scholarly journals Corrigendum: On the Determination of Coordination Numbers of Coupled DEM-DFN Model for Modeling Fractured Rocks

2021 ◽  
Vol 9 ◽  
Author(s):  
Xiaoyi Xu ◽  
Li-Yun Fu ◽  
Ning Liu ◽  
Tongcheng Han
2021 ◽  
Vol 9 ◽  
Author(s):  
Xiaoyi Xu ◽  
Li-Yun Fu ◽  
Ning Liu ◽  
Tongcheng Han

Natural fractured rocks usually contain background granular media and multi-scale fractures. The coordination number is a crucial factor to characterize the connection of microstructural elements. The determination of coordination numbers for modeling fractured rocks is essential to interpret the distribution of cracks related to micromechanical properties. We have built a consistent workflow of discrete element models (DEMs) coupled with discrete fracture networks (DFNs). This DEM-DFN model could provide a simple formulation for high calculation efficiency to model a more realistic and detailed description of fracture system. A series of numerical experiments are set up, aiming to correlate window radius, particle size, and crack length, which will benefit the window selection for measuring coordination numbers based on the crack characteristics. The coordination number determined in the DEM-DFN modeling can be used to identify crack patterns in the spatial distribution.


2000 ◽  
Vol 55 (9) ◽  
pp. 773-784 ◽  
Author(s):  
Hans Bock ◽  
Erik Heigel ◽  
Norbert Nagel

Imidodiphosphates ⊖N[PO(OR)2]2 and Imidodiphosphonates ⊖N[POR2]2 are effective chelating ligands for a variety of metal cations including even Na⊕, for which a lipophilically wrapped hexameric polyion cluster has been structurally characterized. The corresponding hexameric lithium and polyrubidium ion complexes reported here exhibit considerable structural differences: The rather small Li⊕ cations of coordination number five and tetraphenylimidodiphosphate form an isolated hexameric aggregate analogous to the Na⊕ one, whereas the larger Rb⊕ with coordination number seven and (3,4-dimethylphenyl)substituents crystallizes as a chain polymer. Based on the crystal structures, the dominant Coulomb attractions between cations and anions, the spatial requirement of the ligands and the essential phenyl/phenyl interactions in their lipophilic skin are discussed


2000 ◽  
Vol 12 (6) ◽  
pp. 1119-1131 ◽  
Author(s):  
L A Bugaev ◽  
Ph Ildefonse ◽  
A M Flank ◽  
A P Sokolenko ◽  
H V Dmitrienko

2016 ◽  
Vol 88 (3) ◽  
pp. 163-176 ◽  
Author(s):  
Ariel A. Chialvo ◽  
Lukas Vlcek

AbstractWe explore the deconvolution of correlations for the interpretation of the microstructural behavior of aqueous electrolytes according to the neutron diffraction with isotopic substitution (NDIS) approach toward the experimental determination of ion coordination numbers of systems involving oxyanions, in particular, sulfate anions. We discuss the alluded interplay in the title of this presentation, emphasized the expectations, and highlight the significance of tackling the challenging NDIS experiments. Specifically, we focus on the potential occurrence of $N{i^{2 + }} \cdots SO_4^{2 - }$ pair formation, identify its signature, suggest novel ways either for the direct probe of the contact ion pair (CIP) strength and the subsequent correction of its effects on the measured coordination numbers, or for the determination of anion coordination numbers free of CIP contributions through the implementation of null-cation environments. For that purpose we perform simulations of NiSO4 aqueous solutions at ambient conditions to generate the distribution functions required in the analysis (a) to identify the individual partial contributions to the total neutron-weighted distribution function, (b) to isolate and assess the contribution of $N{i^{2 + }} \cdots SO_4^{2 - }$ pair formation, (c) to test the accuracy of the neutron diffraction with isotope substitution based coordination calculations and X-ray diffraction based assumptions, and (d) to describe the water coordination around both the sulfur and oxygen sites of the sulfate anion. We finally discuss the strength of this interplay on the basis of the inherent molecular simulation ability to provide all pair correlation functions that fully characterize the system microstructure and allows us to “reconstruct” the eventual NDIS output, i.e., to take an atomistic “peek” (e.g., see Figure 1) at the local environment around the isotopically-labeled species before any experiment is ever attempted, and ultimately, to test the accuracy of the “measured” NDIS-based coordination numbers against the actual values by the “direct” counting.


1998 ◽  
Vol 54 (3) ◽  
pp. 221-230 ◽  
Author(s):  
G. H. Rao ◽  
I. D. Brown

The distribution of valence among the bonds in the bond graph of an inorganic compound is used to calculate an `entropy'. We show that the distribution of valence that maximizes this entropy (ME) is similar, but not identical, to that obtained using the equal-valence rule (EVR) proposed by Brown [Acta Cryst. (1977), B33, 1305–1310]. Since the ME solutions are maximally non-committal with regard to missing information, they give better predictions of the observed valence distributions than the EVR solutions when lattice constraints or electronic anisotropies are present, but worse predictions when these effects are absent. Since valences calculated using ME are necessarily positive, they give significantly better predictions in cases where EVR predicts a negative bond valence. In the absence of electronic distortions the observed bond graph is either the graph with the highest maximum entropy or it has an entropy within 1% of this value. Since the entropy depends on the oxidation states of the atoms, compounds with the same stoichiometry and cation coordination numbers but different atomic valences may adopt different bond graphs and hence different structures.


Sign in / Sign up

Export Citation Format

Share Document