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A novel series of sphere packings with arbitrarily low density

  • Tadeusz E. Dorozinski and Werner Fischer
Published/Copyright: September 25, 2009
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Zeitschrift für Kristallographie - Crystalline Materials
From the journal Zeitschrift für Kristallographie - Crystalline Materials Volume 221 Issue 5-7

Abstract

The search for a least dense packing of spheres makes sense only under suitable restrictions because otherwise sphere packings of arbitrarily low density may be constructed. As has been shown before, the condition that all spheres have to be equal as well in their size as in their number of contacts is not such an effective restriction. A sharper condition is the demand that all spheres must have congruent patterns of contacts, i.e. that they must coincide in their first neighbourhood. The example presented here proves that also this restriction is not sufficient to avoid sphere packings with densities approaching zero.

Keywords: Sphere packings of low density; Homogeneous sphere packings; Heterogeneous sphere packings
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Published Online: 2009-9-25
Published in Print: 2006-5-1

© by Oldenbourg Wissenschaftsverlag, München

Articles in the same Issue

  1. Editorial: Crystal Chemistry of Intermetallic Compounds
  2. Fritz H. Laves – 100 years young
  3. Fritz H. Laves – an ideal for generations
  4. Gustav E. R. Schulze's pioneering work on Laves phases
  5. Preparation, phase stability and structure of the C36 Laves phase Nb1–xCo2+x
  6. Atom order and thermodynamic properties of the ternary Laves phase Ti(TiyNixAl1–x–y)2
  7. Atomic ordering in the Laves phases L1 V(Co1–xSix)2 (x = 0.43 and 0.56)
  8. Microscopic structures of Laves phases and structurally related compounds: a transmission electron microscopy study
  9. Binary rare earth Laves phases — an overview
  10. Binary intermetallic phases formed by Ca, Sr, Ba, Eu and Yb: similarities and differences
  11. Complexity of hexagonal approximants in the RE13Zn~58 system (RE = Ce, Pr, Nd, Sm, Gd, Tb and Dy)
  12. Reflections on symmetry and formation of axial quasicrystals
  13. Mosaic-like tilings derivated from o-Co4Al13 and m-Co4Al13 crystal structures
  14. High-pressure crystal chemistry of binary intermetallic compounds
  15. Re3B type intermetallics — crystal chemistry, bonding and properties
  16. Ti2Rh6B – a new boride with a double perovskite-like structure containing octahedral Rh6 clusters
  17. On the formation and crystal structure of the Pd6B phase
  18. Crystal growth and magnetic properties of rare earth borosilicides
  19. The effect of transition metal doping on thermal conductivity of YB66
  20. Structure refinements of iron borides Fe2B and FeB
  21. Cubic structure types of rare-earth intermetallics and related compounds
  22. Structural variations in Gd5Si4-xSnx: size vs. electronic effects
  23. Tin flux synthesis of rare-earth metal silicide compounds RESi1.7 (RE = Dy, Ho): a novel ordered structure derived from the AlB2 type
  24. Filling the CoSn host-cell: the HfFe6Ge6-type and the related structures
  25. Synthesis and characterization of Na2Ba4Ga2Sb6 and Li13Ba8GaSb12
  26. Ge40.0Te5.3I8: synthesis, crystal structure, and properties of a new clathrate-I compound
  27. Ag6GeS4X2 (X: Cl, Br): surprisingly no filled Laves phases but the first representatives of a new structure type
  28. Low- and high-temperature structures of YbCuBi
  29. (La3Zx)Al and (Ce3Zx)Al with Z = C, N, O: preparation, physical properties and chemical bonding of metal-rich perovskites
  30. Geometric variations and electron localizations in intermetallics: PbFCl type compounds
  31. A novel series of sphere packings with arbitrarily low density
  32. Books Received
https://doi.org/10.1524/zkri.2006.221.5-7.563
Keywords for this article
Sphere packings of low density; Homogeneous sphere packings; Heterogeneous sphere packings

Articles in the same Issue

  1. Editorial: Crystal Chemistry of Intermetallic Compounds
  2. Fritz H. Laves – 100 years young
  3. Fritz H. Laves – an ideal for generations
  4. Gustav E. R. Schulze's pioneering work on Laves phases
  5. Preparation, phase stability and structure of the C36 Laves phase Nb1–xCo2+x
  6. Atom order and thermodynamic properties of the ternary Laves phase Ti(TiyNixAl1–x–y)2
  7. Atomic ordering in the Laves phases L1 V(Co1–xSix)2 (x = 0.43 and 0.56)
  8. Microscopic structures of Laves phases and structurally related compounds: a transmission electron microscopy study
  9. Binary rare earth Laves phases — an overview
  10. Binary intermetallic phases formed by Ca, Sr, Ba, Eu and Yb: similarities and differences
  11. Complexity of hexagonal approximants in the RE13Zn~58 system (RE = Ce, Pr, Nd, Sm, Gd, Tb and Dy)
  12. Reflections on symmetry and formation of axial quasicrystals
  13. Mosaic-like tilings derivated from o-Co4Al13 and m-Co4Al13 crystal structures
  14. High-pressure crystal chemistry of binary intermetallic compounds
  15. Re3B type intermetallics — crystal chemistry, bonding and properties
  16. Ti2Rh6B – a new boride with a double perovskite-like structure containing octahedral Rh6 clusters
  17. On the formation and crystal structure of the Pd6B phase
  18. Crystal growth and magnetic properties of rare earth borosilicides
  19. The effect of transition metal doping on thermal conductivity of YB66
  20. Structure refinements of iron borides Fe2B and FeB
  21. Cubic structure types of rare-earth intermetallics and related compounds
  22. Structural variations in Gd5Si4-xSnx: size vs. electronic effects
  23. Tin flux synthesis of rare-earth metal silicide compounds RESi1.7 (RE = Dy, Ho): a novel ordered structure derived from the AlB2 type
  24. Filling the CoSn host-cell: the HfFe6Ge6-type and the related structures
  25. Synthesis and characterization of Na2Ba4Ga2Sb6 and Li13Ba8GaSb12
  26. Ge40.0Te5.3I8: synthesis, crystal structure, and properties of a new clathrate-I compound
  27. Ag6GeS4X2 (X: Cl, Br): surprisingly no filled Laves phases but the first representatives of a new structure type
  28. Low- and high-temperature structures of YbCuBi
  29. (La3Zx)Al and (Ce3Zx)Al with Z = C, N, O: preparation, physical properties and chemical bonding of metal-rich perovskites
  30. Geometric variations and electron localizations in intermetallics: PbFCl type compounds
  31. A novel series of sphere packings with arbitrarily low density
  32. Books Received
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