Dislocation-based crack initiation and propagation in single-crystal SrTiO3

Abstract

Understanding the irreversible deformation (dislocation activation and crack formation) of functional oxides, based on which various advanced electronic devices are fabricated, is critical for the optimal structural design and mechanical reliability. Here, we demonstrate the dislocation-based crack initiation and propagation in a model perovskite, single-crystal SrTiO3, at small scale. Using nanoindentation tests with spherical tips and etch pit study, we identify the sequence of the irreversible deformation events occurred in single-crystal (001) SrTiO3. For a locally stressed volume that is free of pre-existing cracks, the material undergoes the following processes: (1) purely elastic deformation; (2) dislocation activation on primary slip planes that are 45° inclined to the surface; (3) dislocation activation on secondary slip planes perpendicular to the surface; (4) crack initiation by dislocation pile-up; followed by (5) concurrent crack propagation and dislocation multiplication and motion at higher loads. Specifically, we focus on the crack formation caused by the dislocation pile-up beneath the spherical indenter. We also identify the favorable crack propagation planes to be {110} when the (001) surface is indented. These findings in cubic SrTiO3 are believed to be applicable for other ceramic materials with cubic structure.

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References

  1. 1

    Nakamura A, Matsunaga K, Tohma J, Yamamoto T, Ikuhara Y (2003) Conducting nanowires in insulating ceramics. Nat Mater 2(7):453–456

    CAS  Article  Google Scholar 

  2. 2

    Ikuhara Y (2009) Nanowire design by dislocation technology. Prog Mater Sci 54(6):770–791

    CAS  Article  Google Scholar 

  3. 3

    Szot K, Speier W, Bihlmayer G, Waser R (2006) Switching the electrical resistance of individual dislocations in single-crystalline SrTiO3. Nat Mater 5(4):312–320

    CAS  Article  Google Scholar 

  4. 4

    Sun B, Haunschild G, Polanco C, Ju JZ, Lindsay L, Koblmuller G, Koh YK (2019) Dislocation-induced thermal transport anisotropy in single-crystal group-III nitride films. Nat Mater 18(2):136–140

    CAS  Article  Google Scholar 

  5. 5

    Khafizov M, Pakarinen J, He L, Hurley DH (2019) Impact of irradiation induced dislocation loops on thermal conductivity in ceramics. J Am Ceram Soc 102:7533–7542

    CAS  Article  Google Scholar 

  6. 6

    Kim SI, Lee KH, Amun H, Kim HS, Hwang SW, Roh JW, Yang DJ, Shin WH, Li XS, Lee YH, Snyder GJ, Kim SW (2015) Dense dislocation arrays embedded in grain boundaries for high-performance bulk thermoelectrics. Science 348:109–114

    CAS  Article  Google Scholar 

  7. 7

    Ren P, Höfling M, Koruza J, Lauterbach S, Jiang X, Frömling T, Khatua DK, Dietz C, Porz L, Ranjan R, Kleebe HJ, Rödel J (2019) High temperature creep-mediated functionality in polycrystalline barium titanate. J Am Ceram Soc 103:1891–1902

    Article  CAS  Google Scholar 

  8. 8

    Di Maio D, Roberts SG (2005) Measuring fracture toughness of coatings using focused-ion-beam-machined microbeams. J Mater Res 20(02):299–302

    Article  CAS  Google Scholar 

  9. 9

    Jaya BN, Kirchlechner C, Dehm G (2015) Can microscale fracture tests provide reliable fracture toughness values? A case study in silicon. J Mater Res 30(05):686–698

    CAS  Article  Google Scholar 

  10. 10

    Uchic MD, Dimiduk DM, Florando JN, Nix WD (2004) Sample dimensions influence strength and crystal plasticity. Science 305:986

    CAS  Article  Google Scholar 

  11. 11

    Li J, Wang H, Zhang X (2019) Nanoscale stacking fault–assisted room temperature plasticity in flash-sintered TiO2. Sci Adv 5:eaaw5519

    CAS  Article  Google Scholar 

  12. 12

    Fang X, Rasinski M, Kreter A, Kirchlechner C, Linsmeier C, Dehm G, Brinckmann S (2019) Plastic deformation of tungsten due to deuterium plasma exposure: Insights from micro-compression tests. Scripta Mater 162:132–135

    CAS  Article  Google Scholar 

  13. 13

    Ghidelli M, Sebastiani M, Johanns KE, Pharr GM (2017) Effects of indenter angle on micro-scale fracture toughness measurement by pillar splitting. J Am Ceram Soc 100(12):5731–5738

