Determination of Three-Dimensional Grain Boundary Connectivity from Two-Dimensional Microstructures

The connectivity of so-called special and general grain boundaries at a quadruple node is known to be nonrandom as a result of crystallographic constraints. Although a quadruple node is a three-dimensional feature, there exist two-dimensional features which are topologically identical. Therefore, the distribution of these two-dimensional features may be used to determine the three-dimensional connectivity. Computer simulations of a three-dimensional microstructure which is virtually serial sectioned are used to validate the proposed approach

Knowledge Surveys

A knowledge survey consists of course learning objectives framed as questions and is given before and after the content of the knowledge survey is presented in class. For each question on the knowledge survey, students respond using a three-point rating of their confidence to correctly answer the question. Knowledge surveys may be used as a pretest before the semester or a new unit begins to help faculty get a sense of what students believe they know about upcoming topics. Knowledge surveys may be conducted electronically through Blackboard or as an in or out of class assignment on paper

Encouraging a Growth Mindset in Engineering Students

A person’s “mindset” guides a great deal of how one approaches life -- and especially how students approach education. While someone with a fixed mindset believes that their intelligence is fixed and unchangeable, someone with a growth mindset believes that their intelligence is changeable and can grow as they learn more. Most people’s mindset lies along a spectrum with these two extremes at either end. In addition to other outcomes, the mindset that a person has determines how they interpret mistakes they make; whereas someone with a fixed mindset thinks mistakes result from their innate lack of ability, someone with a growth mindset views mistakes as opportunities to learn more. It is no secret that students think that some classes are easy and that others are hard. Thermodynamics of Materials (MSE 308) falls into the latter category. Students have heard that the class is difficult and that the time commitment is high; many have also heard that the professor is supportive and is interested in helping students learn. With a fixed mindset, students may be at a disadvantage coming into a class that they think is going to be especially difficult because they don’t believe their hard work will help them succeed. In contrast, students with a growth mindset might appreciate the learning opportunities that a well-structured but difficult class offers. The research questions we addressed were: (1) Will students’ attitudes about their own abilities in what are perceived to be difficult classes change? and (2) Will those students with a more fixed mindset adopt more of a growth mindset? Students’ mindsets were determined using a questionnaire at the beginning and end of the semester. This also asked about their perception of difficult classes. Throughout the semester, we talked about brain-based learning and adopting a growth mindset; students also reflected on the learning process. Anecdotal evidence suggests that students learned a lot about the growth mindset and were able to apply it more in MSE 308, although the numerical data suggests that a stronger intervention is needed to enable students to shift from a fixed mindset to a growth mindset. One outcome of the work is that students’ mindsets were already either in the category of “strong growth mindset” or “growth mindset with some fixed ideas” at the beginning of the semester. While almost half of the students ended up with a stronger growth mindset, some moved more toward a fixed mindset; the explanation for this is a target for future study. Learning about the growth mindset did seem to reinforce the beliefs that many students held about their approaches to learning and difficult courses

Effects of Crystallographic Orientation on the Early Stages of Oxidation in Nickel and Chromium

Surface orientation plays an important role in the oxidation behavior of single crystals where studies have found the relative oxidation rates for surfaces with different orientations. However, most materials are polycrystalline and contain myriad orientations that contribute to the overall oxidation process. Here we determine the effects of orientation on the early stages of oxidation behavior as a function of surface orientation for polycrystalline nickel (face-centered cubic) and chromium (body-centered cubic). After high temperature oxidation, the oxide topography is characterized using optical profilometry and the underlying microstructure is characterized with electron backscatter diffraction (EBSD). By correlating results from EBSD and optical profilometry, the oxide height is determined for each crystallographic orientation. In both Ni and Cr, a strong relationship is observed between the oxidation rate and direction of the surface normal; for Ni, (111) surfaces oxidize slowest, while (100) surfaces in Cr have the lowest oxidation rates. Although orientation-dependent oxidation rates are observed at short times, the effect is diminished at longer oxidation times

