ENERGY LANDSCAPE OF POINT DEFECTS IN BCC METALS

Transcription

1 ENERGY LANDSCAPE OF POINT DEFECTS IN BCC METALS M.-C. Marinica, R. Alexander, L. Ventelon, L. Proville, F. Willaime CEA, DEN, Service de Recherches de Métallurgie Physique Saclay, France

2 Elementary defects induced by irradiation Materials under irradiation for the nuclear industry (e. g. high fluxes of neutrons) neutron E n pka E n -T pka = primary knocked atom T = kinetic energy transferred to the pka T Number of Frenkel pairs : n T / (2.Ed) Defect or Defect clusters Supersaturation of defects T>>E d => displacement cascade eq cv, i cv, i ( T ) interstitial vacancy Isolated selfinterstitials Isolated vacancies. Interstitial clusters. Vacancies clusters. + atomic mixing: ( 10Resplacements /displacement ) M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 2

3 Elementary defects induced by irradiation Annihilation (recombination) Clustering (agglomeration) system tend to recover the ground state (bulk state) + I + V bulk (atom on a lattice site) vacancy : + V n + V m V n+m V + V V 2 interstitial : I n + I m I n+m + Elimination on sinks Dislocation lines (network & loops), Grain-boundaries Free surfaces, voids, bubbles. I + I I 2 annihilation: I n + V m I n-m (V m-n ) + I 2 + V I Importance of the interstitials point defects under irradiation: c ( t 0) c ( t 0) i v Unlike the thermal equilibrium eq eq c ( T ) c ( T ) i v because H f i H f v M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 3

4 MORPHOLOGY OF DEFECT CLUSTERS IN METALS UNDER IRRADIATION n= D 3D 2D # defects in cluster voids SFT 2 nm loops b 2D M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 4

5 MORPHOLOGY OF DEFECT CLUSTERS IN METALS UNDER IRRADIATION n= D 3D 2D # defects in cluster voids SFT 2 nm loops b 2D M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 5

6 OUTLINE 1. Self-interstitial clusters in bcc metals 2. Vacancies in bcc metals M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 6

7 SELF-INTERSTITIAL CLUSTERS IN BCC METALS PERFORM JUNE 2012 PAGE 7 9 NOVEMBRE 2014

8 Morphology: Fe: <110> others: <111> Mobility: (e.g. resistivity Structure and kinetics of interstitial type defects n= recovery experiments) 140 K Fe ~2-10 K - others Stability: n=2-100 Competition between <110>, <111> and <100>? Fe TEM: # SIAs in cluster Fe b=<100> or ½<111> others: b = ½<111> b D. Nguyen-Manh, A. P. Horsfield, et S. L. Dudarev. PRB 73, (2006). W In situ TEM: transformations <111> to <100> and from <100> to <111> Arakawa et al., PRL (2006), Science (2007) Oxford group: X. Yi,M. L. Jenkins., M. Briceño, S. G. Roberts, Z. Zhou and M.A. Kirk: Philos. Mag (2013) M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 8

9 New type of clusters n= # SIAs in cluster F. Gao et all J. Nucl. Mater. 276, 213 (2000). C. Domain, C. S. Becquart, Phys. Rev. B 65, (2001) C.-C. Fu, F. Willaime, and P. Ordejon, Phys. Rev. Lett. 92, (2004). D.A Terentyev et al. Phys. Rev. Lett. 100, (2008) MCM F. Willaime J-P Crocombette Phys. Rev. Lett. (2012) I 2 I 8 Nano-cristals M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 9

10 MORPHOLOGY OF DEFECT CLUSTERS IN METALS UNDER IRRADIATION n= D 3D 2D # defects in cluster voids SFT 2 nm loops 3D b Prediction from atomistic simulations 2D M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 10

11 Building a new type of interstitial clusters How to combine the triangle and ring defects? I 2 I 3 I 3 I 2 3i - 1v 6i - 3v 9i - 6v 12i - 10v 4 triangles 4 rings M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 11

