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The probability of finding a spherical “hole” of a given radius r contains crucial structural information about many-body systems. Such hole statistics, including the void conditional nearest-neighbor probability functions GV(r), have been well studied for hard-sphere fluids in d-dimensional Euclidean space Rd. However, little is known about these functions for hard-sphere crystals for values of r beyond the hard-sphere diameter, as large holes are extremely rare in crystal phases. To overcome these computational challenges, we introduce a biased-sampling scheme that accurately determines hole statistics for equilibrium hard spheres on ranges of r that far extend those that could be previously explored. We discover that GV(r) in crystal and hexatic states exhibits oscillations whose amplitudes increase rapidly with the packing fraction, which stands in contrast to GV(r) that monotonically increases with r for fluid states. The oscillations in GV(r) for 2D crystals are strongly correlated with the local orientational order metric in the vicinity of the holes, and variations in GV(r) for 3D states indicate a transition between tetrahedral and octahedral holes, demonstrating the power of GV(r) as a probe of local coordination geometry. To further study the statistics of interparticle spacing in hard-sphere systems, we compute the local packing fraction distribution f(ϕl) of Delaunay cells and find that, for d ≤ 3, the excess kurtosis of f(ϕl) switches sign at a certain transitional global packing fraction. Our accurate methods to access hole statistics in hard-sphere crystals at the challenging intermediate length scales reported here can be applied to understand the important problem of solvation and hydrophobicity in water at such length scales.
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X-ray and molecular dynamics study of the temperature-dependent structure of FLiNaK
The atomic structure of FLiNaK and its evolution with temperature are examined with x-ray scattering and molecular dynamics (MD) simulations in the temperature range 460–636 °C. In accord with previous studies, it’s observed that the average nearest-neighbor (NN) cation-anion coordination number increases with increasing cation size, going from ∼4 for Li-F to ∼6.4 for K-F. In addition, we find that there is a coupled change in local coordination geometry – going from tetrahedral for Li-F to octahedral for Na to very disordered quasi-cuboidal for K. The varying geometry and coordination distances for the cation-anion pairs cause a relatively constant F-F next-nearest neighbor (NNN) distance of approximately 3.1 Å. This relatively fixed distance allows the F anions to assume an overall correlated structure very similar to that of a hard-sphere liquid with an extended radius which is beyond the normal F ion size but reflects the cation-anion coordination requirements. Careful consideration of the evolution of the experimental atomic distribution functions with increasing temperature shows that the changes in correlation at each distance can be understood within the context of broadening asymmetric neighbor distributions. Within the temperature range studied, the evolution of F-F correlations with increasing temperature is consistent with changes expected in a hard-sphere liquid simply due to decreasing density.
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- Award ID(s):
- 1937829
- PAR ID:
- 10487742
- Publisher / Repository:
- Elsevier Ltd.
- Date Published:
- Journal Name:
- Nuclear Materials and Energy
- Volume:
- 37
- Issue:
- C
- ISSN:
- 2352-1791
- Page Range / eLocation ID:
- 101530
- Subject(s) / Keyword(s):
- Molten salt structure, Molecular dynamics
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1016/j.nme.2023.101530
