The Six-Cornered Snowflake.

Coxeter, H. S. M.; Kepler, Johannes; Hardie, Colin; Whyte, L. L.; Mason, B. F. J.

doi:10.2307/2313830

Cited by 5 publications

(6 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Hooke appears to have been unaware of similar descriptions of the relationship between external crystal form and internal structure made earlier by Johannes Kepler, but they are no less remarkable and also highly relevant to this story. In his booklet of 1611 On the Six-Cornered Snowflake Kepler considered whether any body, similar to the five regular solids and to the fourteen Archimedean solids could be constructed with nothing but rhombi [5]. He found two, the simplest being the rhombic dodecahedron, which he related to the way in which individual cells interlock in honeycomb and, perhaps more indirectly, to the individual seed casings in pomegranates.…”

Section: Some Historical Reflections On Crystal Packingmentioning

confidence: 99%

Molecules in crystals

Spackman¹

2013

Phys. Scr.

139

View full text Add to dashboard Cite

Hirshfeld surface analysis has developed from the serendipitous discovery of a novel partitioning of the crystal electron density into discrete molecular fragments, to a suite of computational tools used widely for the identification, analysis and discussion of intermolecular interactions in molecular crystals. The relationship between the Hirshfeld surface and very early ideas on the internal structure of crystals is outlined, and applications of Hirshfeld surface analysis are presented for three molecules of historical importance in the development of modern x-ray crystallography: hexamethylbenzene, hexamethylenetetramine and diketopiperazine.

show abstract

Section: Some Historical Reflections On Crystal Packingmentioning

confidence: 99%

Molecules in crystals

Spackman¹

2013

Phys. Scr.

139

View full text Add to dashboard Cite

show abstract

“…This is an old problem and can be traced back to the days of Johannes Kepler ͑1571-1630͒ who proposed that close packing ͓either cubic or hexagonal close packing, both of which have maximum densities of /3 ͱ 2 ͑ϳ74%͔͒ is the densest possible sphere packing. 16 The well-known face-centered-cubic ͑fcc͒ lattice structure is an example of the stacking model proposed by Kepler ͑Fig. 5b͒.…”

Section: Multiple Layers Of Close-packed Spheres-thementioning

confidence: 99%

Si Electrodes for Li-Ion Batteries—A New Way to Look at an Old Problem

Beattie

Larcher

Morcrette

et al. 2008

J. Electrochem. Soc.

360

297

View full text Add to dashboard Cite

High-capacity Si-based electrodes could replace carbon-based electrodes in the next generation of Li-ion batteries. Although Si-based electrodes have large gravimetric capacities, they typically suffer from poor cyclability. One reason for the poor cyclability is large volume expansion associated with 3.75 mol of Li reacting with 1 mol of Si. A theoretical approach to design electrodes that can accommodate this large volume expansion is discussed. It is shown that experimental results agree well with the theoretical approach. We show that Si-based electrodes with a relatively low Si content ͑Ͻ33 wt %͒ and high binder content ͑33-56 wt %͒ cycle at large capacities ͑ϳ660 mAh/g͒ for hundreds of cycles. No special electrode processing or cycling procedures are required to achieve high capacities with good cyclability.

show abstract

“…1 notes a few key events in cataloging crystal properties. We start with Kepler (1611) [translated in Kepler et al (1966)] and Steno (see Authier, 2013) who conjectured on the structures of crystals. Hau ¨y (1800) created the first catalog of minerals.…”

Section: Historymentioning

confidence: 99%

Measuring lattices

Andrews,

Bernstein

2023

Acta Cryst Sect A

View full text Add to dashboard Cite

Unit cells are used to represent crystallographic lattices. Calculations measuring the differences between unit cells are used to provide metrics for measuring meaningful distances between three-dimensional crystallographic lattices. This is a surprisingly complex and computationally demanding problem. A review is presented of the current best practice using Delaunay-reduced unit cells in the six-dimensional real space of Selling scalar cells S 6 and the equivalent three-dimensional complex space C 3. The process is a simplified version of the process needed when working with the more complex six-dimensional real space of Niggli-reduced unit cells G 6. Obtaining a distance begins with identification of the fundamental region in the space, continues with conversion to primitive cells and reduction, analysis of distances to the boundaries of the fundamental unit, and is completed by a comparison of direct paths with boundary-interrupted paths, looking for a path of minimal length.

show abstract

The Six-Cornered Snowflake.

Cited by 5 publications

References 0 publications

Molecules in crystals

Molecules in crystals

Si Electrodes for Li-Ion Batteries—A New Way to Look at an Old Problem

Measuring lattices

Contact Info

Product

Resources

About