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arxiv: 2606.03818 · v1 · pith:K7OSNIZDnew · submitted 2026-06-02 · ❄️ cond-mat.mtrl-sci

Fracture energy of 6H-SiC at the microscale: effects of testing geometry and notch preparation

Zhuoqi Lucas Li , Siyang Wang , Ao Li , James O. Douglas , Florian Bouville , Oriol Gavalda-Diaz , Katharina Tinka Marquardt , Finn Giuliani This is my paper

Pith reviewed 2026-06-28 09:08 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci
keywords fracture energy6H-SiCmicroscale testingdouble cantilever beamsingle cantilever beamfocused ion beamnotch preparationannealing
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The pith

Double cantilever beam tests measure 7.5 J/m² fracture energy for the 6H-SiC {10-10} plane while gallium FIB-notched single cantilever beams give more than twice that value.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper measures fracture energy of single-crystal 6H-SiC on the {10-10} plane at the microscale using two geometries. Double cantilever beam specimens under displacement control produce stable crack growth and a repeatable value of 7.5 ± 0.3 J/m². Single cantilever beam specimens prepared by gallium focused ion beam notching return fracture energies more than double this figure. The authors link the elevation to gallium implantation and near-notch residual stresses, and show that vacuum annealing lowers the SCB values into agreement with the DCB result while argon annealing is less effective. The work therefore isolates the separate influences of test geometry and notch preparation on measured fracture properties in ceramics.

Core claim

DCB tests on 6H-SiC yield a fracture energy of 7.5 ± 0.3 J/m² for the {10-10} plane with stable crack growth; SCB tests notched by Ga FIB produce values over twice as high due to implantation and residual stresses, and vacuum annealing brings the SCB results into agreement with DCB while near-cryogenic notching and argon annealing do not.

What carries the argument

Comparison of double cantilever beam (DCB) and single cantilever beam (SCB) microscale geometries combined with gallium focused ion beam notching at varying currents and subsequent vacuum or argon annealing.

If this is right

  • Stable crack growth under displacement control in DCB geometry enables reliable extraction of intrinsic fracture energy.
  • Ga FIB notching at higher currents further increases the apparent fracture energy in SCB tests.
  • Near-cryogenic FIB notching does not eliminate the elevation in measured energy.
  • Vacuum annealing after FIB notching reduces SCB values to match DCB results.
  • Argon annealing is less effective than vacuum annealing at removing the preparation-induced elevation.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Microscale fracture measurements on other brittle ceramics are likely to show similar sensitivity to FIB preparation.
  • DCB geometry may be the more robust choice when the goal is to obtain preparation-independent values.
  • Standard post-FIB vacuum annealing protocols could improve reproducibility across FIB-based fracture studies.
  • The 7.5 J/m² benchmark can be used to test atomistic models of cleavage on the {10-10} plane in SiC.

Load-bearing premise

The DCB result is the intrinsic fracture energy of the {10-10} plane and all differences seen in SCB tests come only from gallium implantation and residual stresses rather than from unaccounted differences in geometry or loading.

What would settle it

A direct measurement showing identical crack-initiation loads in DCB and SCB specimens when both are prepared without gallium ion exposure or when residual stress is removed from FIB-notched SCB specimens.

Figures

Figures reproduced from arXiv: 2606.03818 by Ao Li, Finn Giuliani, Florian Bouville, James O. Douglas, Katharina Tinka Marquardt, Oriol Gavalda-Diaz, Siyang Wang, Zhuoqi Lucas Li.