Crystallographically consistent percolation theory for grain boundary networks

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Materials Science and Engineering, 2005.Includes bibliographical references (p. 127-134).Grain boundaries are known to play a role in many important material properties including creep resistance, ductility and cracking resistance. Although the structure and properties of individual boundaries are important, the overall behavior of the material is determined largely by the connectivity of grain boundaries in the microstructure. Grain boundary networks may be studied in the framework of percolation theory by classifying boundaries as special or general to the property of interest. In standard percolation theory, boundaries are randomly assigned as special or general; however, this approach is invalid in realistic grain boundary networks due to the requirement for crystallographic consistency around any closed circuit in the microstructure. The goal of this work is to understand the effects of these local constraints on the connectivity and percolation behavior of crystallographically consistent grain boundary networks. Using computer simulations and analytical models, the behavior of crystallographically consistent networks is compared to that of randomly-assembled networks at several different length scales. At the most local level, triple junctions and quadruple nodes are found to be preferentially coordinated by special and general boundaries, leading to nonrandom network topologies that are quantified using topological parameters.(cont.) Although the properties of the simulated microstructures, including connectivity length and average cluster radius of gyration, are described by the same scaling exponents as in standard percolation theory, the amplitude prefactors in the scaling relationships are changed as a result of the crystallographic constraint. The percolation threshold, an important parameter in microstructural design, is also found to differ from that of standard percolation theory by as much as ±0.05. Although all of the simulated grain boundary networks studied here are distinctly nonrandom, no two cases have the same behavior, the details of which depend strongly on the specific microstructural model. Therefore, a unified approach for locally correlated percolation problems is developed that allows the effects of the requirement for crystallographic consistency to be compared directly from system to system. This new approach can be extended beyond the study of grain boundary networks to include other locally-correlated percolation problems.by Megan E. Frary.Ph.D

Correlation-Space Description of the Percolation Transition in Composite Microstructures

We explore the percolation threshold shift as short-range correlations are introduced and systematically varied in binary composites. Two complementary representations of the correlations are developed in terms of the distribution of phase bonds or, alternatively, using a set of appropriate short-range order parameters. In either case, systematic exploration of the correlation space reveals a boundary that separates percolating from nonpercolating structures and permits empirical equations that identify the location of the threshold for systems of arbitrary short-range correlation states. Two- and three-dimensional site lattices with two-body correlations, as well as a two-dimensional hexagonal bond network with three-body correlations, are explored. The approach presented here should be generalizable to more complex correlation states, including higher-order and longer-range correlations

Effect of Grain Boundary Engineering on Microstructural Stability During Annealing

Grain boundary engineering, which increases the special boundary fraction, may improve microstructural stability during annealing. Different processing routes are undertaken to establish the effectiveness of each and to better understand which microstructural features determine the resulting stability. We find that multiple cycles of grain boundary engineering result in a material that resists abnormal grain growth better than other processing routes despite similarities in special boundary fraction, grain size, and general boundary connectivity among as-processed materials

Teaching Excellence Through Mindful Reflection

Reflective teaching is examining one’s beliefs about teaching and learning and determining the alignment of those beliefs with what happens within your courses (Reflective Teaching, 2021). The goal is to think critically about one’s teaching to find evidence of effective teaching as well as identifying potential areas for improvement (Palmer, 2017). The tool described here is based on the Framework for Assessing Teaching Effectiveness (FATE) and is intended to help teachers develop self-reflection around teaching and objectively describe their strengths and weaknesses in a manner consistent with the evidence of their teaching practices (Simonson, Earl, and Frary, 2021; Simonson, Frary, and Earl, 2023)

Establishing a Framework for Assessing Teaching Effectiveness

Most institutional practices to evaluate teaching are inadequate, inaccurate, neither improve teaching directly, nor incentivize teaching improvement. This is often because effective teaching is difficult to assess and most tools do not adequately or accurately do so and are often without established standards. Because of this, faculty may be hesitant to change or may not be aware of the need to change their teaching practice or how to effect such change. Here we establish a framework defining effective teaching and develop a tool that considers multiple facets of teaching and will accommodate different approaches, modes, and environments