12 Z16 Frank-Kasper polyhedra Building larger clusters C15 I 2 C15 I 4 C15 I 6 C15 I 8 M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 12

13 Interstitial clusters in Cubic Phase of Laves C15 or MgCu2 C15 BCC M.C. Marinica, F. Willaime, J.-P. Crocombette, Phys. Rev. Lett. (2012) -C15 coherent with the BCC matrix - C15 have 3D structure in oposition to the 2D structure of dislocation loops 9 NOVEMBRE 2014 M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 13

14 TECHNICALITIES Density Functional Theory - ab initio electronic structure calculations - PWSCF (Quantum Espresso) code and VASP recentely to 432 atom supercells Formation energies of selfinterstitial clusters (in all bcc metals) Cascade simulations (Molecular Dynamics) Empirical interatomic potential for Fe - Embedded Atom Method type - Parameters fitted to bulk and point defect properties (DFT database) Energy landscape of interstitial clusters (Activation Relaxation Technique) Representation (Disconnectivity graph) M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 14

15 Large AF moment C15 I 4 C15 Clusters Very stable - 44 µ B C C15 In I1 In 1 1. Very stable 2. Immobile 3. Can growth 4. Large AF moment Growth Immobile M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 15

16 STABILITY OF C15 INTERSTITIAL CLUSTERS IN FE Stability of C15 clusters against traditional loops I para DFT calculations: -PWSCF code, atoms, - tested against pseudopotential (USPP and PAW), semicore states, LDA/GGA, cell size I C15 EAM potentials M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 16

17 Others BCC metals : I4 case 1. Not in other bcc metals para 2. Ta has interesting property C15 9 NOVEMBRE 2014 M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 17

18 LARGE INTERSTITIALS CLUSTERS ENERGY LANDSCAPE: DEVELOPMENT OF INTERATOMIC POTENTIALS FOR MODELLING RADIATION DEFECTS FOR IRON AND TUNGSTEN USING AB INITIO DATA PERFORM JUNE 2012 PAGE 18 9 NOVEMBRE 2014

19 STABILITY OF C15 INTERSTITIAL CLUSTERS IN FE Stability of C15 clusters against traditional loops I para M07: improved by including in the fit a large data base of DFT defect properties (no C15 clusters) I C15 EAM potentials *Malerba et al. JNM 406, 19 (2010) with one typo corrected in: MCM et al, PRL 108, (2012) DFT calculations, GGA-PBE, PAW M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 19

20 Our approach: EAM potential fitted on ab-initio data Data base: Ab-initio / experiment Fitting empirical potential EAM formalism 1. Bulk properties elastic constants, a0 Cohesive energy BCC, FCC 2. Ab-initio database (Typical unit cell with 128 atoms) mono-interstitial (5 configuration) di-,tri-interstials relaxed vacancy 40 Fe liquid configurations (around 100 atoms for each configuration) + F. Ercolessi and J. B. Adams, «Interatomic Potentials from First-Principles Calculations: The Force-Matching Method», Europhys. Lett., 26 (1994) 583 Tests / Transferability Validation of the potential Procedure proposed also in: M. I. Mendelev, D. J. Srolovitz, G. J. Ackland, D. Y. Sun, M. Asta, Phil. Mag., 83 (2003) 3977/ G. J. Ackland, M. I. Mendelev, D. J. Srolovitz, S. Han, A. V. Barashev, J. Phys.: Condens. Matter, 16 (2004) 2629 M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 20

21 Fitting procedure Potential i Experimental data/ ab-initio SIESTA Fitting Potential i+1 tests Relaxation DFT-GGA M03/AM04 M07 POTENTIAL On-the-fly fitting: a) Out off equilibrium configurations are not relaxed b) Equilibrium configurations are relaxed with the previous version of the potential. The ab initio positions are used only in the first cycle. Then only the energies are kept fixed. Fitting procedure is based on adjoint method in order to estimates the derivatives of the objective function M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 21

