Michigan, and University of Minnesota. The principal aim of our program is to create advanced methodologies for quantitative microstructure-property analysis and length scale bridging design, and efficient measurement of structure/time evolution, all implemented using optimized modeling and data mining techniques on HPC and multi-core platforms. The program will deliver algorithms for 3D reconstructions, optimization of microstructures, data storage and retrieval, among others; new mathematical models for microstructure-property relations in materials, a new thin-manifold description of material microstructures; and methodologies/frameworks for microstructure sensitive design as well as experimental validation of process design.

Materials Applications of Aberration-Corrected Lorentz Microscopy [DOE]
The increasing complexity of today's magnetic materials systems must be accompanied by improvements in the methods used to study those materials. In this project, which is a continuation (renewal) of research carried out in a previous DOE grant, we apply phase reconstruction based on the Transport-of-Intensity Equation (TIE) to the three-dimensional study of magnetic field distributions around magnetic samples. The program consists of an experimental component and a modeling component. The modeling component evaluates the accuracy and efficiency of phase reconstructed vector field electron tomography, by using numerical simulations and analytical evaluation of error propagations. This analysis will eventually result in a set of experimental conditions which must be satisfied to carry out successful 3D vector field reconstructions. The experimental work involves acquisition of tilt series phase maps using both the TIE formalism and electron holography. Samples for the experiments will include tips for a magnetic force microscope, patterned microstructures of magnetic material (permalloy and Fe-Co), and natural (magnetotactic bacteria) and man-made (colloidal Cobalt particles) configurations of magnetic nano-particles. The resulting 3D magnetic induction maps will be compared with the results of extensive micromagnetic modeling. The program will also further develop methods for the computation of magnetostatic interactions between nano-particles.

Domain Walls in Ferromagnetic Shape Memory Alloys [NSF]

The microstructure of a material is intimately connected to mechanical, electrical, magnetic and other material properties. Magnetic domain walls (MDWs) separate regions of differently oriented magnetization, and their motion under an applied magnetic field is as fundamental to the overall magnetic properties of a material, as the motion of dislocations is to its mechanical properties. The quantitative study of MDWs by means of Lorentz Transmission Electron Microscopy (LTEM) observation modes has, until recently, been hampered by poor spatial resolution. Spherical aberration correction now provides an opportunity to push the resolution of LTEM down to the single nanometer regime and opens the way to high resolution studies of MDWs.

In this research program, we make use of an aberration-corrected LTEM to study magnetic domain wall behavior in a number of multi-ferroic materials, which exhibit multiple phase transitions, each giving rise to a fine-scale domain microstructure. The interactions between these domains (e.g., twin boundaries and MDWs, or anti-phase boundaries and MDWs) are the main focus of this proposal. The alloys of choice are the ferromagnetic shape memory alloys with compositions near the stoichiometric Ni2MnGa compound and Fe-Pd alloys with around 30 at\% Pd. The research consists of experimental observations of domain walls in static and dynamic conditions, supported by image simulations based on micromagnetic models. In addition, we employ Magnetic Force Microscopy (MFM) and Electron Channeling Contrast Imaging (ECCI) to image microstructural features as well as surface-penetrating defects at a number of different lengthscales.