Crystallographic complexity partition analysis

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Wolfgang Hornfeck
Keyword(s):  
Crystal Structure ◽  
Probability Distributions ◽  
Intermetallic Phase ◽  
Structural Complexity ◽  
Complexity Measures ◽  
Discrete Probability ◽  
Entropy Formula ◽  
Partition Analysis ◽  
Partial Analysis ◽  
Discrete Probability Distributions

Abstract We present an illustrative analysis of the complexity of a crystal structure based on the application of Shannon’s entropy formula in the form of Krivovichev’s complexity measures and extended according to the contributions of distinct discrete probability distributions derived from the atomic numbers and the Wyckoff multiplicities and arities of the atoms and sites constituting the crystal structure, respectively. The results of a full crystallographic complexity partition analysis for the intermetallic phase Mo3Al2C, a compound of intermediate structural complexity, are presented, with all calculations performed in detail. In addition, a partial analysis is discussed for the crystal structures of α- and β-quartz.

scholarly journals Crystal Chemical Relations in the Shchurovskyite Family: Synthesis and Crystal Structures of K2Cu[Cu3O]2(PO4)4 and K2.35Cu0.825[Cu3O]2(PO4)4

Crystals ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 807
Author(s):  
Ilya V. Kornyakov ◽  
Sergey V. Krivovichev
Keyword(s):  
Crystal Structure ◽  
Crystal Structures ◽  
Structural Complexity ◽  
Crystal Chemical ◽  
X Ray Diffraction ◽  
Complexity Measures ◽  
X Ray ◽  
The Family ◽  
Similarities And Differences ◽  
Related Compounds

Single crystals of two novel shchurovskyite-related compounds, K2Cu[Cu3O]2(PO4)4 (1) and K2.35Cu0.825[Cu3O]2(PO4)4 (2), were synthesized by crystallization from gaseous phase and structurally characterized using single-crystal X-ray diffraction analysis. The crystal structures of both compounds are based upon similar Cu-based layers, formed by rods of the [O2Cu6] dimers of oxocentered (OCu4) tetrahedra. The topologies of the layers show both similarities and differences from the shchurovskyite-type layers. The layers are connected in different fashions via additional Cu atoms located in the interlayer, in contrast to shchurovskyite, where the layers are linked by Ca2+ cations. The structures of the shchurovskyite family are characterized using information-based structural complexity measures, which demonstrate that the crystal structure of 1 is the simplest one, whereas that of 2 is the most complex in the family.

scholarly journals Classroom note: An inductive derivation of Stirling numbers of the second kind and their applications in statistics

1997 ◽  
Vol 1 (2) ◽  
pp. 151-157 ◽  
Author(s):  
Anwar H. Joarder ◽  
Munir Mahmood
Keyword(s):  
Probability Distributions ◽  
Stirling Numbers ◽  
Higher Order ◽  
Inductive Method ◽  
Higher Order Moments ◽  
Discrete Probability ◽  
Discrete Probability Distributions

An inductive method has been presented for finding Stirling numbers of the second kind. Applications to some discrete probability distributions for finding higher order moments have been discussed.

INTERACTIVE SIMULATIONS OF DISCRETE PROBABILITY DISTRIBUTIONS

2019 ◽  
Author(s):  
Rubén Darío Santiago Acosta ◽  
Ernesto Manuel Hernández Cooper ◽  
Faustino Yescas Martinez
Keyword(s):  
Probability Distributions ◽  
Discrete Probability ◽  
Discrete Probability Distributions ◽  
Interactive Simulations
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