Charge Distribution and Bond Valence Sum Analysis of Sulfosalts—The ECoN21 Computer Program
Abstract
:1. Introduction
2. The Calculation Procedure
2.1. The Charge Distribution Method
- i—the index of ligands in an HSP;
- j—the index of HSPs in a CP;
- X—the index of crystallographic species of central atoms (or of distinct CP);
- A—the index of crystallographic species of ligands.
2.2. The Bond Valence Sum Method
2.3. Coordination Geometry
- the coordinatesof the centroid—obtained by expressing Equation (18) in terms of orthogonal coordinates and by solving the linear system formed by the partial derivatives for and which are set equal to zero;
- the components of the vector between the centroid and the central atom—indicating the direction opposite to the lone electron pair of the central atom;
- the displacement of the central atom from the centroid;
- the radiusof the LSF sphere—represented by the average distance between the centroid and the ligands;
- the volumeof the LSF sphere;
- the linear eccentricity of the central atom:
- the ‘volume-based’ eccentricity of the central atom, obtained by comparing the volume of the LSF sphere with the volume of the sphere of radius :
- the linear sphericity of the ligand distribution:
- the ‘volume-based’ sphericity of the ligand distribution:
- the volumeof the CP obtained by dividing the CP into tetrahedra delimited by triplets of adjacent vertices and the central atom, and by summation of their volumes;
- the approximation of the ideal polyhedron of maximum volume inscribed in the LSF sphere—established as a function of and number of CP faces;
- the volume of the ideal polyhedron inscribable in the LSF sphere and which has the maximum possible volume for that sphere;
- the volume distortion of the CP:
- the deviation of from :
- the distortion indexof a CP (Baur [32]):
- the bond valence-based distortion index (Brown [27]):
3. The ECoN21 Program
3.1. General Features
- unit cell parameters
- symmetry operators
- atom labels
- atom symbols
- oxidation numbers
- fractional coordinates
- occupancies
3.2. Interpreting the Results
- the , , and values should be close to their corresponding formal oxidation numbers or , respectively. Consequently, the departure from 1.0 of the / and / ratios may also be used to assess the matching between the formal and calculated charges. In the cation-centered description, the / ratio gives a measure of the overall geometric correctness of the structure (atom coordinates, distances), whereas / points to the over- or underbonding effects induced by inadequate calculated charges of the central atoms (e.g., Nespolo et al. [11,12]), making it suitable for measuring the effects of compositional changes in central heterovalent mixed positions. In the anion-centered description, the significance of the two ratios is reversed.
- the mean absolute percentage deviation (Eon and Nespolo [13]) of , , or from the nominal oxidation numbers ( or ) for the entire structure or selected clusters of atoms. These values should be as close as possible to 0%. It may be roughly estimated that global s calculated for the central atoms and larger than 10% point out negative issues in the refinement of the crystal structure. Elevated s for global or local ligands should draw attention to potentially misassigned oxidation numbers of the central atoms.
4. Case Studies
4.1. Rathite (Phase ‘rath7’)—Example of Site Population ‘Bracketing’
4.2. Mutnovskite—From Homoligand and Heteroligand Perspective
4.3. Dalnegroite—The Propagation of Local CD Anomalies
4.4. ECoN and the Polyhedral Distortion
5. Conclusions
Supplementary Materials
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Mixtures | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | ||
M1 | Pb1 | 1.00 | 0.95 | 0.90 | 0.85 | 0.80 | 0.75 | 0.70 | 0.65 | 0.60 | 0.55 | 0.50 | 0.46 |
