ATOMISTIC MODELING OF THE BRITTLE TO DUCTILE TRANSITION OF SILICON. Norwegian University of Science and Technology

Transcription

1 ATOMISTIC MODELING OF THE BRITTLE TO DUCTILE TRANSITION OF SILICON Christian Thaulow Norwegian University of Science and Technology

2 Multiscale Material Modelling and Testing Failure of materials and structures involves many length-scales, from the macroscopic scale to the level of Angstrom where chemical bonds are found.

3 Fracture Mechanics Historical Development

4 Crack Tip Prosess Zone PROSESS ZONE

5 A twinned region and the nucleation of a new grain are visible Farkas, 2005

6 Top Down Analysis Continuum Mechanics Dynamics Phase transformations Atomistic- and Multiscale Modeling Bottom Up Analysis

7 From LARGE Scale testing: 100MN and 10 minutes to Atomistic Mechanics: 10pN and 1 femtosecond

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9 Atomistic Failure Mechanisms

10 Fracture of Silicon

11 Fracture of Silicon Silicon wafers Silicon nanorods Fatal Nature of Cracking in Fatal Silicon nature Devices New Silicon Nanorod Solar Cells Use 99% Less Material

12 What about the fracture toughness? Greer and Hosson (2011) Plasticity in small sized metallic systems: Intrinsic vs. extrinsic size effects Progress in Material Science

13 Brittle to Ductile Transition (BDT) single crystals silicon EXPERIMENTS 1989 Sharp transition from brittle to ductile behavior Samuel and Roberts, 1989

14 Silicon crystal - Diamond fcc structure

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16 Modeling of silicon: Interatomic Potential Several empirical potentials fitted to experimental data: Stillinger-Weber 1 Tersoff 2 EDIP (Environment dependent Interatomic Potential) 3 Problems: 1. Inaccurate description of silicon bonds close to fracture 2. Incorrect predictions of fracture modes (ductility and crack opening instead of brittle). Coupling Tight-Binding or QM with empirical potentials 1. TB/EDIP and TB/Tersoff coupling 4,5 2. DFT/Stillinger-Weber coupling 6 Can model brittle fracture well but too small reactive regions for dislocation emission and plasticity. 1. Stillinger and Weber, PRB 31(8), 5262 (1985); 2. Tersoff, PRL 56(6), 632 (1986); 3. Justo et al, PRB 58(5), 2539 (1998); 4. Abraham et al, Europhys. Lett. 44, 783 (1998); 5. Bernstein and Hess, PRL 91(2), (2003); 6.Csanyi et al, PRL 93(17), (2004).

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18 Reactive force field (ReaxFF) 1 1. A.C.T. van Duin et al, J Phys Chem A 2001; van Duin et al, J Phys Chem A 2003; Chenoweth et al, J Phys Chem A,

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20 never break transition LJ can break ground state

21 QM fitting 28 parameters (compare LJ with 2 parameters)

22 Mechanical properties based on ReaxFF potential Surface energy γ γ ( 110) ( 111) ReaxFF (N/m) Experiment (N/m) Young s Modulus ReaxFF (GPa) Experiment (GPa) E[100] E[110] E[111] Fracture toughness Mode I, 300K ReaxFF (MPa m) Experiment (MPa m) [111] γ is 0.16 ev/å US 2 ; DFT value: 0.13 ev/å Cook, J Mater. Sci. 41, 841 (2006); 2. Hausch et al, PRL 82, 3823 (1999); 3. Wortman and Evans, J. Appl. Phys. 36, 153 (1965); 4. Buehler et al, PRL 99, (2007); 5. Fitzgerald et al, J Mater. Res. 17, 683 (2002); 6. Godet et al, J Phys: Condens. Mater. 15, 6943 (2003).

