First principles calculation on thermodynamic properties and magnetism of κ-carbide and Monte-Carlo cell gas model : 제일원리를 이용한 κ-카바이드의 열역학적, 자기 성질 연구 및 몬테-카를로 셀 개스 모델 개발

다국어 초록 (Multilingual Abstract)

(Fe,Mn)3AlC κ-carbides are important substance in high strength light-weight steels. κ-carbide is known to initiate crack and propagatethe crack or, otherwise, pin the slips and make uniform shear bands. These opposite properties was decided by environment of the system. Therefore phase diagram of Fe-Mn-Al-C quaternary system and κ-carbide is vital for this kind of steels. However, there is no
solid thermodynamic value and stability of κ-carbide. To work towards this goal, the all-electron full potential linearized augmented plane-wave method(FLAPW) was used within the generalized gradient approximation. The formation enthalpies of various κ-carbides are calculated. All of κ-carbides have negative formation enthalpy. The
lowest κ-carbide formation was Fe2MnAlC which is 9.5 kJ per atom-mol lower than the highest formation Fe3AlC. When the carbon position was changed to another octahedral position in Fe2MnAlC, the formation energy becomes positive but magnetic moment was increased. In this research, first-principles calculation result was reassessed using Monte-Carlo cell gas model. The result of Monte-Carlo simulation showed smaller entropy value than configurational entropy caused by implementation problem. However, general temperature dependence of free energy, entropy, specific heat and internal energy is well predicted by simulation. In the future work, we hope to incorporate the calculated energies in to phase diagram calculation methods and modify cell gas model to improve implementation problem.

목차 (Table of Contents)

• Contents
• Nomenclature 7
• 1 Introduction 9
• 1.1 Fe-Mn-Al-C High Manganese and High Aluminum Steels . . 10
• 1.2 κ-carbide . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
• 1.2.1 Formation and Crystal Structure . . . . . . . . . . . 12
• 1.2.2 Different Octahedral Site of Fe2MnAlC κ-carbide . . 14
• 1.2.3 Role of κ-carbide in the Fe-Mn-Al-C and Fe-Al-C System
• . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
• 1.3 Thermodynamics and Kinetics of κ-carbide and Related Phases 19
• 1.4 Previous Work . . . . . . . . . . . . . . . . . . . . . . . . . 29
• 2 First-Principles Calculation 30
• 2.1 Density Functional Theory (DFT) . . . . . . . . . . . . . . 30
• 2.2 The Variational Principle . . . . . . . . . . . . . . . . . . . 31
• 2.3 Hohenberg-Kohn Theorems . . . . . . . . . . . . . . . . . . 32
• 2.4 The Kohn-Sham Equation . . . . . . . . . . . . . . . . . . . 33
• 2.4.1 Local Density Approximation (LDA) . . . . . . . . . 34
• 2.4.2 Generalized Gradient Approximation (GGA) . . . . 35
• 2.5 All Electron Full Potential Linearized Augmented PlaneWave Method (FLAPW) . . . . . . . . . . . . . . . . . . . . . . . 36
• 2.6 Computational Method . . . . . . . . . . . . . . . . . . . . 39
• 3 Monte-Carlo Simulation 42
• 3.1 Partition Function . . . . . . . . . . . . . . . . . . . . . . . 42
• 3.2 Free Energy, Internal Energy, Specific heat and Entropy . . 43
• 3.3 Metropolis method . . . . . . . . . . . . . . . . . . . . . . . 45
• 3.4 Wang-Landau method . . . . . . . . . . . . . . . . . . . . . 45
• 4 Results and Discussions 49
• 4.1 Lattice Parameter Optimization . . . . . . . . . . . . . . . . 49
• 4.2 Formation Enthalpy . . . . . . . . . . . . . . . . . . . . . . 52
• 4.3 Magnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
• 4.4 Electronic structure . . . . . . . . . . . . . . . . . . . . . . 57
• 4.5 Monte-Carlo Simulation . . . . . . . . . . . . . . . . . . . . 79
• 5 Conclusion 87
• Reference 89