22 EAM potential fitted on ab-initio data 1. Self-trapped configurations (I4) 2. Stabilized at high temperature D.A Terentyev, T.P.C Klaver, P. Olsson, M.-C. Marinica, F. Willaime, C. Domain, L. Malerba, Phys. Rev. Lett. 100, (2008) AM DFT M07 M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 22

23 STABILITY AT LARGER SIZES IN FE (M07 EAM POTENTIAL) 1.5 nm C15 <111> loops 35 SIA cluster M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 23

24 Energy (ev) ORIGIN OF THE LOW ENERGY OF C15 CLUSTERS BCC C15 Low energy of C15 structure Fe FM C15 Volume (Å 3 /at.) FM bcc Low energy of the interface (cubic structures) «delocalized» defect : 2n BCC atoms replaced by 3n C15 atoms to make a n interstitial cluster (Eshelby inclusion) 9 NOVEMBRE 2014 M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 24

25 MORPHOLOGY OF DEFECT CLUSTERS IN METALS UNDER IRRADIATION n= D 3D 2D # defects in cluster voids SFT 2 nm loops 3D b Prediction from atomistic simulations 2D M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 25

26 NUCLEATION OF C15 CLUSTERS IN CASCADES Observed in cascades - D.J. Bacon, F. Gao, Yu.N. Osetsky JNM 276 (2000) 1 - F. Gao et al. JNM 276 (2000) 213 Cascades using M07 potential: - 20 kev ~ 5% of the SIAs are in C15 type clusters - 80 kev ~ 10% of the SIAs are in C15 type clusters (no temperature effect: 300 K, 500 K, 900 K) 13 SIA cluster (F. Gao acknowledged for providing atomic positions) M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 26

27 W EAM Potentials 1. Bulk properties elastic constants, a0 Cohesive energy BCC, FCC 2. Ab-initio database mono-interstitial (5 configuration) di-,tri-interstials relaxed vacancy 40 W liquid configurations M.-C. Marinica, L. Ventelon, M. R. Gilbert, L. Proville, S. L. Dudarev, J. Marian, G. Bencteux, and F. Willaime, «Interatomic potentials for modelling radiation defects and dislocations in tungsten», J. Phys.: Cond. Matter, 25, (2013) NOVEMBRE 2014 M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 27

28 W EAM Potential:surfaces and Gamma-surfaces Unrelaxed surface energies: (110) the most stable Relative stabilities: (110) vs (100) OK (100) vs (111) Not OK. (100) too low; (111) is not too high All others mostly OK GSF energies: - Mostly OK for EAM2 and EAM NOVEMBRE 2014 M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 28

29 W EAM Potential: Bain path Good shape and agreement with the DFT BCC, BCT minima ; FCC - saddle point It is not the case in Ackland or Dudarev potential 9 NOVEMBRE 2014 M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 29

30 W EAM Potential: Dislocation EAM2-4 the resulting Peierls barrier exhibits a single-hump profile, in agreement with the DFT. The EAM4 predicts a barrier height that agrees best with the DFT values Only EAM3 has the good glide plane. Excellent prediction for KP formation energy 1.63 ev Recent value is 1.53 ev (DFT + FK line tension model) [1]D. BRUNNER, «COMPARISON OF FLOW-STRESS MEASUREMENTS ON HIGH-PURITY TUNGSTEN SINGLE CRYSTALS WITH THE KINK-PAIR THEORY», MATER. TRANS. JIM, VOL. 41, P , M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 30

31 EAM Potentials: Discussion & Summary SIA VAC Surfaces Phonons Screw d 1,2 N>2 1,2 N>2 GSF p 0 p 0 P Gp Fe-Mendelev /- +/- +/- +/- + +/ Fe-Marinica Fe-Ackland-Mendelev /- +/- +/- +/- + +/ Fe-Gordon Mendelev /- +/- + +/ Fe-Proville /- +/- + +/- +/- +/- + + Fe-Alexander /- +/- +/- +/- + +/ /- + W-EAM4-Marinica /- +/- + +/ /- + - W-EAM3-Marinica /- + +/- +/- +/- +/ /- + Probably we try to ask too much. A good approach is to: - design potentials adapted for a well defined problem. - Use the potentials as imaginary experiment s in order to understand the physics 9 NOVEMBRE 2014 M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 31