Figure 1
Figure 1. Figure 1: Geometries employed for micromechanical fracture toughness/energy measurement. (a) Schematic and (c) electron micrograph of a DCB. (b) Schematic and (d) electron micrograph of an SCB with a straight-through notch. For the DCB geometry, l denotes the beam height, 2d the total cantilever arm width, a the crack length, and t the beam thickness. For the SCB geometry, w denotes the beam width, a the crack lengt… view at source ↗
Figure 2
Figure 2. Figure 2: (a) The DCB testing process, illustrating slow and stable crack growth along the prismatic {101ത0} plane at different time points. At 540 s, retraction of the indenter tip results in crack closure. (b) Fracture along the prismatic plane of the 6H-SiC single crystal in DCB 4, highlighting the straight and smooth fracture surface created during loading. Scale bars: 3 µm. (c) Fracture energy values measured a… view at source ↗
Figure 3
Figure 3. Figure 3: (a) Fracture energy, Gc, and (b) fracture toughness, KIc, measured for the eight sample groups (RT10, RT30, Cryo10, Cryo30, Cryo50, Va600, Va800, and Ar800). Bar heights indicate the mean value for each group, and open diamonds denote individual measurements. Error bars represent standard deviations. Dashed horizontal lines mark the corresponding values obtained from DCB tests (Gc = 7.5 J/m2 in (a) and KIc… view at source ↗
Figure 4
Figure 4. Figure 4: SEM images of the SCBs after annealing treatment: (a) 600 °C in vacuum for 1 h (Va600), (b) 800 °C in vacuum for 1 h (Va800) and (c) 800 °C in Ar for 1 h (Ar800). Red arrows in (a) and (b) highlight the representative surface features observed after annealing. Scale bar: 5 µm. (d) Higher-magnification view of the notch region outlined in (c), showing Ga particles within the notch [PITH_FULL_IMAGE:figures/… view at source ↗
Figure 5
Figure 5. Figure 5: EDS Ga maps overlaid on SEM images for the (a) as-fabricated (non-annealed) specimen and specimens annealed for 1 h at (b) 600 °C in vacuum (Va600), (c) 800 °C in vacuum (Va800), and (d) 800 °C in Ar (Ar800). Red arrows highlight the same representative surface features in [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
read the original abstract

Micromechanical testing enables small-scale fracture energy measurements, but values depend strongly on geometry and specimen preparation. Here, the fracture energy of the single-crystal 6H-SiC {10-10} plane was measured using microscale double cantilever beam (DCB) and single cantilever beam (SCB) geometries. DCBs showed stable crack growth under displacement control and obtained 7.5 +- 0.3 J/m2. In contrast, SCBs notched by a Ga focused ion beam gave fracture energies over twice this value, indicating Ga implantation and near-notch residual stresses. Increasing the final notching current increased the measured fracture energy further. Although near-cryogenic notching limited ion-beam-induced damage, it did not reconcile SCB-derived values with DCB test results. Vacuum annealing substantially lowered the fracture energy and brought SCB results into close agreement with DCB measurements, whereas annealing in argon was less effective. Our findings highlight the importance of careful sample preparation and testing geometry selection for reliable fracture property measurement in ceramic materials.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 3 minor

Summary. The manuscript reports microscale fracture toughness measurements on the {10-10} cleavage plane of single-crystal 6H-SiC. Double-cantilever-beam (DCB) specimens tested under displacement control exhibit stable crack growth and yield a fracture energy of 7.5 ± 0.3 J/m². Single-cantilever-beam (SCB) specimens notched by Ga focused-ion-beam milling return values more than twice as large; the elevation is ascribed to Ga implantation and near-notch residual stresses. Increasing the final FIB current further raises the measured energy, while near-cryogenic milling does not eliminate the discrepancy. Vacuum annealing of the SCBs lowers the fracture energy into close agreement with the DCB result, whereas argon annealing is less effective. The work concludes that both testing geometry and notch preparation must be chosen carefully for reliable ceramic fracture data.

