Influence of Grain Boundary Character on Point Defect Formation Energies in BCC Fe

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1 Influence of Grain Boundary Character on Point Defect Formation Energies in BCC Fe Vacancy M.A. Tschopp 1, M.F. Horstemeyer 1, F. Gao 2, X. Sun 2, M. Khaleel 2 Self-interstitial atom 1 Center for Advanced Vehicular Systems, Mississippi State University 2 Pacific Northwest National Laboratory 1

2 Outline Introduction/Motivation Simulation Methodology Simulation Results Grain boundary (GB) energy & structure Vacancy formation energies Self-Interstitial Atom (SIA) formation energies Comparison of Vacancy/SIA binding energies to grain boundary sites Conclusion 2

Introduction They found that (i) interstitials

How does grain boundary character influence

3 Introduction They found that (i) interstitials are absorbed by the GB, which then acts as a source, (iii) emitting interstitials to annihilate vacancies in the bulk. How does grain boundary character influence interstitial and vacancy annihilation? Can we evaluate their sink strength? 3

4 Research outline The objective of this research is to understand how grain boundary character influences the formation energies of vacancies and interstitials in BCC Fe. Build GB database Examine structure & energy Iteratively remove/add atoms to evaluate energy Study how GB character affects vacancy / intersitial 4

5 Simulation Methodology GB were obtained by multiple translations of the two crystals, followed by energy minimization Symmetric Tilt Grain Boundary (STGB) <100> and <110> STGBs used for GB database, using Mendelev et al. (2003) Fe potential 5

6 <100> and <110> STGB Energy Plots A D C A A B C A The GB energy evolution as a function of misorientation angle between the two grains. 6

7 <100> STGB Structural Units Example of structural units for <100> STGBs. 7

8 <110> STGB Structural Units Example of structural units for <110> STGBs. 8

9 <100> STGB Vacancy Formation Energies Procedure 1.Atom is removed 2.System is relaxed via energy minimization 3.New system energy is obtained 4.Vacancy formation energy is calculated for the removed atom 5.Reiterate over all atoms within 2 nm of GB Vacancy formation energy for each removed atom for three <100> STGBs. 9

10 Low Angle GB Vacancy Formation Energies Vacancy formation energy for each removed atom for four <100> low angle STGBs (<15 degrees). Note the low formation energies near the dislocations. 10

11 Vacancy Formation Energy vs. Distance E vf,bulk 1.72eV Cu nm Cu Fe Vacancy formation energy as a function of distance for all <100> STGBs. 11

12 Vacancy Formation Energy vs. GB energy No low angle boundaries in this study. Trend isn t entirely correct for Fe. Cu <100> Fe <110> Vacancy formation energy as a function of energy for all <100>/<110> STGBs. 12

13 Vacancy Formation Energy vs. Sigma Value General <110> Grain Boundary Vacancy formation energy as a function of Sigma value for all <100>/<110> STGBs. Note that only a few low Sigma boundaries exhibit formation energies different from the rest. 13

14 <100> STGB Interstitial Formation Energies Procedure 1.Atom is added 0.5 Angstroms away 2.System is relaxed via energy minimization 3.New system energy is obtained 4.Interstitial formation energy is calculated for the removed atom 5.Reiterate over all atoms within 2 nm of GB Added atom (blue) Interstitial formation energy for each position for three <100> STGBs. 0.5 Angstroms 14

15 Comparison of Formation Energies Normalized by formation energies in bulk SIA vacancy SIA vacancy SIA vacancy Comparison of the formation energies for vacancies vs. interstitials as a function of position along the grain boundary for three <100> STGBs. Interstitials tend to have lower formation energies relative to their bulk formation energy. 15

16 Interstitial Formation Energy vs. GB energy Note that GBs significantly decrease the formation energies of interstitials, as compared with those of vacancies. Cu Fe <100> <110> Interstitial formation energy as a function of energy for all <100>/<110> STGBs. 16

17 Site preference based on binding energy The relationship between the binding energy for vacancies and interstitials over all potential GB sites. Interstitial Vacancy Red line denotes whether the system energy is reduced more by an interstitial or vacancy occupying a particular site. For all potential sites, in all <100>/<110> grain boundaries sampled Energy is reduced more by interstitials occupying grain boundary sites! 17

18 Future Work Running molecular dynamics simulations to examine the influence of point defect concentration & temperature on self-diffusivity of Fe. MA Tschopp, MF Horstemeyer, M Tonks, P Millett 18

19 Future Work Fe-He interatomic potential design MA Tschopp, KN Solanki, MI Baskes, F Gao, X Sun, M Khaleel 19

20 Summary In summary 1. Grain boundary sites are more favorable energetically for interstitials than vacancies 2. Grain boundary structure affects the formation energies of vacancies and interstitials low Sigma GBs, low angle GBs, and <100> vs. <110> STGBs 3. Distance of approximately 5-8 Angstroms from boundary where formation energies for point defects are reduced Thank you!!! 20

Computational Framework for Assessing Grain Boundary Structure-Property Relationships at Nanoscale

Computational Framework for Assessing Grain Boundary Structure-Property Relationships at Nanoscale M.A. Tschopp, M.F. Horstemeyer Center for Advanced Vehicular Systems (CAVS), Mississippi State University