32 Relative stability of SIA clusters TEM: two families of dislocation loops are observed under electron or neutron irradiation: <100> and 1/2<111> depending on conditions Large time-space scale simulations, cluster dynamics, KMC, OKMC, require valuable inputs for the growth of point-defect clusters Formation energy based on atomistic calculations Formation energies of large dislocation loops: potentialdependent DD05 For 1000 SIA you have a spread over 120 ev in results between various potentials: 20 % of the absolute values M07 There is a possibility to have potential independent values? Poster: Ab initio based modelling of the energetics of nanometric interstitial clusters in W Rebecca Alexander, SRMP, CEA Saclay, France <100> with two habit planes: {100} and {110} 1/2<111> {110} M.-C. Marinica, CEA Saclay EFDA Kick-off Meeting, Paris, 01 April PAGE 32

33 DI-VACANCIES IN BCC METALS PERFORM JUNE 2012 PAGE 33 9 NOVEMBRE 2014

34 Binding Energy (ev) METAL DEPENDENCE OF DI-VACANCY BINDING ENERGIES IN BCC METALS Binding Energy (ev) Binding Energy (ev) DFT Fe Mendelev 1 NN 2 NN V Nb Ta c2v A cv exp( Fb / kbt ) A: geometrical factor, Fb: binding free energy (Fb >0 attraction) L. Ventelon, F. Willaime, C.-C. Fu, M. Heran, et I. Ginoux, JNM, 425, 16 (2012) attractive repulsive Cr Mo W M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 34

35 Energy landscape of di-vacancy in tungsten - 1NN us slightly attractive or repulsive depending on DFT: exchange correlation functional, PP approximation etc - 2 NN is strongly repulsive - 3 to 5 NN slightly repulsive or attractive L. Ventelon, F. Willaime, C.-C. Fu, M. Heran, et I. Ginoux, JNM, 425, 16 (2012). a M Muzyk et al, PRB, (2011) - VASP b1 L. Ventelon et al, JNM (2012) - PWSCF b2 Ventelon et al, JNM (2012) - SIESTA c C. Becquart et al, JNM, (2010) - VASP M.-C. Marinica et al. J. Phys.: Cond. Matter, 25, , oct NOVEMBRE 2014 M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 35

36 DI-VACANCY IN BCC METALS: BAND FILLING EFFECT DFT predictions: strong band filling effect W: electronic entropy contribution should be important S ( T ) E T el F M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 36

37 Free Energy: electronic + vibrational The free energy is the sum of the electronic and vibrational free energy F( V, T, N ) F ( V, T, N ) F ( V, T, N ) el vib F ( V, T, N ) E V, T, N TS V, T, N el el el F ( V, T, N ) U ( V, T, N ) TS V, T, N vib vib vib 9 NOVEMBRE 2014 M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 37

38 Free energy: DFT vibrational contribution 2.2 k B 5.4 k B 7.0 k B Vacancy: - negative interaction entropy - 1NN gives the upper limit (-1.0 kb) SIA - 2NN gives the lower limit (-2.6 kb) kb for mono-sia in W kb for di-sia in W 9 NOVEMBRE 2014 M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 38

39 Free energy: electronic contribution F ( V, T, N ) E V,0, N F ( V, T, N ) E V,0, N E V, T, N TS ( V, T, N ) el DFT el DFT el el At 3400 K we have: - Almost 1.4 kb contribution for mono-vacancy - 1NN 0.0 kb interaction entropy - 2NN -1.0 kb interaction entropy S ( T ) E T el F 9 NOVEMBRE 2014 M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 39

