2013
DOI: 10.1180/minmag.2013.077.3.05
|View full text |Cite
|
Sign up to set email alerts
|

Abstract: Structural complexity of minerals is characterized using information contents of their crystal structures calculated according to the modified Shannon formula. The crystal structure is considered as a message consisting of atoms classified into equivalence classes according to their distribution over crystallographic orbits (Wyckoff sites). The proposed complexity measures combine both size- and symmetry-sensitive aspects of crystal structures. Information-based complexity parameters have been calculated for … Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
1
1
1

Citation Types

8
209
1
3

Year Published

2013
2013
2023
2023

Publication Types

Select...
6
1

Relationship

0
7

Authors

Journals

citations
Cited by 221 publications
(221 citation statements)
references
References 108 publications
(145 reference statements)
8
209
1
3
Order By: Relevance
“…4 Geometrical parameters of hydrogen bonding system in the crystal structures of clinoclase and gilmarite viewpoint of the information amount per unit cell, the structural arrangement of gilmarite is much simpler than that of clinoclase. According to the Goldsmith's simplexity principle (Goldsmith 1953) and its current interpretation (Krivovichev 2013(Krivovichev , 2015, this may indicate that gilmarite is a metastable phase crystallized under some kinetically favored conditions. This suggestion is corroborated by the comparison of the values of physical density, which is equal to 4.264 g/cm 3 for gilmarite and 4.397 g/cm 3 for clinoclase.…”
Section: Resultsmentioning
confidence: 99%
See 3 more Smart Citations
“…4 Geometrical parameters of hydrogen bonding system in the crystal structures of clinoclase and gilmarite viewpoint of the information amount per unit cell, the structural arrangement of gilmarite is much simpler than that of clinoclase. According to the Goldsmith's simplexity principle (Goldsmith 1953) and its current interpretation (Krivovichev 2013(Krivovichev , 2015, this may indicate that gilmarite is a metastable phase crystallized under some kinetically favored conditions. This suggestion is corroborated by the comparison of the values of physical density, which is equal to 4.264 g/cm 3 for gilmarite and 4.397 g/cm 3 for clinoclase.…”
Section: Resultsmentioning
confidence: 99%
“…According to this approach developed by Krivovichev (2012Krivovichev ( , 2013, the complexity of a crystal structure can be quantitatively characterized by the amount of Shannon information it contains measured in bits (binary digits) per atom (bits/atom) and Eby and Hawthorne (1990); coordinates of H atoms are optimized using DFT method per unit cell (bits/cell), respectively. The concept of Shannon information, also known as Shannon entropy, used here originates from information theory and its application to various problems in graph theory, chemistry, biology, etc.…”
Section: Structural Complexity Calculationsmentioning
confidence: 99%
See 2 more Smart Citations
“…(H5O2)2SO4, CaMgSi2O6, K2S5O16, Na2B4O7, Na2PO3F, CaCrF5 and TeI4 (Brown,1977), KVO3 (Rutherford, 1990), Ca2B2Si2O8, Sr3Ti2O7, Ba2FeSi2O7, Sr3Zr2O7, Y2SiBe2O7 and KFeFPO4 (Urusov & Orlov, 1999), scapolite, (Hawthorne & Sokolova, 2008), milarite (Gagné & Hawthorne, 2016a). Here, we use a priori bond-valence calculations to calculate a priori bondlengths in a series of rock-forming minerals of different complexity (as measured by the topological information content ; Krivovichev, 2012Krivovichev, , 2013 and degrees of complication. These calculations allow assessment of the strain in a crystal structure and provide a way to examine the effect of bond topology on variation in observed bond-lengths for the same ion-pair in different bond topologies.…”
Section: Is Used Extensively In Crystallography Andmentioning
confidence: 99%