23 Case 1: {110} cleavage fracture plane in the <100> and <110> directions. Semiconductors, MEMS devices Case 2: {111} cleavage fracture plane in the <110> and <112> directions. Fundamental studies Case 3: {100} cleavage fracture plane In the <011> direction. Not observed in practice Case 1 and 2: Brittle fracture at all temperatures

24 Case 3: {100} cleavage fracture plane in the <011> direction atoms, 200Å long and wide, thickness 15Å

25 Ductile Brittle - Transition Fracture energy 900K 1200K 1500K Ductile 850K 800K? DBT 700K 200K 500K 600K Brittle Temperature

26 200K brittle

27 500K still brittle Kslow 500Kslow ,02 0,04 0,06 0,08 0,1 0,12

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29 BRITTLE DUCTILE Atomistic Study of Crack-Tip Cleavage to Dislocation Emission Transition in Silicon Single Crystal Dipanjan Sen,Christian Thaulow Stella V. Schieffer Alan Cohen and Markus J. Buehler PRL 104, (2010)

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31 Crack motion at different temperatures 200K 47ps 200K 55ps 200K 60ps Crack propagation snapshots at low Temp- brittle fracture 1200K 36ps 1200K 46ps 1200K 55ps Crack propagation snapshots at high Temp- ductile fracture (slip vector analysis) 1 1. Zimmermann et al, PRL 87, (2001).

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33 Atomistic mechanism at the crack tip at time of dislocation emission [100] [011] 1200K 41ps Ledge formation 5-7 ring cluster formation around crack tip

34 Details of crack tip motion at low and high T [100] [011] [100] [011] 200 K: Crack proceeds in a jagged manner by small steps along (111) planes 200K 55ps 200K 56ps [100] [011] [100] [011] 1200 K: Crack forms ledges and small amorphous zones consisting of 5-7 defects 1200K K 0.040

35 a b

36 Schematic of crack tip mechanisms observed At low T, brittle fracture by small crack steps on (111) plane, expected as (111) surface energies are lower. At high T, dislocation emission followed by crack arrest, by a cascade of mechanisms: a) small ( 10 Å) disordered zone formed consisting of 5-7 rings at crack tip reducing mode I stress intensity at the tip b) ledge formation on (111) planes c) dislocation emission at the ledge due to increased mode II loading

37 Larger model Increase the thickness of the model from 15 to 100 Å, atoms Example of crack front structure at two positions along the crack front. Thaulow, C; Sen, D and Buehler MJ (2011), Atomistic Study of the Effect of Crack Tip Ledges on the Nucleation of Dislocations in Silicon Single Crystals at Elevated Temperature Materials Science & Engineering A 528, pp

38 Several dislocation loop nucleation events seen Crack front is rough due to formation of several ledges

39 Analysis of the partial dislocation loop emission at the crack tip on the lower crack surface The crack did not come to a complete arrest, as was the case for the thinner specimen

40 Experiments: Formation of ledges along the crack front {111} and {110} orientations Observed an almost continuous array of ledges on the crack surface.

41 Ledges are formed naturally on the {001} system Other mechanisms must be responsible for ledge formation observed for the {111} and {110} orientations Inhomogeneous materials Crack propagation on parallel planes Crack front waves Mirror-mist-hackle mechanisms

42 bcc_fe

43 Dislocation emission at ledges?? Introduction of ledges along the crack front in the models angledstep_x110y1-10 angledjog_x111y1-10

44 step_x110y1-10, atoms step_x111y11-2, atoms step_x111y1-10, atoms jog_x110y1-10, atoms Angledjog_x111y1-10 jog_x111y11-2, atoms jog_x111y1-10, atoms 256 processors, GRASP run on Njord Result: We were not able to generate dislocations from pre-formed ledges Si100_ledge100_x100y011

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47 Crack front waves Can crack front waves explain the roughness of cracks? E. Bouchaud, J.-P. Bouchaud, D. Fisher, S. Ramananthan, J. Rice

48 Thank you

49 Everything is waves Effect of reflected Rayleigh waves on arrest of propagating cracks Thaulow, C and Burget W (1990) «The emission of Rayleigh waves from brittle fracture initiation, and the possible effect of the reflected waves on crack arrest» Fatigue and Fracture of Engineering materials and Structures, Vol 13, No 4, pp

50 Rayleigh Waves Effect of surface waves emitted from the crack tip Rayleigh wave Process zone Plastic zone

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52 ASTM crack arrest test

53 Shaddow optics The diameter of the caustic is proportional with the stress intensity factor

54 The crack speed slows down when the stress intensity starts to increase Why??

55 Extension of the crack surface

56 Acoustic Emission transducers

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