    CAS  Article  Google Scholar 

  14. 14

    Bruns S, Petho L, Minnert C, Michler J, Durst K (2019) Fracture toughness determination of fused silica by cube corner indentation cracking and pillar splitting. Mater Des. https://doi.org/10.1016/j.matdes.2019.108311

    Article  Google Scholar 

  15. 15

    Sebastiani M, Johanns KE, Herbert EG, Carassiti F, Pharr GM (2014) A novel pillar indentation splitting test for measuring fracture toughness of thin ceramic coatings. Phil Mag 95(16–18):1928–1944

    Google Scholar 

  16. 16

    Lodes MA, Hartmaier A, Göken M, Durst K (2011) Influence of dislocation density on the pop-in behavior and indentation size effect in CaF2 single crystals: Experiments and molecular dynamics simulations. Acta Mater 59(11):4264–4273

    CAS  Article  Google Scholar 

  17. 17

    Oliver WC, Pharr GM (1992) An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J Mater Res 7(6):1564–1583

    CAS  Article  Google Scholar 

  18. 18

    Freund LB, Suresh S (2003) Thin film materials-Stress, Defect formation and surface evolution. Cambridge University Press, Cambridge

    Google Scholar 

  19. 19

    Fang X, Kreter A, Rasinski M, Kirchlechner C, Brinckmann S, Linsmeier C, Dehm G (2018) Hydrogen embrittlement of tungsten induced by deuterium plasma: Insights from nanoindentation tests. J Mater Res 33(20):3530–3536

    CAS  Article  Google Scholar 

  20. 20

    Schuh CA, Mason JK, Lund AC (2005) Quantitative insight into dislocation nucleation from high-temperature nanoindentation experiments. Nat Mater 4(8):617–621

    CAS  Article  Google Scholar 

  21. 21

    Mason JK, Lund AC, Schuh CA (2006) Determining the activation energy and volume for the onset of plasticity during nanoindentation. Phys Rev B 73(5):054102

    Article  CAS  Google Scholar 

  22. 22

    Gao Y, Bei H (2016) Strength statistics of single crystals and metallic glasses under small stressed volumes. Prog Mater Sci 82:118–150

    CAS  Article  Google Scholar 

  23. 23

    Johnston WG (1960) An observation of crack formation in MgO. Phil Mag 5(52):407–408

    CAS  Article  Google Scholar 

  24. 24

    Ku RC, Johnston TL (1964) Fracture strength of MgO bicrystals. Phil Mag 9(98):231–247

    CAS  Article  Google Scholar 

  25. 25

    Swain MV, Lawn BR (1969) A study of dislocation arrays at spherical indentations in LiF as a function of indentation stress and strain. Phys Stat Sol 35:909–923

    CAS  Article  Google Scholar 

  26. 26

    Hagan JT (1979) Micromechanics of crack nucleation during indentations. J Mater Sci 14:1975–2980. https://doi.org/10.1007/BF00611482

    Article  Google Scholar 

  27. 27

    Lewin M, Baeumer C, Gunkel F, Schwedt A, Gaussmann F, Wueppen J, Meuffels P, Jungbluth B, Mayer J, Dittmann R, Waser R, Taubner T (2018) Nanospectroscopy of infrared phonon resonance enables local quantification of electronic properties in doped SrTiO3 ceramics. Adv Func Mater 28(42):1802834

    Article  CAS  Google Scholar 

  28. 28

    Heisig T, Baeumer C, Gries UN, Mueller MP, La Torre C, Luebben M, Raab N, Du H, Menzel S, Mueller DN, Jia CL, Mayer J, Waser R, Valov I, De Souza RA, Dittmann R (2018) Oxygen exchange processes between oxide memristive devices and water molecules. Adv Mater 30(29):1800957

    Article  CAS  Google Scholar 

  29. 29

    Taeri S, Brunner D, Sigle W, Rühle M (2004) Deformation behaviour of strontium titanate between room temperature and 1800 K under ambient pressure. Z Mettllkd 95(6):433

    CAS  Article  Google Scholar 

  30. 30

    Gumbsch P, Taeri-Baghbadrani S, Brunner D, Sigle W, Ruhle M (2001) Plasticity and an inverse brittle-to-ductile transition in strontium titanate. Phys Rev Lett 87(8):085505

    CAS  Article  Google Scholar 

  31. 31

    Patterson EA, Major M, Donner W, Durst K, Webber KG, Rodel J (2016) Temperature-dependent deformation and dislocation density in SrTiO3 (001) single crystals. J Am Ceram Soc 99(10):3411–3420