Significance. If the DCB value is confirmed to be free of preparation artifacts, the result supplies a much-needed microscale benchmark for the intrinsic fracture energy of 6H-SiC, a material central to high-temperature power electronics and structural applications. The demonstration that vacuum annealing can largely remove FIB-induced elevation offers a concrete protocol that other groups can adopt. The geometry comparison also supplies a cautionary data set for the growing field of micromechanical fracture testing.

major comments (2)
  1. [Results] The central claim that the DCB result (7.5 ± 0.3 J/m²) represents the intrinsic {10-10} fracture energy while the SCB elevation is caused solely by Ga implantation and residual stresses requires that the two cantilever geometries return identical values on a preparation-free specimen. No finite-element validation or control experiment (identical notch preparation on both geometries, or FIB-free notching on DCBs) is presented to establish this equivalence. Differences in moment arm, crack-front constraint, or the compliance-based data-reduction formulas could therefore contribute to the observed factor-of-two discrepancy (Results section, Fig. 5 and associated text).
  2. [Methods] Error propagation and statistical treatment of the reported uncertainties are not described. The DCB value is given as 7.5 ± 0.3 J/m², yet the number of independent specimens, the scatter within each geometry, and the propagation of load, displacement, and dimensional uncertainties into G are not stated (Methods and Results sections).
minor comments (3)
  1. [Abstract] The abstract states that “increasing the final notching current increased the measured fracture energy further,” but the corresponding data are not shown in a figure or table; a supplementary plot or table would strengthen the claim.
  2. [Throughout] Notation for the fracture energy (G or Γ) is used inconsistently between the abstract and the main text; a single symbol should be adopted throughout.
  3. [Methods] The orientation of the {10-10} plane relative to the cantilever axes is stated only in the abstract; a schematic in the Methods section would clarify the loading configuration.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which help clarify the interpretation of our results. We respond to each major comment below.

read point-by-point responses

  1. Referee: [Results] The central claim that the DCB result (7.5 ± 0.3 J/m²) represents the intrinsic {10-10} fracture energy while the SCB elevation is caused solely by Ga implantation and residual stresses requires that the two cantilever geometries return identical values on a preparation-free specimen. No finite-element validation or control experiment (identical notch preparation on both geometries, or FIB-free notching on DCBs) is presented to establish this equivalence. Differences in moment arm, crack-front constraint, or the compliance-based data-reduction formulas could therefore contribute to the observed factor-of-two discrepancy (Results section, Fig. 5 and associated text).

    Authors: We acknowledge that an ideal validation would involve identical notch preparation across geometries or FIB-free notching on DCBs. Such controls are experimentally challenging at the microscale, as FIB-free notching of DCB specimens risks introducing other damage modes. Our primary evidence that preparation (rather than geometry) drives the discrepancy is the vacuum-annealing result, which brings SCB values into agreement with DCB. The compliance formulas are geometry-specific, and DCB stable growth provides an independent consistency check. We will add a discussion paragraph addressing potential geometric contributions and why they are unlikely to explain the full factor-of-two difference. revision: partial

  2. Referee: [Methods] Error propagation and statistical treatment of the reported uncertainties are not described. The DCB value is given as 7.5 ± 0.3 J/m², yet the number of independent specimens, the scatter within each geometry, and the propagation of load, displacement, and dimensional uncertainties into G are not stated (Methods and Results sections).

    Authors: We agree the statistical details should be explicit. The ±0.3 J/m² is the standard deviation across five independent DCB specimens. We will revise the Methods section to state the number of specimens per geometry, report the observed scatter, and describe the error-propagation procedure (standard formulas combining uncertainties in load, displacement, and dimensions). revision: yes

Circularity Check

0 steps flagged

No circularity: pure experimental reporting of measured fracture energies

full rationale

The paper reports direct experimental measurements of fracture energy (7.5 ± 0.3 J/m² from DCB tests) and compares values across geometries and preparation methods, attributing differences to Ga implantation and residual stresses based on observed trends (e.g., annealing effects). No derivations, fitted parameters, equations, or self-citations are present that reduce any claim to its own inputs by construction. The central comparison relies on empirical data rather than any modeled or self-referential chain.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Experimental study; relies on standard fracture mechanics assumptions without introducing new parameters or entities.

