Leverage analysis and structure refinement of minerals
-
Marcello Merli
,
Luciano Ungaretti
Abstract
Leverage analysis allows detection of the reflections that have the greatest influence on the estimate of a refined variable. We have applied leverage analysis in the structure refinement of some rock-forming minerals, in the attempt of settling the best procedures to obtain accurate and reliable results. Attention has been focused on those variables (e.g., the refined site-scatterings) which are fundamental to the determination of site populations, which in turn are the basis for the study of order-disorder processes and petrogenetic modeling. A garnet (pyrope) and an amphibole (tremolite) were used to test the procedure, being illustrative of different symmetries and structural complexity. As the omission of reflections with high leverage on a particular variable may strongly decrease the accuracy in its estimate, the results indicate that systematic procedures for data truncation [either on the basis of (low or high) sin θ/λ, high ΔF/θFo or of low I/σI] are potentially dangerous.
The choice of a correctly ionized model is shown to be critical to obtain accurate estimates of the refined site-scatterings. The set of reflections with the highest leverage value with respect to a peculiar group of variables was found to be nearly invariant within isomorphous solid-solutions; this implies that the results of this work are valid throughout the amphibole and garnet compositional spaces. The warnings proposed to the treatment and refinement of X-ray diffracted data may be of general utility in the structure refinement of minerals.
© 2015 by Walter de Gruyter Berlin/Boston
Articles in the same Issue
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- A crystal chemical re-evaluation of amphibole/melt and amphibole/clinopyroxene DTi values in petrogenetic studies
- Mineralogy of mafic xenoliths and their reaction zones in the olivine lamproite from Prairie Creek Arkansas and the paragenesis of haggertyite, Ba [Fe6Ti5Mg]O19
- Magmatic anhydrite in granitic rocks: First occurrence and potential petrologic consequences
- Crystal chemistry of Al-rich biotites coexisting with muscovites in peraluminous granites
- Spectroscopic and structural properties of synthetic micas on the annite-siderophyllite binary: Synthesis, crystal structure refinement, Mössbauer, and infrared spectroscopy
- Thermodynamic properties of tremolite: A correction and some comments
- Raman spectroscopic characteristics of Mg-Fe-Ca pyroxenes
- Hydrogen in diopside: Diffusion profiles
- Diffusion of C and O in calcite at 100 MPa
- Solubility and stability of zeolites in aqueous solution: II. Calcic clinoptilolite and mordenite
- TEM and SFM of exsolution and twinning in an alkali feldspar
- Equation of state of magnetite and its high-pressure modification: Thermodynamics of the Fe-O system at high pressure
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- The absolute energy positions of conduction and valence bands of selected semiconducting minerals
- Antiferroelectric phase transition in titanite: Excess entropy and short range order
- P4/n and P4nc long-range ordering in low-temperature vesuvianites
- Tetrahedral vacancies and cation ordering in low-temperature Mn-bearing vesuvianites: Indication of a hydrogarnet-like substitution
- Sodic-ferripedrizite, a new monoclinic amphibole bridging the magnesium-iron-manganese-lithium and the sodium-calcium groups
- The crystal structure of peprossiite-(Ce), an anhydrous REE and Al mica-like borate with square-pyramidal coordination for Al
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- Letters. In-situ Raman spectra of dissolved silica species in aqueous fluids to 900 °C and 14 kbar
- Quetzalcoatlite: A new octahedral-tetrahedral structure from a 2 × 2 × 40 μm3 crystal at the Advanced Photon Source-GSE-CARS Facility
- Bonding and dynamics of Mg in pyrope: a theoretical investigation
- Structure of a new Al-rich phase, [K, Na]0.9[Mg, Fe]2[Mg, Fe, Al, Si]6O12, synthesized at 24 GPa
- Core level electron binding energies of realgar (As4S4)
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Articles in the same Issue
- Iron concentration and the physical processes of dynamic oxidation in an alkaline earth aluminosilicate glass
- A crystal chemical re-evaluation of amphibole/melt and amphibole/clinopyroxene DTi values in petrogenetic studies
- Mineralogy of mafic xenoliths and their reaction zones in the olivine lamproite from Prairie Creek Arkansas and the paragenesis of haggertyite, Ba [Fe6Ti5Mg]O19
- Magmatic anhydrite in granitic rocks: First occurrence and potential petrologic consequences
- Crystal chemistry of Al-rich biotites coexisting with muscovites in peraluminous granites
- Spectroscopic and structural properties of synthetic micas on the annite-siderophyllite binary: Synthesis, crystal structure refinement, Mössbauer, and infrared spectroscopy
- Thermodynamic properties of tremolite: A correction and some comments
- Raman spectroscopic characteristics of Mg-Fe-Ca pyroxenes
- Hydrogen in diopside: Diffusion profiles
- Diffusion of C and O in calcite at 100 MPa
- Solubility and stability of zeolites in aqueous solution: II. Calcic clinoptilolite and mordenite
- TEM and SFM of exsolution and twinning in an alkali feldspar
- Equation of state of magnetite and its high-pressure modification: Thermodynamics of the Fe-O system at high pressure
- Optimization of site occupancies in minerals using quadratic programming
- Leverage analysis and structure refinement of minerals
- The absolute energy positions of conduction and valence bands of selected semiconducting minerals
- Antiferroelectric phase transition in titanite: Excess entropy and short range order
- P4/n and P4nc long-range ordering in low-temperature vesuvianites
- Tetrahedral vacancies and cation ordering in low-temperature Mn-bearing vesuvianites: Indication of a hydrogarnet-like substitution
- Sodic-ferripedrizite, a new monoclinic amphibole bridging the magnesium-iron-manganese-lithium and the sodium-calcium groups
- The crystal structure of peprossiite-(Ce), an anhydrous REE and Al mica-like borate with square-pyramidal coordination for Al
- Crystal chemistry of the new mineral brandholzite, Mg(H2O)6[Sb(OH)6]2, and of the synthetic analogues M2+(H2O)6[Sb(OH)6]2 (M2+ = Mg, Co)
- Letters. In-situ Raman spectra of dissolved silica species in aqueous fluids to 900 °C and 14 kbar
- Quetzalcoatlite: A new octahedral-tetrahedral structure from a 2 × 2 × 40 μm3 crystal at the Advanced Photon Source-GSE-CARS Facility
- Bonding and dynamics of Mg in pyrope: a theoretical investigation
- Structure of a new Al-rich phase, [K, Na]0.9[Mg, Fe]2[Mg, Fe, Al, Si]6O12, synthesized at 24 GPa
- Core level electron binding energies of realgar (As4S4)
- Oxidation of {100} and {111} surfaces of pyrite: Effects of preparation method
