Interactions in Sphere Packings

2001 ◽  
Vol 215 (5) ◽  
Author(s):  
J. Hauck ◽  
K. Mika
Keyword(s):  
Sphere Packings ◽  
Homogeneous Sphere ◽  
Circle Packings

The circle packings including non-periodic packings and 41 homogeneous sphere packings with 4≤ T

A transition path from the zinc-blende to the NaCl type

2000 ◽  
Vol 215 (6) ◽  
Author(s):  
Heidrun Sowa
Keyword(s):  
Sphere Packing ◽  
Sphere Packings ◽  
Transition Path ◽  
Homogeneous Sphere ◽  
Zinc Blende ◽  
Wyckoff Position ◽  
Silicon And Germanium ◽  
Binary Compounds ◽  
Diamond Configuration ◽  
Diamond Type

In order to find a transition path from the zinc-blende to the NaCl type both structures are described with the aid of heterogeneous sphere packings. If all atoms in such crystal structures are replaced by like ones, atomic arrangements result that correspond to homogeneous sphere packings belonging to the diamond type or forming a cubic primitive lattice, respectively.It is shown, that a diamond configuration may be deformed into a cubic primitive lattice within the Wyckoff position Imma 4(e) mm2 0,¼,z. The corresponding phase transition in binary compounds from the zinc-blende to the NaCl type can be described as a deformation of a heterogeneous sphere packing in the subgroup Imm2 of Imma. Since no bonds have to be broken this type of transition is displacive.In addition, structural relations between high-pressure phases of semiconductors like silicon and germanium and related AB compounds are shown.

Monoclinic sphere packings. III. Trivariant lattice complexes of P2/c and P21/c

2019 ◽  
Vol 75 (2) ◽  
pp. 325-335
Author(s):  
Heidrun Sowa
Keyword(s):  
Sphere Packing ◽  
The Other ◽  
Monoclinic Space Group ◽  
Sphere Packings ◽  
Homogeneous Sphere ◽  
Space Group

All homogeneous sphere packings were derived that refer to the trivariant lattice complexes of monoclinic space-group types P2/c and P21/c. In total, sphere packings of 55 types have been found. The maximal inherent symmetry is monoclinic for 17 types while the other types comprise at least one sphere packing with cubic (four cases), hexagonal (six cases), tetragonal (eight cases) or orthorhombic (20 cases) symmetry.

Orthorhombic sphere packings. V. Trivariant lattice complexes of space groups belonging to crystal class 222

2014 ◽  
Vol 70 (6) ◽  
pp. 591-604 ◽  
Author(s):  
Heidrun Sowa
Keyword(s):  
Sphere Packing ◽  
Tetragonal Symmetry ◽  
Orthorhombic Symmetry ◽  
Sphere Packings ◽  
Homogeneous Sphere ◽  
Space Group ◽  
Space Groups ◽  
Characteristic Space ◽  
Different Types ◽  
Crystal Class

This paper completes the derivation of all types of homogeneous sphere packing with orthorhombic symmetry. The nine orthorhombic trivariant lattice complexes belonging to the space groups of crystal class 222 were examined in regard to the existence of homogeneous sphere packings and of interpenetrating sets of layers of spheres. Altogether, sphere packings of 84 different types have been found; the maximal inherent symmetry is orthorhombic for only 36 of these types. In addition, interpenetrating sets of 63nets occur once. All lattice complexes with orthorhombic characteristic space group give rise to 260 different types of sphere packing in total. The maximal inherent symmetry is orthorhombic for 160 of these types. Sphere packings of 13 types can also be generated with cubic, those of seven types with hexagonal and those of 80 types with tetragonal symmetry. In addition, ten types of interpenetrating sphere packing and two types of sets of interpenetrating sphere layers are obtained. Most of the sphere packings can be subdivided into layer-like subunits perpendicular to one of the orthorhombic main axes.

Monoclinic sphere packings. II. Trivariant lattice complexes with mirror symmetry

2018 ◽  
Vol 74 (2) ◽  
pp. 143-147
Author(s):  
Heidrun Sowa
Keyword(s):  
Mirror Symmetry ◽  
Sphere Packings ◽  
Homogeneous Sphere ◽  
Monoclinic Lattice

All homogeneous sphere packings were derived that refer to the three trivariant monoclinic lattice complexes with mirror symmetry. In total, 29 types of sphere packings have been found. Only for three types is the maximal inherent symmetry of their sphere packings monoclinic whereas the inherent symmetry is orthorhombic for 13 types, tetragonal for eight types, hexagonal for four types and cubic for one type.

On the density of homogeneous sphere packings

2005 ◽  
Vol 61 (4) ◽  
pp. 426-434 ◽  
Author(s):  
E. Koch ◽  
H. Sowa ◽  
W. Fischer
Keyword(s):  
Sphere Packings ◽  
Homogeneous Sphere

Monoclinic sphere packings. I. Invariant, univariant and bivariant lattice complexes

2016 ◽  
Vol 72 (3) ◽  
pp. 357-365 ◽  
Author(s):  
Heidrun Sowa ◽  
Werner Fischer
Keyword(s):  
Monoclinic Crystal System ◽  
Sphere Packings ◽  
Monoclinic Crystal ◽  
Homogeneous Sphere ◽  
Crystal System

All homogeneous sphere packings were derived that refer to the two invariant, the four univariant and the three bivariant lattice complexes belonging to the monoclinic crystal system. In total, sphere packings of 29 types have been found. Only for five types is the maximal inherent symmetry of their sphere packings monoclinic whereas the inherent symmetry is orthorhombic for nine types, tetragonal for five types, hexagonal for six types and cubic for four types.

Sphere configurations with the symmetry R[unk]m 18(h) .m

1999 ◽  
Vol 214 (6) ◽  
Author(s):  
H. Sowa ◽  
E. Koch
Keyword(s):  
Sphere Packings ◽  
Homogeneous Sphere

AbstractIn deriving all sphere configurations which may occur with symmetryIn addition, the possible deformations of all homogeneous sphere packings in the subgroups

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