    CAS  Article  Google Scholar 

  32. 32

    Fang X, Ding K, Janocha S, Minnert C, Rheinheimer W, Frömling T, Durst K, Nakamura A, Rödel J (2020) Nanoscale to microscale reversal in room-temperature plasticity in SrTiO3 by tuning defect concentration. Scripta Mater 188:228–232

    CAS  Article  Google Scholar 

  33. 33

    Fang X, Porz L, Ding K, Nakamura A (2020) Bridging the gap between bulk compression and indentation test on room-temperature plasticity in oxides: case study on SrTiO3. Crystals https://doi.org/10.3390/cryst10100933

  34. 34

    Javaid F, Stukowski A, Durst K (2017) 3D Dislocation structure evolution in strontium titanate: spherical indentation experiments and MD simulations. J Am Ceram Soc 100(3):1134–1145

    CAS  Article  Google Scholar 

  35. 35

    Javaid F, Johanns KE, Patterson EA, Durst K (2018) Temperature dependence of indentation size effect, dislocation pile-ups, and lattice friction in (001) strontium titanate. J Am Ceram Soc 101(1):356–364

    CAS  Article  Google Scholar 

  36. 36

    Javaid F, Bruder E, Durst K (2017) Indentation size effect and dislocation structure evolution in (001) oriented SrTiO3 Berkovich indentations: HR-EBSD and etch-pit analysis. Acta Mater 139:1–10

    CAS  Article  Google Scholar 

  37. 37

    Kondo S, Mitsuma T, Shibata N, Ikuhara Y (2016) Direct observation of individual dislocation interaction processes with grain boundary. Sci Adv 2:e1501926

    Article  CAS  Google Scholar 

  38. 38

    Shim S, Bei H, George EP, Pharr GM (2008) A different type of indentation size effect. Scripta Mater 59(10):1095–1098

    CAS  Article  Google Scholar 

  39. 39

    Bei H, Xia YZ, Barabash RI, Gao YF (2016) A tale of two mechanisms: Strain-softening versus strain-hardening in single crystals under small stressed volumes. Scripta Mater 110:48–52

    CAS  Article  Google Scholar 

  40. 40

    Gaillard Y, Tromas C, Woirgard J (2010) Pop-in phenomenon in MgO and LiF: Observation of dislocation structures. Philos Mag Lett 83(9):553–561

    Article  CAS  Google Scholar 

  41. 41

    Tromas C, Gaillard Y, Woirgard J (2006) Nucleation of dislocations during nanoindentation in MgO. Phil Mag 86(33–35):5595–5606

    CAS  Article  Google Scholar 

  42. 42

    Gaillard Y, Tromas C, Woirgard J (2003) Study of the dislocation structure involved in a nanoindentation test by atomic force microscopy and controlled chemical etching. Acta Mater 51(4):1059–1065

    CAS  Article  Google Scholar 

  43. 43

    Li W, Bei H, Qu J, Gao Y (2013) Effects of machine stiffness on the loading–displacement curve during spherical nano-indentation. J Mater Res 28(14):1903–1911

    CAS  Article  Google Scholar 

  44. 44

    Johnson KL (1985) Contact Mechanics. Cambridge University Press, Cambridge, London

    Book  Google Scholar 

  45. 45

    Lawn BR, Cook RF (2011) Probing material properties with sharp indenters: a retrospective. J Mater Sci 47(1):1–22. https://doi.org/10.1007/s10853-011-5865-1

    CAS  Article  Google Scholar 

  46. 46

    Morris JR, Bei H, Pharr GM, George EP (2011) Size effects and stochastic behavior of nanoindentation pop in. Phys Rev Lett 106(16):165502

    CAS  Article  Google Scholar 

  47. 47

    Wachtman JB, Cannon WR, Matthewson MJ (2009) Mechanical properties of ceramics. Wiley, Hoboken

    Book  Google Scholar 

  48. 48

    Moon W-J, Saka H (2000) Toughening of a brittle material by means of dislocation subboundaries. Philos Mag Lett 80(7):461–466

    CAS  Article  Google Scholar 

  49. 49

    Moon W-J, Ito T, Uchimura S, Saka H (2004) Toughening of ceramics by dislocation sub-boundaries. Mater Sci Eng A 387–389:837–839

    Article  CAS  Google Scholar 

  50. 50

    Xu G, Argon AS, Ortiz M (1997) Critical configurations for dislocation nucleation from crack tips. Philos Mag A 75(2):341–367

    CAS  Article  Google Scholar 

  51. 51

    Meyer K, Gragert E (1964) Deformations- und RiBstrukturen in NaCl-Kristallen bei der StoBbearbeitung. Phys Stat Sol 6:803–815

