60th Annual Report on Research 2015

Research Results

Steel is a key component of the petroleum industry and its properties, structural as well as mechanical, are governed by the microstructures that form during processing.  Carbon-based steels form a wide range of microstructures that are essentially composites of iron, either ferrite or austenite, and iron carbides.  The most common and important iron carbide is cementite, Fe₃C.  While these microstructures have been well studied, there are still many outstanding questions regarding the interfacial properties.  The goal of this project is to investigate the use of modern computational tools, notably atomistic methods, to investigate the interfaces between iron and cementite to gain deeper understanding of the interfaces they form.

The first step in simulating the interfaces is to identify and characterize the available interatomic potentials that describe the Fe-C interactions.  We identified several interatomic forms that potentially will work for the iron carbon system: the embedded atom method (EAM), modified embedded atom method (MEAM) and Tersoff.  Within those general formulations, we identified 2 parameterizations in each category, giving us a total of 6 potentials to test.  We performed rigorous tests on these potentials which included the formation energies and lattice constants of a number of relevant structures, including FCC and BCC iron, diamond, graphite, cementite (Fe₃C), rocksalt FeC, as well as other known iron carbides and carbon defects in iron.

One interesting result we found from this process was the predictions of the EAM potentials compared to the MEAM and Tersoff potentials.  Since EAM is not able to represent strong directional bonds, it is unable model diamond or graphite.  This is not surprising; however what is surprising is the ability of the Hepburn EAM formulation to capture the structures within the metal rich compositions between iron and FeC.  The EAM potential has a significantly lower computational cost than the other potentials, allowing for quicker, albeit less accurate, simulations which is very useful in identifying potential problems to be corrected before the more expensive potentials are used.  Additionally, it was shown that the Lau EAM potential poorly modeled the elastic constants of cementite, likely precluding its use.

To further test the potentials and their ability to represent the iron carbide systems, we investigated ability of each interatomic potential to predict the entire convex hull. In the iron carbon system, only two structures are stable at low temperatures: ferrite and graphite.  Fe₃C is a metastable structure and occurs through processing, despite its ubiquitous presence in carbon steels.  To construct the convex hull and test a wide range of structures, we used an evolutionary algorithm to sample a wide range of iron carbides and potentially identify structures that, while experimentally shouldn't be there, are potentially favored by poorly fit interatomic potentials.  Specifically, we used the program USPEX with 50 initial random guesses along with 10 common iron carbide structures, and evolved them over 45 generations.  The convex hulls of two potentials are shown in Figure 1, for the MEAM parameterization of Lee and the Tersoff parameterization of Henriksson.  We note that the MEAM Lee potential erroneously predicts a very low energy structure at a composition of Fe₅C₄.  This suggests that there are potentially serious flaws in the MEAM Lee potential which preclude its further use in the study of interfaces.  The convex hull of the Tersoff Henriksson, however, reproduces what we expect: only iron and graphite are stable.  This prediction was consistent with both the formulations of the Tersoff potentials, suggesting that these potentials are more robust.  The testing of these potentials therefore seems to eliminate the MEAM Lee and EAM Lau potentials.  Thus, it appears that without further guidance, it is appropriate to pursue the remaining four potentials in an initial study of interfacial energies and structures.

As an initial investigation of the interfaces between a-iron (ferrite) and cementite, we created an interface between these crystals in the Bagaryatskii orientation (Figure 2).  This choice was made because the ease in setting up the orientation relationships as it involves the alignment of high symmetry directions in both crystals.  This orientation relationship is:

where q denotes cementite and a denotes ferrite.  This interface was constructed by creating a large box of atoms of both cementite and ferrite, in order to minimize the in-plane lattice mismatch in both directions.  The structure was then allowed to relax and the interfacial energy and interface structure can then be determined.  One actual simulation is shown in Figure 3a, highlighting the whole box of cementite and ferrite atoms used.  Figures 3b and 3c shows the structure of the interface, in the normal plane and profile respectively, which presents interesting results that will be further analyzed in the coming year.  It appears that the interface can be well described by a set of orthogonal interfacial dislocations and the regular spacing can be well described with dislocation theory.  This has potential great impact if such structures in the interfaces can be identified for the orientation relationships we are interested in this project.  Additionally the methodology developed to model this system is easily translatable to the more complicated orientation relationships that will be evaluated next.

Impact

The impact of this research to date has been primarily on the development of both the PI and the graduate students career.  Notably, the availability of this research project allowed the PI to recruit one of the best graduate students in our department who would have otherwise left with his Masters degree.  The PI has been able to train Mr. Guziewski in the area of atomistic modeling, providing him with a new career path.  In addition, this new direction has allowed the PI to gain recognition in the area of modeling interfaces, an area he was not previously known for.  This has allowed for the initiation of additional collaborations with groups who are interested in modeling interfaces of ceramics.