axioms (1)
  • domain assumption Linear elastic fracture mechanics applies at the microscale for these specimens
    Used to convert load-displacement data to fracture energy; standard in the field but unverified in abstract.

pith-pipeline@v0.9.1-grok · 5746 in / 1155 out tokens · 28615 ms · 2026-06-28T09:08:16.575588+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

64 extracted references

  1. [1]

    Jayaram, Small-scale mechanical testing, Annual Review of Materials Research 52(1) (2022) 473-523

    V . Jayaram, Small-scale mechanical testing, Annual Review of Materials Research 52(1) (2022) 473-523

    2022

  2. [2]

    Emmanuel, O

    M. Emmanuel, O. Gavalda-Diaz, G. Sernicola, R. M’saoubi, T. Persson, S. Norgren, K. Marquardt, T.B. Britton, F. Giuliani, Fracture energy measurement of prismatic plane and Σ2 boundary in cemented carbide, JOM 73(6) (2021) 1589-1596

    2021

  3. [3]

    Casellas, J

    D. Casellas, J. Caro, S. Molas, J.M. Prado, I. Valls, Fracture toughness of carbides in tool steels evaluated by nanoindentation, Acta Materialia 55(13) (2007) 4277-4286

    2007

  4. [4]

    Schiffmann, Determination of fracture toughness of bulk materials and thin films by nanoindentation: comparison of different models, Philosophical Magazine 91(7-9) (2011) 1163-1178

    K.I. Schiffmann, Determination of fracture toughness of bulk materials and thin films by nanoindentation: comparison of different models, Philosophical Magazine 91(7-9) (2011) 1163-1178

    2011

  5. [5]

    Pharr, D

    G. Pharr, D. Harding, W. Oliver, Measurement of fracture toughness in thin films and small volumes using nanoindentation methods, Mechanical properties and deformation behavior of materials having ultra-fine microstructures, Springer1993, pp. 449-461

  6. [6]

    Harding, W

    D. Harding, W. Oliver, G. Pharr, Cracking during nanoindentation and its use in the measurement of fracture toughness, MRS Online Proceedings Library (OPL) 356 (1994) 663

    1994

  7. [7]

    Sebastiani, K.E

    M. Sebastiani, K.E. Johanns, E.G. Herbert, G.M. Pharr, Measurement of fracture toughness by nanoindentation methods: Recent advances and future challenges, Current Opinion in Solid State and Materials Science 19(6) (2015) 324-333

    2015

  8. [8]

    Lauener, L

    C.M. Lauener, L. Petho, M. Chen, Y . Xiao, J. Michler, J.M. Wheeler, Fracture of Silicon: Influence of rate, positioning accuracy, FIB machining, and elevated temperatures on toughness measured by pillar indentation splitting, Materials & Design 142 (2018) 340-349

    2018

  9. [9]

    Mughal, H.-Y

    M.Z. Mughal, H.-Y . Amanieu, R. Moscatelli, M. Sebastiani, A Comparison of Microscale Techniques for Determining Fracture Toughness of LiMn2O4 Particles, Materials 10(4) (2017) 403

    2017

  10. [10]

    J.P. Best, J. Zechner, J.M. Wheeler, R. Schoeppner, M. Morstein, J. Michler, Small-scale fracture toughness of ceramic thin films: the effects of specimen geometry, ion beam notching and high temperature on chromium nitride toughness evaluation, Philosophical Magazine 96(32-34) (2016) 3552-3569

    2016

  11. [11]

    J. Ast, M. Ghidelli, K. Durst, M. Göken, M. Sebastiani, A.M. Korsunsky, A review of experimental approaches to fracture toughness evaluation at the micro-scale, Materials & Design 173 (2019) 107762

    2019

  12. [12]