    CAS  Article  Google Scholar 

  52. 52

    Stroh AN (1957) A theory of the fracture of metals. Adv Phys 6(24):418–465

    Article  Google Scholar 

  53. 53

    Koehler JS (1952) The production of large tensile stresses by dislocations. Phys Rev 85(3):480–481

    Article  Google Scholar 

  54. 54

    Zener C (1948) The micro-mechanism of fracture, Fracturing of metals. Cleveland, American Society for Metals , Cleveland, pp 3–31

    Google Scholar 

  55. 55

    Stroh AN (1954) The formation of cracks as a result of plastic flow. Proc R Soc A Math Phys Eng Sci 223:404–414

    Google Scholar 

  56. 56

    Stroh AN (1955) The Formation of Cracks in Plastic Flow II. Proc R Soc A Math Phys Eng Sci 232:548–560

    Google Scholar 

  57. 57

    Xiao ZM, Chen BJ (2001) Stress analysis for a Zener-Stroh crack interacting with a coated inclusion. Int J Solids Struct 38:5007–5018

    Article  Google Scholar 

  58. 58

    Fan H, Xiao ZM (1997) A Zener-Stroh crack near an interface. Int J Solids Struct 34(22):2829–2842

    Article  Google Scholar 

  59. 59

    Zhang Y, Ma L (2019) Surface Zener-Stroh crack model to slip band due to contact. Arch Appl Mech 90(2):221–234

    Article  Google Scholar 

  60. 60

    Woo S, Jeong H, Lee SA, Seo H, Lacotte M, David A, Kim HY, Prellier W, Kim Y, Choi WS (2015) Surface properties of atomically flat poly-crystalline SrTiO3. Sci Rep 5:8822

    Article  CAS  Google Scholar 

  61. 61

    Lathabai S, Rödel J, Dabbs T, Lawn BR (1991) Fracture mechanics model for subthreshold indentation flaws: Part I Equilibrium fracture. J Mater Sci 26:2157–2168. https://doi.org/10.1007/BF00549183

    CAS  Article  Google Scholar 

  62. 62

    Hagan JT (1980) Shear deformation under pyramidal indentations in soda-lime glass. J Mater Sci 15:1417–1424. https://doi.org/10.1007/BF00752121

    CAS  Article  Google Scholar 

  63. 63

    Swain MV, Hagan JT (1976) Indentation plasticity and the ensuing fracture of glass. J Phys D Appl Phys 9:2201

    CAS  Article  Google Scholar 

  64. 64

    Basu S, Barsoum MW, Kalidindi SR (2006) Sapphire: a kinking nonlinear elastic solid. J Appl Phys 99(6):063501

    Article  CAS  Google Scholar 

  65. 65

    Barsoum MW, Murugaiah A, Kalidindi SR, Zhen T (2004) Kinking nonlinear elastic solids, nanoindentations, and geology. Phys Rev Lett 92:255508

    CAS  Article  Google Scholar 

  66. 66

    Lawn B (1993) Fracture of brittle solids. Cambridge University Press, Cambridge

    Book  Google Scholar 

  67. 67

    Anderson TL (2005) Fracture Mechanics_Fundamentals and Applications. CRC Press, New York

    Google Scholar 

  68. 68

    Frank FC, Lawn BR (1967) On the theory of Hertzian fracture. Proc R Soc A Math Phys Eng Sci 299:291–307

    Google Scholar 

  69. 69

    Weertman J (1996) Dislocation based Fracture Mechanics. World Scientific Publishing Co Pte Ltd, New York

    Book  Google Scholar 

  70. 70

    Sudharshan Phani P, Oliver WC (2020) Critical examination of experimental data on strain bursts (pop-in) during spherical indentation. J Mater Res. https://doi.org/10.1557/jmr.2019.416

    Article  Google Scholar 

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Acknowledgements

X. Fang gratefully acknowledges the financial support of Athene Young Investigator Programme (TU Darmstadt) and the Deutsche Forschungsgemeinschaft (DFG, No. 414179371). K. Ding thanks the DFG for financial support (FA 1662/1-1). K. Durst thanks the DFG for financial support (DU 424/11-1). A. Nakamura acknowledges the financial support of JST PRESTO Grant Number JPMJPR199A and JSPS KAKENHI Grant Numbers JP19H05786, JP17H06094 and JP18H03840, Japan. We thank Prof. J. Rödel for the helpful discussion and comments. The helpful comments from the anonymous reviewers are also gratefully acknowledged.

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Fang, X., Ding, K., Minnert, C. et al. Dislocation-based crack initiation and propagation in single-crystal SrTiO3. J Mater Sci 56, 5479–5492 (2021). https://doi.org/10.1007/s10853-020-05587-2

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