Tl1 | 0.00 | 0.05 | 0.10 | 0.15 | 0.20 | 0.25 | 0.30 | 0.35 | 0.40 | 0.45 | 0.50 | 0.54 | |
charge | 2.00 | 1.95 | 1.90 | 1.85 | 1.80 | 1.75 | 1.70 | 1.65 | 1.60 | 1.55 | 1.50 | 1.46 | |
M2 | Pb2 | 0.46 | 0.51 | 0.56 | 0.61 | 0.66 | 0.71 | 0.76 | 0.81 | 0.86 | 0.91 | 0.96 | 1.00 |
Tl2 | 0.54 | 0.49 | 0.44 | 0.39 | 0.34 | 0.29 | 0.24 | 0.19 | 0.14 | 0.09 | 0.04 | 0.00 | |
charge | 1.46 | 1.51 | 1.56 | 1.61 | 1.66 | 1.71 | 1.76 | 1.81 | 1.86 | 1.91 | 1.96 | 2.00 | |
S1 | −1.98 | −1.98 | −1.98 | −1.98 | −1.98 | −1.98 | −1.98 | −1.98 | −1.98 | −1.98 | −1.99 | −1.99 | |
S2 | −2.04 | −2.04 | −2.03 | −2.03 | −2.03 | −2.03 | −2.02 | −2.02 | −2.02 | −2.02 | −2.01 | −2.01 | |
S3 | −2.08 | −2.07 | −2.06 | −2.05 | −2.04 | −2.03 | −2.02 | −2.01 | −2.00 | −1.99 | −1.98 | −1.97 | |
S4 | −2.01 | −2.02 | −2.03 | −2.04 | −2.05 | −2.06 | −2.07 | −2.08 | −2.09 | −2.10 | −2.11 | −2.12 | |
S5 | −2.33 | −2.33 | −2.34 | −2.34 | −2.34 | −2.34 | −2.34 | −2.35 | −2.35 | −2.35 | −2.35 | −2.35 | |
S6 | −1.99 | −2.00 | −2.00 | −2.00 | −2.00 | −2.00 | −2.00 | −2.01 | −2.01 | −2.01 | −2.01 | −2.01 | |
S7 | −2.14 | −2.14 | −2.14 | −2.13 | −2.13 | −2.12 | −2.12 | −2.11 | −2.11 | −2.10 | −2.10 | −2.10 | |
S8 | −1.61 | −1.61 | −1.61 | −1.62 | −1.62 | −1.62 | −1.62 | −1.62 | −1.63 | −1.63 | −1.63 | −1.63 | |
CD- (%) | |||||||||||||
S (M1) 1 | 5.15 | 5.01 | 4.87 | 4.73 | 4.60 | 4.49 | 4.38 | 4.26 | 4.15 | 4.20 | 4.26 | 4.30 | |
S (M2) 2 | 6.61 | 6.66 | 6.71 | 6.76 | 6.83 | 6.91 | 6.98 | 7.06 | 7.14 | 7.22 | 7.30 | 7.36 | |
S (M1–M2) 3 | 6.35 | 6.30 | 6.25 | 6.20 | 6.16 | 6.13 | 6.09 | 6.06 | 6.04 | 6.11 | 6.22 | 6.29 | |
CC 4 | 2.94 | 2.96 | 2.99 | 3.01 | 3.04 | 3.06 | 3.08 | 3.10 | 3.12 | 3.14 | 3.16 | 3.18 | |
6.67 | 6.63 | 6.59 | 6.55 | 6.51 | 6.49 | 6.46 | 6.44 | 6.41 | 6.49 | 6.56 | 6.62 | ||
BVS− (%) | |||||||||||||
M1 | 23.85 | 21.90 | 19.79 | 17.57 | 15.22 | 12.74 | 10.18 | 7.39 | 4.44 | 1.29 | 2.07 | 4.86 | |
M2 | 15.21 | 11.32 | 7.69 | 4.29 | 1.08 | 1.93 | 4.77 | 7.40 | 9.95 | 12.36 | 14.64 | 16.40 | |
M1–M2 | 19.53 | 16.61 | 13.74 | 10.93 | 8.15 | 7.34 | 7.47 | 7.40 | 7.19 | 6.82 | 8.35 | 10.63 |
Homoligand | Heteroligand | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Cations | Ligands | Anions | Anions | ||||||||
Pb1 | 9 | S–Se2 | 2.760 | 1.403 | S–Se1 | –2.147 | 2.024 | 1.252 | S–Se1 | –2.108 | 2.021 |
S–Se1 | 2.853 | 1.211 | S–Se2 | –2.016 | 1.054 | S–Se2 | –1.889 | ||||
S–Se1 | 2.853 | 1.211 | I–Cl–Br | –0.691 | 1.054 | I–Cl–Br | –1.001 | ||||
S–Se2 | 3.194 | 0.553 | 0.421 | ||||||||
S–Se1 | 3.637 | 0.085 | 0.047 | ||||||||
S–Se1 | 3.637 | 0.085 | 0.047 | ||||||||
I–Cl–Br | 3.534 | 0.323 | 1.220 | ||||||||
I–Cl–Br | 3.570 | 0.122 | 0.846 | ||||||||
I–Cl–Br | 3.570 | 0.122 | 0.846 | ||||||||
: | 5.115 | : | 6.785 | ||||||||
Pb2 | 8 | S–Se1 | 2.907 | 1.402 | 2.121 | 1.371 | 1.968 | ||||
S–Se1 | 2.907 | 1.402 | 1.371 | ||||||||
S–Se1 | 3.269 | 0.712 | 0.680 | ||||||||
S–Se1 | 3.269 | 0.712 | 0.680 | ||||||||
S–Se2 | 3.447 | 0.431 | 0.405 | ||||||||
S–Se2 | 3.447 | 0.431 | 0.405 | ||||||||
I–Cl–Br | 3.047 | 1.128 | 1.226 | ||||||||
I–Cl–Br | 3.446 | 0.432 | 0.515 | ||||||||
: | 6.648 | : | 6.652 | ||||||||
As–Bi | 3 | S–Se1 | 2.241 | 1.004 | 2.855 | 1.004 | 3.011 | ||||
S–Se1 | 2.241 | 1.004 | 1.004 | ||||||||
S–Se2 | 2.246 | 0.992 | 0.992 | ||||||||
: | 3.000 | : | 3.000 | ||||||||
13.01 | 4.03 | 3.69 | 1.02 |
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Ilinca, G. Charge Distribution and Bond Valence Sum Analysis of Sulfosalts—The ECoN21 Computer Program. Minerals 2022, 12, 924. https://doi.org/10.3390/min12080924
Ilinca G. Charge Distribution and Bond Valence Sum Analysis of Sulfosalts—The ECoN21 Computer Program. Minerals. 2022; 12(8):924. https://doi.org/10.3390/min12080924
Chicago/Turabian StyleIlinca, Gheorghe. 2022. "Charge Distribution and Bond Valence Sum Analysis of Sulfosalts—The ECoN21 Computer Program" Minerals 12, no. 8: 924. https://doi.org/10.3390/min12080924