Research ArticleEARTH SCIENCES

Low-temperature plasticity of olivine revisited with in situ TEM nanomechanical testing

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Science Advances  11 Mar 2016:
Vol. 2, no. 3, e1501671
DOI: 10.1126/sciadv.1501671
  • Fig. 1 Critical stress for plastic flow as a function of temperature.

    The red circle was obtained by including our in situ dislocation velocity measurements in our dislocation dynamics (DD) numerical model. The other points indicate experimental measurements taken from different sources in literature [E&G79 (5); M&J90 (31); Rat04 (6); Drui11 (8); Long11 (7); Dem13 (2); Dem14 (32); Kra15 (36)]. Full (empty) symbols are used to visualize mechanical data obtained by deforming single-crystal (polycrystalline) olivine samples. The new rheological law for olivine single crystals is shown with a dashed line.

  • Fig. 2 In situ TEM nanomechanical testing.

    (A) Optical image of the PTP device used for in situ TEM tensile experiments. The compression of the semicircular end in (A) induces uniaxial tension in the middle gap shown in (B) and (C). (B and C) Scanning electron microscope (SEM) images showing the transfer of an FIB-prepared olivine sample onto the PTP device and the mounting of the sample in the middle gap using electron beam–deposited platinum (Pt), respectively. (D) WBDF-TEM image of the olivine sample DefOl-4 mounted on the PTP device before deformation. The scratch and the pulling direction are perpendicular to the (112) plane. The sample is oriented in a two-beam condition with the vector Embedded Image perpendicular to the pulling direction. (E) Zoom on the damaged layer underneath the polished surface surrounded by the rectangle in (D). Several dislocation loops can be observed. (F) WBDF-TEM image showing the nucleation of a dislocation loop (white arrowhead) in the (110) plane from the damaged layer during in situ TEM straining. The pulling direction is indicated by white arrows in (F).

  • Fig. 3 TEM measurements of the mobility of screw dislocations.

    (A to F) Video frames captured during the in situ deformation of sample DefOl-3 under a constant load of 384 μN (resolved shear stress, 0.89 GPa). A movie is available in the Supplementary Materials. The loop expands from the scratch and develops, allowing propagation of the screw segment (arrowed) to be followed across the specimen. A table describing the different experiments is included in the Supplementary Materials. (G) Velocities (in nm s−1) of screw dislocations versus stress (in GPa). Data from the DefOl-3 experiment are presented for all raw measurements (empty diamonds) and weighted means at each stress (indigo diamonds). v1(τ) is the fit introduced in the DD model (see the Supplementary Materials). These velocities correspond to a screw dislocation segment of length 0.8 μm.

  • Fig. 4 Dislocation dynamics simulations.

    (A) Sketch of the DD simulation box. Single-slip conditions and uniaxial loading are applied along the y direction (loading direction). The angle between the loading axis and glide direction for the easiest [001](110) slip system is 45°. Dislocations (plus or x symbols) are superimposed on a color background, which represents the component σyy of the stress field induced by the dislocation microstructure and the imposed external forces. (B) Stress-strain curve obtained from the DD numerical model by using the dislocation velocity inferred from the PTP experiments.

  • Table 1 Values of the parameters defining the new rheological law reported in Eq. 1 and shown in Fig. 1 (dashed red line).
    AQσ0pq
    1 × 106 (s−1)566±74 (kJ/mol)3.8±0.7 (GPa)0.52

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/2/3/e1501671/DC1

    Materials and Methods

    Fig. S1. Stereographic plot (planes) of the beam strained in the microscope as viewed along the electron beam direction.

    Fig. S2. FIB preparation of olivine specimens for in situ TEM nanomechanical testing.

    Fig. S3. SEM measurements of the cross-sectional area of the tensile sample.

    Fig. S4. True stress–true strain curve of olivine sample deformed elastically up to 3.4 GPa and 0.021 strain.

    Fig. S5. WBDF-TEM imaging of dislocations.

    Fig. S6. Force cycles applied to the sample “DefOl-3.”

    Fig. S7. Experimental procedure used to measure the velocity of dislocations at low resolved shear stresses in sample “DefOl-4.”

    Fig. S8. Critical stress for source opening as a function of the loop radius.

    Fig. S9. Snapshots from in situ TEM tensile experiment at constant load of 365 μN applied on sample “DefOl-2.”

    Fig. S10. Calculation of the image forces on a dislocation parallel to the free surfaces of a 200-nm-thick foil (green band).

    Fig. S11. Example of the measurement of the velocity of a screw dislocation (segment arrowed) within a single cycle.

    Fig. S12. Dislocation velocity as a function of the resolved shear stress: influence of the fit on the DD results.

    Fig. S13. Influence of the initial dislocation density on the DD results.

    Fig. S14. Influence on the dislocation length on the DD results.

    Fig. S15. Histograms of the stresses experienced by the dislocations in the DD simulations and of the resulting strains.

    Table S1. Intensity (and dhkl) of the most efficient reflections in olivine (calculated with the “electron diffraction” software).

    Table S2. Summary of the in situ TEM tensile experiments achieved in the present study.

    Movie S1. The in situ deformation of sample DefOl-3 under a constant load of 360 μN (resolved shear stress, 0.82 GPa).

    References (3335)

  • Supplementary Materials

    This PDF file includes:

    • Materials and Methods
    • Fig. S1. Stereographic plot (planes) of the beam strained in the microscope as viewed along the electron beam direction.
    • Fig. S2. FIB preparation of olivine specimens for in situ TEM nanomechanical testing.
    • Fig. S3. SEM measurements of the cross-sectional area of the tensile sample.
    • Fig. S4. True stress–true strain curve of olivine sample deformed elastically up to 3.4 GPa and 0.021 strain.
    • Fig. S5. WBDF-TEM imaging of dislocations.
    • Fig. S6. Force cycles applied to the sample “DefOl-3.”
    • Fig. S7. Experimental procedure used to measure the velocity of dislocations at low resolved shear stresses in sample “DefOl-4.”
    • Fig. S8. Critical stress for source opening as a function of the loop radius.
    • Fig. S9. Snapshots from in situ TEM tensile experiment at constant load of 365 μN applied on sample “DefOl-2.”
    • Fig. S10. Calculation of the image forces on a dislocation parallel to the free surfaces of a 200-nm-thick foil (green band).
    • Fig. S11. Example of the measurement of the velocity of a screw dislocation (segment arrowed) within a single cycle.
    • Fig. S12. Dislocation velocity as a function of the resolved shear stress: influence of the fit on the DD results.
    • Fig. S13. Influence of the initial dislocation density on the DD results.
    • Fig. S14. Influence on the dislocation length on the DD results.
    • Fig. S15. Histograms of the stresses experienced by the dislocations in the DD simulations and of the resulting strains.
    • Table S1. Intensity (and dhkl) of the most efficient reflections in olivine (calculated with the “electron diffraction” software).
    • Table S2. Summary of the in situ TEM tensile experiments achieved in the present study.
    • Legend for movie S1
    • References (33–35)

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    Other Supplementary Material for this manuscript includes the following:

    • Movie S1 (.mp4 format). The in situ deformation of sample DefOl-3 under a constant load of 360 μN (resolved shear stress, 0.82 GPa).

    Files in this Data Supplement:

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