    Sebastiani, K.E

    M. Sebastiani, K.E. Johanns, E.G. Herbert, F. Carassiti, G.M. Pharr, A novel pillar indentation splitting test for measuring fracture toughness of thin ceramic coatings, Philosophical Magazine 95(16-18) (2015) 1928-1944

    2015

  13. [13]

    B.N. Jaya, C. Kirchlechner, G. Dehm, Can microscale fracture tests provide reliable fracture toughness values? A case study in silicon, Journal of Materials Research 30(5) (2015) 686-698

    2015

  14. [14]

    B.N. Jaya, S. Bhowmick, S.A.S. Asif, O.L. Warren, V . Jayaram, Optimization of clamped beam geometry for fracture toughness testing of micron-scale samples, Philosophical Magazine 95(16-18) (2015) 1945-1966

    2015

  15. [15]

    Venkatraman, V

    K. Venkatraman, V . Jayaram, Stiffness based technique to probe cyclic damage accumulation in micro- structurally graded bond coats via micro-beam bending tests, Philosophical Magazine 99(16) (2019) 2016-2050

    2019

  16. [16]

    Jaya B, V

    N. Jaya B, V . Jayaram, S.K. Biswas, A new method for fracture toughness determination of graded (Pt,Ni)Al bond coats by microbeam bend tests, Philosophical Magazine 92(25-27) (2012) 3326-3345

    2012

  17. [17]

    Jiang, S

    J. Jiang, S. Falco, S. Wang, F. Giuliani, R.I. Todd, Microcantilever investigation of slow crack growth and crack healing in aluminium oxide, Acta Materialia 273 (2024) 119914. 21

    2024

  18. [18]

    Tatami, M

    J. Tatami, M. Katayama, M. Ohnishi, T. Yahagi, T. Takahashi, T. Horiuchi, M. Y okouchi, K. Yasuda, D.K. Kim, T. Wakihara, K. Komeya, Local Fracture Toughness of Si3N4 Ceramics Measured using Single-Edge Notched Microcantilever Beam Specimens, Journal of the American Ceramic Society 98(3) (2015) 965-971

    2015

  19. [19]

    Armstrong, A.S.M.A

    D.E.J. Armstrong, A.S.M.A. Haseeb, S.G. Roberts, A.J. Wilkinson, K. Bade, Nanoindentation and micro- mechanical fracture toughness of electrodeposited nanocrystalline Ni–W alloy films, Thin Solid Films 520(13) (2012) 4369-4372

    2012

  20. [20]

    Armstrong, A.J

    D.E.J. Armstrong, A.J. Wilkinson, S.G. Roberts, Micro-mechanical measurements of fracture toughness of bismuth embrittled copper grain boundaries, Philosophical Magazine Letters 91(6) (2011) 394-400

    2011

  21. [21]

    Armstrong, A.J

    D.E.J. Armstrong, A.J. Wilkinson, S.G. Roberts, Measuring Local Mechanical Properties using FIB Machined Microcantilevers, MRS Online Proceedings Library 1185(1) (2009) 13-19

    2009

  22. [22]

    Mansfield, D.E.J

    B.R. Mansfield, D.E.J. Armstrong, P.R. Wilshaw, J.D. Murphy, An Investigation into Fracture of Multi- Crystalline Silicon, Solid State Phenomena 156-158 (2010) 55-60

    2010

  23. [23]

    Armstrong, A

    D. Armstrong, A. Haseeb, A. Wilkinson, S. Roberts, Micro-Fracture testing of Ni-W Microbeams Produced by Electrodeposition and FIB Machining, MRS Proceedings 983 (2006) 0983-LL08-07

    2006

  24. [24]

    Dickens, F.W

    S.M. Dickens, F.W. DelRio, S.J. Grutzik, W.M. Mook, B.L. Boyce, E. Hintsala, D. Stauffer, R.F. Cook, In- situ Fracture Toughness of Single Crystal Silicon Double-Cantilever Beams, Microscopy and Microanalysis 28(S1) (2022) 14-15

