Research ArticleQUANTUM SOLIDS

Equilibrium shape of 4He crystal under zero gravity below 200 mK

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Science Advances  23 Oct 2015:
Vol. 1, no. 9, e1500825
DOI: 10.1126/sciadv.1500825
  • Fig. 1 Transformation of a 4He crystal with nonhorizontal c-facet via a sudden reduction of gravity.

    (A to L) Gravity values and times elapsed are presented in each frame. The orientation of the c-facet was inclined from the horizontal plane. Under gravity, a rough horizontal surface covered most part of the crystal, and a c-facet appeared in a small portion of the crystal in the vicinity of the wall, as indicated by the arrows in (A). Under zero-gravity conditions, the crystal transformed into a different stable shape, and c-facet, a-facet, and s-facet became visible.

  • Fig. 2 Transformation of a 4He crystal with nearly horizontal c-facet via a sudden reduction of gravity.

    (A to R) The reduction of gravity did not significantly affect the crystal shape (A to C). The successive pictures (D to P) show the deformation process of the 4He crystal by an acoustic wave pulse and the subsequent relaxation process after the pulse was turned off. The deformed crystal relaxed to an equilibrium shape different from the initial shape. After the zero-gravity period (Q and R), the crystal recovered the initial shape as in (A).

  • Fig. 3 Time evolution of the temperature and gravity.

    Temperature of the sample cell and the mixing chamber due to the application of acoustic wave pulse was recorded with the gravity.

  • Fig. 4 Comparison of the facet-like flat surface parallel to the c-facet of the final relaxed crystal in Fig. 2 with the theoretical curve obtained using Eq. 1.

    (A and B) This comparison suggests that the true facet appears on the narrow area between the open arrows and the vicinal surface occupies the other area. Around the two-headed arrows, the curve deviates from the surface, where the surface transforms from the vicinal state to the rough state. The open circle located at the intersection point between the perpendicular bisectors (the dashed lines) of the c-facet and s-facet indicates the origin in the Wulff construction.

  • Table 1 Distances from the Wulff’s origin of the crystal to each facet and the interfacial free energy derived from the distances.

    Crystal 1 (2) corresponds to the relaxed crystal in Fig. 1 (2). The indices represent each facet (c, a, and s). Errors are derived from the ambiguity in the determination of the Wulff’s origin.

    hc (mm)hahsαa (erg/cm2)αs
    Crystal 19.110.310.60.195 ± 0.0110.200 ± 0.009
    Crystal ± 0.0150.184 ± 0.009

Supplementary Materials

  • Supplementary Materials

    Other Supplementary Material for this manuscript includes the following:

    • Movie S1 (.mov format). A movie of Fig. 1.
    • Movie S2 (.mov format). A movie of Fig. 2.

    Files in this Data Supplement:

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