40 Free energy: Di-vacancy Formation free energy Binding free energy - At 800 K 1NN di-vacancy becomes stable - At 1800 K even 2NN di-vacancy becomes stable - At 2500 K 1NN becomes more stable than 2NN 9 NOVEMBRE 2014 M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 40

41 SUMMARY Unexpected results obtained from DFT/EAM calculations in transition metals: 1. Di-vacancies in bcc metals: temperature stabilize the di-vacancy 2. Self-interstitials in bcc metals : 3D crystalline structure predicted for self-interstitial clusters in bcc metals - Very low energy structures in Fe, and to a lesser extend in Ta - are formed in cascades - can grow by capturing <110> dumbbells - have large antiferromagnetic moments in Fe - are immobile M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 41

42 Fe EAM potentials: screw dislocation Refitting by changing the weights in objective function in order to have more equilibrated potential L. Proville, D. Rodney, and M.-C. Marinica, Nature Materials, 11 (2012) 845 SIA VAC Surfaces Phonons Screw d 1,2 N>2 1,2 N>2 P Gp Fe-Mendelev /- +/- +/- +/- + +/ Fe-Marinica Fe-Ackland-Mendelev /- +/- +/- +/- + +/ M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 42

43 Fe EAM potentials: screw dislocation SIA VAC Surfaces Phonons Screw d 1,2 N>2 1,2 N>2 P Gp Fe-Mendelev /- +/- +/- +/- + +/ Fe-Marinica Fe-Ackland-Mendelev /- +/- +/- +/- + +/ Fe-Proville /- +/- +/- + + M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 43

44 Discussion: Escaping time Ackland 04 H. Xu, R. E. Stoller, Y. N. Osetsky Cascade defect evolution processes: Comparison of atomistic methods JNM, 443, (2013) 66 A97 A04 M07 D09 M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 44

45 Discussion: Escaping time Ackland 04 H. Xu, R. E. Stoller, Y. N. Osetsky Cascade defect evolution processes: Comparison of atomistic methods JNM, 443, (2013) years at 700 K A04 A04 M07 M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 45

46 Energy Goal: Finite temperature corrections of an energy landscape T= 0 K a. T > 0 K a. Changes in the relative stability of the energy landscape F=E-TS Reaction coordinate b. b. Rearranging of the energy landscape 9 NOVEMBRE 2014 M. Athènes et al J. Comp. Phys., 2010 M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 46

47 Fidelity n= n= Competition between <110>, <111> and <100>? # SIAs in cluster Exploring the energy landscape of Ab initio DFT Entropy small SIA clusters in Fe Empirical potential # atoms M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 47

48 The Activation Relaxation Technique (ART) A method to explore a potential energy surface: search for saddle points and local minima X i A. Barkema, N. Mousseau PRL (1998) ; Phys. Rev. B (2000) E. Cances, F. Legoll, M.C. Marinica, F. Willaime, J. Chem. Phys (2009) M.C. Marinica, F. Willaime, N. Mousseau, Phys. Rev. B, (2011) C i X i+1 X I is known the others minima {X i } and the saddle points {C i } must be revealed by the method: 0 K method, local information; partial Hessian Fast, adapted for defects Tested for Fe, Cu, Zr, W, Si, SiC M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 48

49 I 3 I M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 49

50 Application to I n : ART+HA I 2 I 3 I 4 M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 50

51 C15 Clusters 1. Very stable 2. Immobile 3. Can growth 4. Large AF moment CEA 26 NOV 2012 PAGE 51

52 Large AF moment C15 I 4 C15 Clusters - 44 µ B 1. Very stable 2. Immobile 3. Can growth 4. Large AF moment CEA 26 NOV 2012 PAGE 52

53 Magnetic Moment C15 I 2 C15 I 3 C15 I 4 DFT: 2.26 µ B (bulk reference) - 33 µ B - 37 µ B - 44 µ B M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 53

54 Large AF moment C15 I 4 C15 Clusters Very stable - 44 µ B 1. Very stable 2. Immobile 3. Can growth 4. Large AF moment M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 54