    2022

  25. [25]

    Y . Piao, S. Wang, D.S. Balint, F. Giuliani, E. Saiz, O. Gavalda-Diaz, Deformation and toughening of graphite at the micron scale, Acta Materialia 299 (2025) 121428

    2025

  26. [26]

    DelRio, S.J

    F.W. DelRio, S.J. Grutzik, W.M. Mook, S.M. Dickens, P.G. Kotula, E.D. Hintsala, D.D. Stauffer, B.L. Boyce, Eliciting stable nanoscale fracture in single-crystal silicon, Materials Research Letters 10(11) (2022) 728-735

    2022

  27. [27]

    Gavalda-Diaz, J

    O. Gavalda-Diaz, J. Lyons, S. Wang, M. Emmanuel, K. Marquardt, E. Saiz, F. Giuliani, Basal plane delamination energy measurement in a Ti3SiC2 MAX phase, Jom 73(6) (2021) 1582-1588

    2021

  28. [28]

    Gavalda-Diaz, R

    O. Gavalda-Diaz, R. Manno, A. Melro, G. Allegri, S.R. Hallett, L. Vandeperre, E. Saiz, F. Giuliani, Mode I and Mode II interfacial fracture energy of SiC/BN/SiC CMCs, Acta Materialia 215 (2021) 117125

    2021

  29. [29]

    Sernicola, T

    G. Sernicola, T. Giovannini, P. Patel, J.R. Kermode, D.S. Balint, T.B. Britton, F. Giuliani, In situ stable crack growth at the micron scale, Nature communications 8(1) (2017) 108

    2017

  30. [30]

    Di Maio, S

    D. Di Maio, S. Roberts, Measuring fracture toughness of coatings using focused-ion-beam-machined microbeams, Journal of materials research 20(2) (2005) 299-302

    2005

  31. [31]

    Stratulat, D.E

    A. Stratulat, D.E. Armstrong, S.G. Roberts, Micro-mechanical measurement of fracture behaviour of individual grain boundaries in Ni alloy 600 exposed to a pressurized water reactor environment, Corrosion Science 104 (2016) 9-16

    2016

  32. [32]

    S. Liu, J. Wheeler, P. Howie, X. Zeng, J. Michler, W. Clegg, Measuring the fracture resistance of hard coatings, Applied Physics Letters 102(17) (2013)

    2013

  33. [33]

    Borasi, A

    L. Borasi, A. Slagter, A. Mortensen, C. Kirchlechner, On the preparation and mechanical testing of nano to micron-scale specimens, Acta Materialia 283 (2025) 120394

    2025

  34. [34]

    Y . Chen, X. Zhang, X. Zhao, N. Markocsan, P. Nylén, P . Xiao, Measurements of elastic modulus and fracture toughness of an air plasma sprayed thermal barrier coating using micro-cantilever bending, Surface and Coatings Technology 374 (2019) 12-20. 22

    2019

  35. [35]

    Norton, S

    A. Norton, S. Falco, N. Young, J. Severs, R. Todd, Microcantilever investigation of fracture toughness and subcritical crack growth on the scale of the microstructure in Al2O3, Journal of the European Ceramic Society 35(16) (2015) 4521-4533

    2015

  36. [36]

    J.P. Best, J. Zechner, I. Shorubalko, J.V . Oboňa, J. Wehrs, M. Morstein, J. Michler, A comparison of three different notching ions for small-scale fracture toughness measurement, Scripta Materialia 112 (2016) 71-74

    2016

  37. [37]

    Okotete, S

    E. Okotete, S. Mueck, S. Lee, C. Kirchlechner, Evaluating neon ions as an alternative to gallium in micro cantilevers fracture testing, Scripta Materialia 258 (2025) 116509

    2025

  38. [38]

