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Density Functional Theory Studies of Solute-Grain Boundary Interaction

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Density Functional Theory Studies of Solute-Grain Boundary Interaction A DENSITY FUNCTIONAL THEORY ANALYSIS OF SOLUTE-DEFECT INTERACTION ENERGIES IN FCC IRON: FUNDAMENTAL ORIGINS AND INDUSTRIAL APPLICATION by Michael Hoerner A Thesis submitted to the Faculty and the Board of Trustees of the Colorado School of Mines in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Metallurgical and Materials Engineering). Golden, Colorado Date _________________________ Signed: ____________________ Michael Hoerner Signed: ____________________ Dr. John Speer Thesis Advisor Golden, Colorado Date _________________________ Signed: ____________________ Dr. Angus Rockett Professor and Head Department of Metallurgical and Materials Engineering ii ABSTRACT This project was initiated to develop an understanding of the origin of solute drag on fcc Fe (austenite) grain boundaries and explain differences in the experimentally observed solute drag effects of different solutes in steels, and use this understanding to predict solutes which could be of industrial interest as grain growth inhibitors in austenite. The 3-d and 4-d (period 4 and 5) transition metal elements on the periodic table are considered as substitutional solutes with specific attention given to selected solutes (Nb, Mn, Cr, Mo, and Ni) that are of particular interest to the steel industry. Atomistic modeling using both density functional theory (DFT) and molecular dynamics (MD) are used to achieve these goals. The simulations provided thermodynamic solute-boundary binding energies as well as information about the electronic structure of the system which was accessed using both density of states analysis and direct observation of the calculated charge density. The calculated thermodynamic solute-boundary binding energies correlate strongly with experimental data sets on the effects of solutes on both austenite grain coarsening and austenite recrystallization. The strong correlation with experimental results provides confidence in the modelling work and enables the results to be used to suggest solutes of interest for possible future experimentation as alloying elements. Of particular interest, according to the results, are Y, Zr, and Sc, with possible specialized applications for Pd, Ag, and Cd. The filled kite is identified as a fundamental building block for the grain boundary structure of fcc Fe tilt grain boundaries. This structure is found to function as a chemical sub- structure within the grain boundary. This study characterizes the chemical structure of the filled kite through topological analysis of the charge density and density of states analysis. Further, the solute-defect interaction energy with this structure is relatively independent of the orientation of the filled kite with respect to the grain boundary, leading to the conclusion that understanding the interaction of defects with this structure enables a more complete understanding of the interaction of solutes with general grain boundaries. The most significant finding of this work, presented in Chapter 4, is that the solute-defect interaction energy can be predicted based upon the elemental properties of the solute-solvent system and the structure, both electronic and geometric, of the grain boundary. The chemical and strain interaction energies can be separated by considering changes in the Bader volume and Bader charge, respectively, of the solute and solvent atoms as they move from the bulk to the iii defect. Through this separation of the chemical and strain energies, it is determined that the chemical hardness, the second derivative of the energy with respect to the electron count, of the solute relative to the solvent is the fundamental elemental property leading to the chemical energy of segregation just as the volume of the solute relative to the solvent is the fundamental elemental property leading to the strain energy of segregation. iv TABLE OF CONTENTS ABSTRACT ................................................................................................................................ iii LIST OF FIGURES ....................................................................................................................... ix LIST OF TABLES .........................................................................................................................xv LIST OF SYMBOLS ................................................................................................................... xvi LIST OF ABBREVIATIONS .................................................................................................... xviii CHAPTER 1 INTRODUCTION .....................................................................................................1 1.1 The Importance of Understanding Solute Defect Interactions ......................................2 1.2 Industrial Relevance: Experimental Solute Drag in Steel..............................................2 1.2.1 Solute Drag in Grain Coarsening, Recrystallization, and Phase Transformations ..3 1.2.2 Early Experimental Work: Prior Austenite Grain Size Measurements ...................8 1.2.3 Early Experimental Work: Optical Profilometry ...................................................10 1.3 Theoretical Models of Solute Drag and Solute-Boundary Interaction ........................14 1.4 Computational Modeling of Solute Drag and Solute-Boundary Interactions ..............16 1.4.1 Density Functional Theory ....................................................................................16 1.4.2 Molecular Dynamics as a Tool for the Kinetic Study of Grain Boundaries ..........27 CHAPTER 2 OVERVIEW OF SIMULATION AND ANALYSIS METHODS .........................36 2.1 Atomistic Modeling Software Packages ......................................................................36 2.2 The Structure of Tilt Grain Boundaries: Coincident Site Lattices and General Tilt Boundaries ...................................................................................................................37 2.3 The Range of Solute-Solute and Solute-Boundary Energetic Interactions ..................38 2.4 Analysis Techniques ....................................................................................................43 2.4.1 Bader Analysis of the Charge Density ...................................................................43 v 2.4.2 Density of States Analysis .....................................................................................43 CHAPTER 3 THE FILLED KITE MORPHOLOGICAL UNIT ..................................................48 3.1 The Filled Kite Structure .............................................................................................48 3.2 Consistency of Site Behavior for a Given Solute Across Multiple Grain Boundaries ...................................................................................................................50 3.3 Morphology of the Filled Kite, Preferential Solute Site, and Unstable Solute Site in Fe ................................................................................................................................55 3.4 Preferential and Unstable Site Energies and Density of States in Pure Fe Systems ....56 CHAPTER 4 THE ORIGIN OF SOLUTE-BOUNDARY INTERACTION ENERGY ...............59 4.1 The Need for a General Model for Solute-Defect Interactions ....................................59 4.2 A General Theoretical Model for Solute-Defect Interactions ......................................59 4.2.1 Solute-Defect Strain Energy ..................................................................................62 4.2.2 Solute-Defect Chemical (Electronic) Energy ........................................................65 4.2.3 Model Prediction of Solute-Grain Boundary Interaction Energies........................69 4.3 The Relative Roles and Importance of Strain and Chemical Energy in Controlling the Solute-Defect Interaction Energy ...........................................................................71 CHAPTER 5 COMPARISON OF EXPERIMENTAL DATA AND SOLUTE-BOUNDARY INTERACTION ENERGIES ........................................................................................................75 5.1 Solute Drag on Austenite Grain Coarsening ................................................................75 5.2 Solute Drag on Recrystallization .................................................................................76 5.2.1 Static Recrystallization ..........................................................................................77 5.2.2 Dynamic Recrystallization .....................................................................................77 5.3 Applications and Implications of Simulation Relationships with Experimental Data 79 CHAPTER 6 CONCLUSIONS AND FUTURE WORK ..............................................................80 6.1 Industrial Applications .................................................................................................80 vi 6.2 Grain Boundary Structure ............................................................................................81 6.3 Solute-Defect Interaction Energy ................................................................................81 6.4 Opportunities for Future Simulation Work ..................................................................82 6.5 Opportunities for Future Experimental Work ..............................................................82 6.6 Opportunities for Improvement of the General Model for Solute-Defect Interaction .83 6.6.1 Understanding the Materials
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