55 Large AF moment C15 I 4 C15 Clusters Very stable - 44 µ B 1. Very stable 2. Immobile 3. Can growth 4. Large AF moment Immobile M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 55

56 Energy (ev) - M07 EAM potential for Fe - Activation Relaxation Technique (ART) - disconnectivity graph representation O. M. Becker and M. Karplus, J. Chem. Phys. 106, 1495 (1997) D. J. Wales, M. A. Miller, and T. Walsh, Nature 394, 758 (1998) 1. Two basins: C15 and parallel dumbells ; confirms that C15 is the lowest energy structure 2. shows that it is immobile (confirmed by MD simulation over ms) 3.. Older clusters identify a particular branch of the C15 basin M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 56

57 Growth of C15 Clusters C15 n 110 C15 1 n 1 I I I C15 I 2 C15 I 3 C15 I 4 - ARTn M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 57

58 C C I I I Bulk dumbbell migration Doesn t exceed the barrier for <110> dumbbell migration M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 58

59 Bulk dumbbell C C I I I migration I I C C15 I 4 Doesn t exceed the barrier for <110> dumbbell migration M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 59

60 Example: di-interstitial NUCLEATION OF C15 CLUSTERS IN CASCADES A97 A04 M07 D09 Result depends on the potential ; M07 more reliable (according to DFT) Lower energy barriers are not excluded In the absence of low energy barrier (from right to left), nucleation from isolated SIAs (electron irradiation) is unlikely M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 60

61 Discussion Discussion «tetra-interstitial» 18 interstitials+14 vacancies Proposed in Mo R.C. Pasianot, V.P. Ramunni Comp. Mat. Sc. 48, 783 (2010) M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 61

62 SIA clusters in W <100> and ½<111> 9 NOVEMBRE 2014 M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 62

63 SIA clusters in W 9 NOVEMBRE 2014 M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 63

64 SIA clusters in W 9 NOVEMBRE 2014 M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 64

65 DISCUSSION: OTHER OBSERVED CLUSTERS D.J. Bacon, F. Gao, Yu.N. Osetsky JNM 276 (2000) 1 «This symmetric, three-dimensional cluster was created in about half the cascades simulated. Higher-order SIA clusters in -iron exhibit more complicated variants of defects such as these [F. Gao et al. JNM 276 (2000) 213]». M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 65

66 DISCUSSION:PROPERTIES OF «SESSILE» CLUSTERS F. Gao et al. JNM 276 (2000) In Fe, sessile clusters include 3D symmetrical clusters, that can grow by retaining their 3D symmetrical structure - According to the Finnis-Sinclair potential, these clusters are metastable wrt dislocation loops Present work: 8 and 19 SIA clusters - these structures were rediscovered while searching for low energy configurations - they have a well identified crystalline structure (C15 Laves phase) - they are much more stable than loops according to DFT calculations (from 4 to at least 8 SIAs) M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 66

67 Di-interstitial Z16 Frank-Kasper polyhedra 1. Low formation energy (ab initio): ev (compared to 110 cluster, 0.12 ev binding energy) 2. Very large antiferromagnetic moment: -33 µ B compared to the bulk! (-8 µ B in the case of <110> dumbbell) 3. Small formation volume (ab initio) 4. Large formation entropy (some empirical potential): + 24 k B (4 k B in the case of 110) M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 67

68 Identification of the crystal structure: C15 Laves phase Cubic Phase of Laves C15 or MgCu 2 MgCu 2 M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 68

69 Summary Based on EAM formalism we have fitted potentials for Fe and W. Using EAM-DFT interaction we were able to: Fe - predict a new class of SIA clusters in iron (using adapted potentials for W SIAs) - demonstrate the existence of <100> loops in W - show the effect of the temperature on the relative stability of <100> and <111> loops 9 NOVEMBRE 2014 M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 69