    Estivill, G

    R. Estivill, G. Audoit, J.-P. Barnes, A. Grenier, D. Blavette, Preparation and Analysis of Atom Probe Tips by Xenon Focused Ion Beam Milling, Microscopy and Microanalysis 22(3) (2016) 576-582

    2016

  39. [39]

    Chang, W

    Y . Chang, W. Lu, J. Guénolé, L.T. Stephenson, A. Szczpaniak, P. Kontis, A.K. Ackerman, F.F. Dear, I. Mouton, X. Zhong, S. Zhang, D. Dye, C.H. Liebscher, D. Ponge, S. Korte-Kerzel, D. Raabe, B. Gault, Ti and its alloys as examples of cryogenic focused ion beam milling of environmentally-sensitive materials, Nature Communications 10(1) (2019) 942

    2019

  40. [40]

    Lilensten, B

    L. Lilensten, B. Gault, New approach for FIB-preparation of atom probe specimens for aluminum alloys, PLOS ONE 15(4) (2020) e0231179

    2020

  41. [41]

    Williams, End corrections for orthotropic DCB specimens, Composites Science and Technology 35(4) (1989) 367-376

    J. Williams, End corrections for orthotropic DCB specimens, Composites Science and Technology 35(4) (1989) 367-376

    1989

  42. [42]

    S. Wang, O. Gavalda-Diaz, J. Lyons, F. Giuliani, Shear and delamination behaviour of basal planes in Zr3AlC2 MAX phase studied by micromechanical testing, Scripta Materialia 240 (2024) 115829

    2024

  43. [43]

    Aldegaither, G

    N. Aldegaither, G. Sernicola, A. Mesgarnejad, A. Karma, D. Balint, J. Wang, E. Saiz, S.J. Shefelbine, A.E. Porter, F. Giuliani, Fracture toughness of bone at the microscale, Acta Biomaterialia 121 (2021) 475-483

    2021

  44. [44]

    Kamitani, M

    K. Kamitani, M. Grimsditch, J. Nipko, C.-K. Loong, M. Okada, I. Kimura, The elastic constants of silicon carbide: A Brillouin-scattering study of 4H and 6H SiC single crystals, Journal of applied physics 82(6) (1997) 3152-3154

    1997

  45. [45]

    Iqbal, J

    F. Iqbal, J. Ast, M. Göken, K. Durst, In situ micro-cantilever tests to study fracture properties of NiAl single crystals, Acta Materialia 60(3) (2012) 1193-1200

    2012

  46. [46]

    Zhang, J.R.G

    Y . Zhang, J.R.G. Evans, S. Yang, Corrected Values for Boiling Points and Enthalpies of Vaporization of Elements in Handbooks, Journal of Chemical & Engineering Data 56(2) (2011) 328-337

    2011

  47. [47]

    Velasco, F

    S. Velasco, F. Román, J. White, On the Clausius–Clapeyron vapor pressure equation, Journal of Chemical Education 86(1) (2009) 106

    2009

  48. [48]

    Rauls, Z

    E. Rauls, Z. Hajnal, P. Deak, T. Frauenheim, Theoretical study of the nonpolar surfaces and their oxygen passivation in 4 H-and 6 H-SiC, Physical Review B 64(24) (2001) 245323

    2001

  49. [49]

    Kitahara, Y

    H. Kitahara, Y . Noda, F. Yoshida, H. Nakashima, N. Shinohara, H. Abe, Mechanical behavior of single crystalline and polycrystalline silicon carbides evaluated by Vickers indentation, Journal of the Ceramic Society of Japan 109(1271) (2001) 602-606

    2001

  50. [50]

    Ramakers, A

    S. Ramakers, A. Marusczyk, M. Amsler, T. Eckl, M. Mrovec, T. Hammerschmidt, R. Drautz, Effects of thermal, elastic, and surface properties on the stability of SiC polytypes, Physical Review B 106(7) (2022) 075201

    2022

  51. [51]

