Research ArticleAPPLIED PHYSICS

Origin of giant negative piezoelectricity in a layered van der Waals ferroelectric

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Science Advances  19 Apr 2019:
Vol. 5, no. 4, eaav3780
DOI: 10.1126/sciadv.aav3780
  • Fig. 1 Piezoelectric effect and lattice dimensionality.

    (A and B) Illustrations of negative (A) and positive (B) longitudinal piezoelectric effects, where the lattice contracts or elongates when the electric field is along the direction of the spontaneous polarization. (C) A schematic that outlines the lattice dimensionalities of three representative ferroelectric materials: 1D PVDF, 2D CuInP2S6 (CIPS), and 3D Pb(Zr0.4Ti0.6)O3 (PZT). The bottom part shows the energy scales of the inter- and intramolecular bonds. PVDF is known to have a negative piezoelectric coefficient, as schematically shown in (A), while 3D ferroelectrics usually show positive piezoelectric coefficients as illustrated in (B).

  • Fig. 2 Piezoelectricity of ferroelectric solids with different lattice dimensionalities.

    (A to C) Polarization–electric field (P-E) hysteresis loops of PVDF (A), CIPS (B), and PZT (C). (D to F) Corresponding S-E hysteresis loops of PVDF (D), CIPS (E), and PZT (F). (G and H) Hysteresis loops of effective d33 (amplitude) and phase signals obtained by ac piezoresponse measurement for PVDF (G), CIPS (H), and PZT (I). The polarization switching sequence is denoted by the numbers and arrows in (A) and represented using the same color code in all plots.

  • Fig. 3 Simplified rigid ion model for piezoelectricity in polar solids.

    (A to C) Correlations between crystal structures and dipole charges for PVDF (A), CIPS (B), and PZT (C). (D) Negative piezoelectric effect in polar solid with discontinuous (broken) lattice. (E) Positive piezoelectric effect in polar solid with continuous lattice. The unit cell of the lattice is indicated by the dashed box. The polarization and electric field directions are denoted by the arrows. The lower parts show the pair potential energy profiles of the corresponding chemical bonds. The negative ions are taken as a reference point for the relative changes of bond lengths.

  • Fig. 4 Atomistic origin of the giant negative longitudinal piezoelectricity in CIPS.

    (A) Refined unit cell structure of CIPS viewed along the b axis. The foremost sheet of atoms parallel to (010) plane is highlighted, while the rest are attenuated. The size of the Cu atom indicates its occupancy at the corresponding site. (B) The cross-sectional electron density map of the atomic plane highlighted in (A). The gray dashed lines denote the upper and lower sulfur planes. Red dashed lines indicate the possible interlayer Cu─S bonding across the vdW gap. (C) Calculated changes of the vdW distance d and the layer thickness r of CIPS as a function of strain along c axis. Solid lines are linear fits. (D) Evolution of the free energy E (blue) and the change of ferroelectric polarization P (red) as a function of lattice constant along the c axis under different conditions: triangle, all Cu occupying metastable site; circle, ¼ Cu occupying metastable site; square, all Cu occupying ground-state site. The insets show the corresponding atomic structures. (E) Electron density profile along the blue dashed line shown in (B). The asymmetric distribution of Cu due to the partial occupancy of the metastable site can be fitted by two Gaussian peaks (solid lines).

  • Table 1 A list of extracted materials parameters.

    Ps, spontaneous polarization; ε33, relative permittivity; d33, longitudinal piezoelectric coefficient; Q33, longitudinal electrostriction coefficient; Eb, intermolecular bond energy; C33, Young’s modulus. The numbers in the parentheses are the intramolecular bond energies.

    MaterialPs (μC/cm2)ε33 (at 10 kHz)d33 (pm/V) (at 10 kHz)Q33 (m4/C2)Eb (kJ/mol)C33 (GPa)Coupling factor k33
    PVDF-TrFE (70/30)88.2−25−2.2<20 (290–495)1–30.1–0.16
    CuInP2S6440−95−3.4<20 (280–440)20–300.71–0.88
    Pb(Zr0.4Ti0.6)O360170500.02370–800100–1500.41–0.5

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/4/eaav3780/DC1

    Section S1. Full data series of the P-E and S-E measurements

    Section S2. Dynamic piezoelectric measurements

    Section S3. Intrinsic piezoelectric response of CIPS by in situ micro-XRD

    Section S4. Quantitative determination of the electrostriction coefficient Q33

    Section S5. The “dimensional model” and Maxwell strain

    Section S6. Thickness-dependent piezoelectric response, clamping effect, and electromechanical coupling factor

    Fig. S1. Voltage-dependent P-E and S-E hysteresis curves.