70 EAM potential fitted on experimental and ab-initio data d SIA =2.1 A a 1NN =2.44 A a 2NN =2.87 A They add to standard bulk properties: - FCC, BCC, lattice parameters + - elastic constants, - Unrelaxed vacancy - Some mono self interstitials configurations - Surface energies. F. Ercolessi and J. B. Adams Europhys. Lett., 26 (1994) 583 Force matching method on liquid iron configuration. d > 2.0 A DFT-GGA M. I. Mendelev, D. J. Srolovitz, G. J. Ackland, D. Y. Sun, M. Asta, Phil. Mag., 83 (2003) 3977/ G. J. Ackland, M. I. Mendelev, D. J. Srolovitz, S. Han, A. V. Barashev, J. Phys.: Condens. Matter, 16 (2004) 2629 M03/AM04 M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 70

71 EAM potentials fitted on experimental data The empirical potentials which are fitted only on the Johnson (1965) bulk properties are not very reliable when Johnson and Oh (1989) used for point defects such as interstitials and Harrison et al. (1989) vacancies. Haftel et al. (1990) An example: One of the best potential for iron Calder and Bacon (1993) developed by G. Ackland in 97 and which fit very well the perfect bulk properties as: Simonelli et al. (1993) - FCC, BCC, lattice parameters Ackland et al. (1997) - elastic constants, Ludwig et al. (1998) - phonons spectrum. G. J. Ackland et al. Phil. Mag. A, 75, (1997) fitted only on the bulk properties Fails for description of mono interstitial in iron: <110> dumbbell Huang scattering Migration: - E m =0.3 ev - E m (I 2 )=0.4 ev (resistivity recovery) WHY? D. Nguyen-Manh, A. P. Horsfield, et S. L. Dudarev. PRB 73, (2006). C. Domain, C. S. Becquart, Phys. Rev. B 65, (2001) C.-C. Fu, F. Willaime, and P. Ordejon, Phys. Rev. Lett. 92, (2004). M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 71

72 EAM potential fitted on ab-initio data With this new Fe potentials we are able to be in good agreement over many ab-intio data which are not included in the fit: DFT-GGA M03/AM04 M07 Exp DFT-GGA Mendel ev 2.35±0.20 ev M ev 1.84 ev 2.12 ev Rotation/migration of 1 SIA migration of mono vacancy *Malerba et al. JNM 406, 19 (2010) with one typo corrected in: Mihai-Cosmin Marinica et al, PRL 108, (2012) M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 72

73 STABILITY OF C15 INTERSTITIAL CLUSTERS IN FE Stability of C15 clusters against loops I para M07: improved by including in the fit a large data base of DFT defect properties (no C15 clusters) I C15 EAM potentials DFT calculations: PWSCF code, 250 atoms, tested against pseudopotential (USPP and PAW), semicore states, LDA/GGA, cell size M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 73

74 Relative stability of large clusters Calculations based on the anisotropic elasticity approximation there is a change in relative stability at 500 K. S. L. Dudarev, R. Bullough, et P. M. Derlet, «Effect of the alphagamma Phase Transition on the Stability of Dislocation Loops in bcc Iron», Phys. Rev. Lett., vol. 100, , (2008). J. Marian, B. D. Wirth, et J. M. Perlado, «Mechanism of Formation and Growth of $?100?$ Interstitial Loops in Ferritic Materials», Phys. Rev. Lett., 88, , [H. Xu, R. E. Stoller, Y. N. Osetsky, et D. Terentyev, «Solving the Puzzle of 100 Interstitial Loop Formation in bcc Iron», Physical Review Letters, vol. 110, (2013). M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER PAGE 74

75 Relative stability of large clusters <100> with two habit planes: {100} and {110} 1/2<111> {110} Dudarev 2005 Ackland 97 Formation energies of large dislocation loops: potentialdependent For 1000 SIA you have a spread over 120 ev in results between various potentials: 20 % of the absolute values AM 2004 M07 M.-C. Marinica ICTP-IAEA Conference Trieste NOVEMBER