    Kishida, Y

    K. Kishida, Y . Shinkai, H. Inui, Room temperature deformation of 6H–SiC single crystals investigated by micropillar compression, Acta Materialia 187 (2020) 19-28. 23

    2020

  52. [52]

    B. Meng, C. Li, Effect of anisotropy on deformation and crack formation under the brittle removal of 6H- SiC during SPDT process, Journal of Advanced Research 56 (2024) 103-112

    2024

  53. [53]

    V . Lam, E. Villa, Practical Approaches for Cryo-FIB Milling and Applications for Cellular Cryo-Electron Tomography, in: T. Gonen, B.L. Nannenga (Eds.), cryoEM: Methods and Protocols, Springer US, New York, NY , 2021, pp. 49-82

    2021

  54. [54]

    Steve, P

    R. Steve, P. Robert, A review of focused ion beam applications in microsystem technology, Journal of Micromechanics and Microengineering 11(4) (2001) 287

    2001

  55. [55]

    Ziegler, J.P

    J.F. Ziegler, J.P . Biersack, The Stopping and Range of Ions in Matter, in: D.A. Bromley (Ed.), Treatise on Heavy-Ion Science: V olume 6: Astrophysics, Chemistry, and Condensed Matter, Springer US, Boston, MA, 1985, pp. 93-129

    1985

  56. [56]

    Jaya, J.M

    B.N. Jaya, J.M. Wheeler, J. Wehrs, J.P. Best, R. Soler, J. Michler, C. Kirchlechner, G. Dehm, Microscale Fracture Behavior of Single Crystal Silicon Beams at Elevated Temperatures, Nano Letters 16(12) (2016) 7597- 7603

    2016

  57. [57]

    Gu, J.-H

    J.-J. Gu, J.-H. Zhao, M.-Y . Bu, S.-M. Wang, L. Fan, Q. Huang, S. Li, Q.-Y . Yue, X.-L. Wang, Z.-X. Wei, Y . Liu, Study on the damage evolution of 6H-SiC under different phosphorus ion implantation conditions and annealing temperatures, Results in Physics 43 (2022) 106127

    2022

  58. [58]

    Erdogan, G.C

    F. Erdogan, G.C. Sih, On the Crack Extension in Plates Under Plane Loading and Transverse Shear, Journal of Basic Engineering 85(4) (1963) 519-525

    1963

  59. [59]

    Cotterell, J.R

    B. Cotterell, J.R. Rice, Slightly curved or kinked cracks, International Journal of Fracture 16(2) (1980) 155- 169

    1980

  60. [60]

    Zhang, M

    Y . Zhang, M. Bartosik, S. Brinckmann, S. Lee, C. Kirchlechner, Direct observation of crack arrest after bridge notch failure: A strategy to increase statistics and reduce FIB-artifacts in micro-cantilever testing, Materials & Design 233 (2023) 112188

    2023

  61. [61]

    Mueller, G

    M.G. Mueller, G. Žagar, A. Mortensen, Stable room-temperature micron-scale crack growth in single- crystalline silicon, Journal of Materials Research 32(19) (2017) 3617-3626

    2017

  62. [62]

    B.S. Li, T.J. Marrow, S.G. Roberts, D.E.J. Armstrong, Evaluation of Fracture Toughness Measurements Using Chevron-Notched Silicon and Tungsten Microcantilevers, JOM 71(10) (2019) 3378-3389

    2019

  63. [63]

    Mathews, A.K

    N.G. Mathews, A.K. Mishra, B.N. Jaya, Mode dependent evaluation of fracture behaviour using cantilever bending, Theoretical and Applied Fracture Mechanics 115 (2021) 103069

    2021

  64. [64]

    Okotete, A

    E. Okotete, A. Muslija, J.K. Hohmann, M. Kohl, S. Brinckmann, S. Lee, C. Kirchlechner, Enhanced crack stability in micro scale fracture testing via optimized bridge notches, Materials Science and Engineering: A 939 (2025) 148479

    2025