    Fig. S2. Frequency-dependent P-E and S-E hysteresis curves.

    Fig. S3. Voltage-displacement phase relationship in dynamic piezoelectric measurements.

    Fig. S4. Frequency-dependent piezoelectric response.

    Fig. S5. Determining the static d33 from S-E curves.

    Fig. S6. PFM images with box-in-box patterns written.

    Fig. S7. In situ XRD measurements of the CIPS lattice parameter under electric field.

    Fig. S8. Quantitative determination of electrostriction coefficient Q33 by linearly fitting the S-P2 curves.

    Fig. S9. Quantitative determination of electrostriction coefficient Q33 by Q33 = d33/2ε33Ps.

    Fig. S10. Lattice anomaly around the ferroelectric-paraelectric phase transition.

    Fig. S11. Comparison between the dimensional model and reduced lattice dimensionality induced negative piezoelectricity.

    Fig. S12. Switching the polarization of CIPS for single-crystal x-ray crystallography.

    Fig. S13. Calculated DOS of CIPS.

    Fig. S14. Calculated energy and polarization changes as a function of applied strain.

    Fig. S15. Energy and polarization changes as a function of interlayer Cu ratio.

    Fig. S16. Dynamic piezoelectric measurements of CIPS flakes with different thicknesses.

    Fig. S17. Nanoindentation test of CIPS single crystal.

    Data file S1. Crystallographic information file (CIF) of unpoled CIPS crystal.

    Data file S2. Crystallographic information file (CIF) of poled CIPS crystal.

    References (5778)

  • Supplementary Materials

    The PDF file includes:

    • Section S1. Full data series of the P-E and S-E measurements
    • Section S2. Dynamic piezoelectric measurements
    • Section S3. Intrinsic piezoelectric response of CIPS by in situ micro-XRD
    • Section S4. Quantitative determination of the electrostriction coefficient Q33
    • Section S5. The “dimensional model” and Maxwell strain
    • Section S6. Thickness-dependent piezoelectric response, clamping effect, and electromechanical coupling factor
    • Fig. S1. Voltage-dependent P-E and S-E hysteresis curves.
    • Fig. S2. Frequency-dependent P-E and S-E hysteresis curves.
    • Fig. S3. Voltage-displacement phase relationship in dynamic piezoelectric measurements.
    • Fig. S4. Frequency-dependent piezoelectric response.
    • Fig. S5. Determining the static d33 from S-E curves.
    • Fig. S6. PFM images with box-in-box patterns written.
    • Fig. S7. In situ XRD measurements of the CIPS lattice parameter under electric field.
    • Fig. S8. Quantitative determination of electrostriction coefficient Q33 by linearly fitting the S-P2 curves.
    • Fig. S9. Quantitative determination of electrostriction coefficient Q33 by Q33 = d33/2ε33Ps.
    • Fig. S10. Lattice anomaly around the ferroelectric-paraelectric phase transition.
    • Fig. S11. Comparison between the dimensional model and reduced lattice dimensionality induced negative piezoelectricity.
    • Fig. S12. Switching the polarization of CIPS for single-crystal x-ray crystallography.
    • Fig. S13. Calculated DOS of CIPS.
    • Fig. S14. Calculated energy and polarization changes as a function of applied strain.
    • Fig. S15. Energy and polarization changes as a function of interlayer Cu ratio.
    • Fig. S16. Dynamic piezoelectric measurements of CIPS flakes with different thicknesses.
    • Fig. S17. Nanoindentation test of CIPS single crystal.
    • References (5778)

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    Other Supplementary Material for this manuscript includes the following:

    • Data file S1 (.cif format). Crystallographic information file (CIF) of unpoled CIPS crystal.
    • Data file S2 (.cif format). Crystallographic information file (CIF) of poled CIPS crystal.

    Files in this Data Supplement:

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