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Roebling Medal Paper. Toward theoretical mineralogy: A bond-topological approach

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Published/Copyright: April 3, 2015
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American Mineralogist
From the journal American Mineralogist Volume 100 Issue 4

Abstract

The patterns of linkage of chemical bonds in space contain significant energetic information that may be used as the basis of a theoretical approach to the structure and chemical composition of minerals. This approach combines aspects of graph theory, bond-valence theory, and the moments approach to the electronic-energy density-of-states to interpret topological aspects of crystal structures, and allows consideration of many issues of crystal structure, mineral composition, and mineral behavior that are not addressed by established theoretical methods. The chemical composition of a mineral is controlled by the weak interaction between the structural unit and the interstitial complex. The principle of correspondence of Lewis acidity-basicity asserts that stable structures will form when the Lewisbase strength of the structural unit closely matches the Lewis-acid strength of the interstitial complex. This principle allows analysis of the factors that control the chemical compositions and aspects of the structural arrangements of minerals, and provides a mechanism to understand the relations between structure, the speciation of its constituents in aqueous solution, and its mechanism of crystallization. (H2O) groups in the structural unit limit the polymerization of the structural unit in one or more directions, controlling the polymerization of the structural unit. This is a major cause of structural diversity in oxygen-based minerals, and accounts for the systematic distribution in mineral species from the core to the surface of the Earth.

The moments approach to the electronic-energy density-of-states provides a bond-topological interpretation of the energetics of a structure. When comparing structures, the most important structural differences involve the first few disparate moments of the electronic-energy density-of-states. We may classify chemical reactions according to the lowest-order moment of the electronic-energy density-ofstates that is conserved, which allows us to identify the principal structural changes that drive chemical change: (1) coordination number for discontinuous reactions, and (2) short-range order for continuous reactions. This relation between the bond topology of a structure and its enthalpy of formation from constituent oxides is indicated by a correlation between change in anion-coordination number and reduced enthalpy of formation for the reactions [6]Mgm[4]SinO(m+2n) = mMgO+nSiO2.

Keywords : Bond topology; graph theory; bond-valence theory; electronic-energy density-of-states; polyhedron linkage; chemical composition; structural unit; interstitial complex
Received: 2014-7-4
Accepted: 2014-9-10
Published Online: 2015-4-3
Published in Print: 2015-4-1

© 2015 by Walter de Gruyter Berlin/Boston

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  26. Density functional investigation of the thermo-physical and thermo-chemical properties of 2M1 muscovite
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https://doi.org/10.2138/am-2015-5114
Keywords for this article
Bond topology; graph theory; bond-valence theory; electronic-energy density-of-states; polyhedron linkage; chemical composition; structural unit; interstitial complex

Articles in the same Issue

  1. Highlights and Breakthroughs. Clays are messy—also on Mars
  2. Highlights and Breakthroughs. Tweed, Twins, and Holes: A link between mineralogy and materials science
  3. Highlights and Breakthroughs. Bursting the bubble of melt inclusions
  4. Review. Mineralogy, materials science, energy, and environment: A 2015 perspective
  5. Crossroads in Earth and Planetary Materials. Block-by-block and layer-by-layer growth modes in coral skeletons
  6. Roebling Medal Paper. Toward theoretical mineralogy: A bond-topological approach
  7. Investigating Petrologic Indicators of Magmatic Processes in Volcanic Rocks. Petalite under pressure: Elastic behavior and phase stability
  8. Investigating Petrologic Indicators of Magmatic Processes in Volcanic Rocks. Pre-eruptive magma mixing and crystal transfer revealed by phenocryst and microlite compositions in basaltic andesite from the 2008 eruption of Kasatochi Island volcano
  9. What Lurks in the Martian Rocks and Soil? Investigations of Sulfates, Phosphates, and Perchlorates. Akaganéite and schwertmannite: Spectral properties and geochemical implications of their possible presence on Mars
  10. Special Collection: Mechanisms, Rates, and Timescales of Geochemical Transport Processes in the Crust and Mantle. Timescales of exhumation and cooling inferred by kinetic modeling: An example using a lamellar garnet pyroxenite from the Variscan Granulitgebirge, Germany
  11. Special Collection: Glasses, Melts, and Fluids, as Tools for Understanding Volcanic Processes and Hazards. Constraints on the origin of sub-effusive nodules from the Sarno (Pomici di Base) eruption of Mt. Somma-Vesuvius (Italy) based on compositions of silicate-melt inclusions and clinopyroxene
  12. Special Collection: Glasses, Melts, and Fluids, as Tools for Understanding Volcanic Processes and Hazards. Experiments and models on H2O retrograde solubility in volcanic systems
  13. Special Collection: Glasses, Melts, and Fluids, as Tools for Understanding Volcanic Processes and Hazards. Melt inclusion CO2 contents, pressures of olivine crystallization, and the problem of shrinkage bubbles
  14. Special Collection: Glasses, Melts, and Fluids, as Tools for Understanding Volcanic Processes and Hazards. Spatio-temporal constraints on magma storage and ascent conditions in a transtensional tectonic setting: The case of the Terceira Island (Azores)
  15. Special Collection: Glasses, Melts, and Fluids, as Tools for Understanding Volcanic Processes and Hazards. Bubbles matter: An assessment of the contribution of vapor bubbles to melt inclusion volatile budgets
  16. The origin and implications of clay minerals from Yellowknife Bay, Gale crater, Mars
  17. The whole-block approach to measuring hydrogen diffusivity in nominally anhydrous minerals
  18. Atom probe tomography of isoferroplatinum
  19. Structural investigation of (130) twins and rutile precipitates in chrysoberyl crystals from Rio das Pratinhas in Bahia (Brazil)
  20. Carbon speciation in silicate-C-O-H melt and fluid as a function of redox conditions: An experimental study, in situ to 1.7 GPa and 900 °C
  21. Kinetic behavior of partially dehydroxylated kaolinite
  22. The fall and rise of metamorphic zircon
  23. Eckermannite revised: The new holotype from the Jade Mine Tract, Myanmar—crystal structure, mineral data, and hints on the reasons for the rarity of eckermannite
  24. In-situ oxygen isotope and trace element geothermometry of rutilated quartz from Alpine fissures
  25. Synchrotron micro-spectroscopic examination of Indonesian nickel laterites
  26. Density functional investigation of the thermo-physical and thermo-chemical properties of 2M1 muscovite
  27. Complex IR spectra of OH– groups in silicate glasses: Implications for the use of the 4500 cm–1 IR peak as a marker of OH– groups concentration
  28. Versatile Monazite: Resolving Geological Records and Solving Challenges in Materials Science. Monazite, zircon, and garnet growth in migmatitic pelites as a record of metamorphism and partial melting in the East Humboldt Range, Nevada
  29. The Second Conference on the Lunar Highlands Crust and New Directions. Revised mineral and Mg# maps of the Moon from integrating results from the Lunar Prospector neutron and gamma-ray spectrometers with Clementine spectroscopy
  30. The Second Conference on the Lunar Highlands Crust and New Directions. Low-pressure crystallization of a volatile-rich lunar basalt: A means for producing local anorthosites?
  31. Fluids in the Crust. Experimental constraints on fluid-rock reactions during incipient serpentinization of harzburgite
  32. Minerals in the human body. Crystal chemical and structural modifications of erionite fibers leached with simulated lung fluids
  33. Letter. Competition between two redox states in silicate melts: An in-situ experiment at the Fe K-edge and Eu L3-edge
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