Research ArticlePHYSICAL SCIENCES

Soft crystal martensites: An in situ resonant soft x-ray scattering study of a liquid crystal martensitic transformation

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Science Advances  27 Mar 2020:
Vol. 6, no. 13, eaay5986
DOI: 10.1126/sciadv.aay5986
  • Fig. 1 RSoXS of BP LCs.

    (A) Fabrication scheme for BP LC sandwich cells. (B) Optical micrographs of single crystals of BPI(110) (top) and BPII(100) (bottom) under crossed polarizers, and the corresponding Kossel diagrams (insets). Structures of the (C) body-centered cubic (BCC) BPI and (F) simple cubic BPII. RSoXS geometry for (D) the BPI, with the (110) orientation out-of-plane, and (G) the BPII, with the (100) orientation out-of-plane. Lattice projections and simulated scattering patterns for (E) BPI(110) and (H) BPII(100), where scattering patterns for single crystals correspond to solid peaks and scattering patterns for small, randomly oriented polycrystals correspond to dotted rings. The first Brillouin zone is shown in yellow.

  • Fig. 2 LC phases during heating and cooling of BP LC sandwich cells.

    Optical micrographs (top) of sandwich cell LC textures, under crossed polarizers and corresponding RSoXS scattering pattern (bottom) during (A) heating [LC phase sequence, cholesteric (Chol.) → BPI → BPII → isotropic (Iso.)] and (B) cooling (Iso. → BPII → BPI → Chol.). The periodic horizontal peaks visible in the RSoXS pattern of Iso. phase are due to the underlying chemical pattern.

  • Fig. 3 RSoXS scattering patterns of BP LCs during heating.

    RSoXS scattering pattern of (A) BPI at 41.0°C and (B) BPII at 42.8°C during heating.

  • Fig. 4 RSoXS of BP soft crystals during cooling.

    RSoXS pattern of (A) single-crystal BPII(100) at 43.0°C and (B) polycrystalline BPI(110), which has a distinct set of polycrystals with four different in-plane orientations, θ, of −9.75°, −80.25°, 9.75°, and 80.25° at 40.7°C during cooling, where θ is an angle difference between [001] of BPI(110) lattice and lattice vector of the underlying chemically patterned stripes. (C) Scattering peaks of the {112}BPI plane appear near the scattering peaks of the {011}BPII plane and merge with one another during the transformation. (D) Schematic of the BPI(110) lattice after martensitic transformation from single-crystalline BPI(100).

  • Fig. 5 Proposed mechanism of cross-hatched structure formation during the martensitic transformation.

    (A) Model highlighting the transformation of eight unit cells of BPII(100) (2 × 2 × 2) to BPI(110),−9.75°. All the strain components are idealized values. (B) Four BPI(110) lattices, which can be transformed from single-crystalline BPII(100), and their strain values in global coordination after the transformation. (C) 64 × 64 single-crystalline BPII(100) and transformed 32 × 32 BPII(110),−9.75°. (D) Representative twin 1 and twin 2 lamellae formation. (E) Idealized cross-hatched structure formation, which consists of twin 1 and twin 2 and actual cross-hatched structure of BPI(110) after the martensitic transformation (inset).

  • Table 1 Lattice constants of BPI during various phase transformation conditions, including with (w MT) and without a martensitic transformation (w/o MT).

    All the measured values are the average of the lattice constants acquired between 41° and 42°C.

    LatticeaBPI (nm)cBPI (nm)c/a
    BPITheoretical2502501
    BPIheating, w/o MT242.2 ± 1.2242.2 ± 2.01.00
    BPIcooling, w MT231.7 ± 2.2236.4 ± 0.71.02
  • Table 2 Modeled and measured strain components of the BPI(110) lattices after the martensitic transformation from BPII(100).

    ϵb and ϵc are the normal strain components in their lattice coordination, and ϵx, ϵy, and γxy are the strain components in the xy global coordination.

    Latticeθ (°)ϵbϵcϵxϵyγxy
    ModeledBPI(110), −9.75°−9.75−0.1720.172−0.1620.162−0.115
    BPI(110), −80.25°−80.25−0.1720.1720.162−0.162−0.115
    BPI(110), 9.75°9.75−0.1720.172−0.1620.1620.115
    BPI(110), 80.25°80.25−0.1720.1720.162−0.1620.115
    MeasuredBPI(110), −9.75°−9.52−0.1710.163−0.1620.154−0.109
    BPI(110), −80.25°−80.77−0.1700.1570.149−0.162−0.104
    BPI(110), 9.75°10.55−0.1660.179−0.1540.1680.124
    BPI(110), 80.25°81.3−0.1610.1660.159−0.1530.098

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/6/13/eaay5986/DC1

    Note S1. Misaligned BP domains

    Note S2. Continuum simulations

    Note S3. Lattice strain calculation during the martensitic transformation

    Note S4. Transformation pathway with shear strain

    Fig. S1. RSoXS intensity profiles of BPI and BPII during heating.

    Fig. S2. RSoXS peak indexing of misaligned domains.

    Fig. S3. RSoXS peak indexing during the BPII to BPI martensitic transformation.

    Fig. S4. Model system for the lattice transformation from BPII(100) to BPI(110).

    Fig. S5. Transformation pathway with shear strain.

    Fig. S6. Variation in half-pitch length (p/2) of chiral nematic during heating and cooling.

    Fig. S7. The evolution of the scattering intensity and corresponding lattice constant during heating and cooling.

    Fig. S8. Reconfiguration of disclination network during the martensitic transformation from BPII to BPI.

    Fig. S9. Reconfiguration of disclination network on the yz and xz plane.

    Table S1. Measured d-spacing and strain components of BPI(110) lattices at the beginning of the martensitic transformation from BPII(100).

    Movie S1. Reconfiguration of disclination network during martensitic transformation.

    References (2527)

  • Supplementary Materials

    The PDF file includes:

    • Note S1. Misaligned BP domains
    • Note S2. Continuum simulations
    • Note S3. Lattice strain calculation during the martensitic transformation
    • Note S4. Transformation pathway with shear strain
    • Fig. S1. RSoXS intensity profiles of BPI and BPII during heating.
    • Fig. S2. RSoXS peak indexing of misaligned domains.
    • Fig. S3. RSoXS peak indexing during the BPII to BPI martensitic transformation.
    • Fig. S4. Model system for the lattice transformation from BPII(100) to BPI(110).
    • Fig. S5. Transformation pathway with shear strain.
    • Fig. S6. Variation in half-pitch length (p/2) of chiral nematic during heating and cooling.
    • Fig. S7. The evolution of the scattering intensity and corresponding lattice constant during heating and cooling.
    • Fig. S8. Reconfiguration of disclination network during the martensitic transformation from BPII to BPI.
    • Fig. S9. Reconfiguration of disclination network on the yz and xz plane.
    • Table S1. Measured d-spacing and strain components of BPI(110) lattices at the beginning of the martensitic transformation from BPII(100).
    • Legend for movie S1
    • References (2527)

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    Other Supplementary Material for this manuscript includes the following:

    • Movie S1 (.avi format). Reconfiguration of disclination network during martensitic transformation.

    Files in this Data Supplement:

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