Outlier recognition in crystal-structure least-squares modelling by diagnostic techniques based on leverage analysis.

The identification of the actual outliers in a least-squares crystal-structure model refinement and their subsequent elimination from the data set is a non-trivial task that has to be carried out carefully when a high level of accuracy of the estimates is required. One of the most suitable tools for detecting the influence of each data entry on the regression is the identification of ;leverage points'. On the other hand, the recognition of the actual statistical outliers is effectively possible by using some diagnostics as a function of the leverage, such as Cook's distance, DFFITS and FVARATIO. The evaluation of these estimators makes it possible to achieve a reliable identification of the…

Characterization of the pressure induced Ringwoodite to Mg-perovskite+Mg-wuestite phase transition by Catastrophe Theory

A computational study of point defects and diffusion in enstatite

In order to contribute to the understanding of diffusion processes in enstatite (Mg2Si2O6), we have used atomistic simulation techniques to study point defects in this mineral. We present results for a variety of Scottky and Frenkel defects of all atomic species present in it. We have furthermore calculated the activation energy for magnesium diffusion. We break diffusion down into a succession of hops between neighboring sites. Each hop is associated with a migration energy barrier. By making a series of hops, the diffusing ion may cross the unit cell. The maximum migration energy necessary to attain movement in a direction is the activation energy for diffusion in that direction. The defe…

Investigating structural properties of crystal at high pressures by means of Bader analysis of the electron density: some methodological warning

Ab-initio investigation of the thermodynamic stability of the magnesio-wüstite solid solution under Earth’s lower mantle conditions

Regression diagnostics applied in kinetic data processing: Outlier recognition and robust weighting procedures

An efficient protocol, based on advanced statistical diagnostics and robust fitting techniques applied to the least-squares processing of kinetic data of chemical reactions, is presented and discussed. The procedure, which is aimed at obtaining highly accurate estimation of the fitting parameters, consists of the identification of the outliers that remarkably impair the fitting by means of the so-called “leverage analysis” and some related diagnostics. This approach allows the elimination of the actually aberrant observations from the data set and/or their robust weighting to inhibit the negative effects induced on the data fitting, with consequent reduction of the bias introduced into the …

M1-site in dioctahedral micas: a novel approach from information theory to fix its content

The reliability of the Maximum Entropy Method MEM) to reconstruct finite temperature electron density (ED) is here discussed, investigating the case of periclase (MgO). A theoretical electron density has been generated by quantum mechanic calculations and folded with a function simulating atomic thermal motion, in order to produce a reference errorless ED [q(r)REF]. The Fourier coefficients of q(r)REF have been calculated, and used as “observed” diffraction intensities to reconstruct via MEM the original ED. The electron density attained by MEM [q(r)MEM] and q(r)REF have been compared with each other (pixel-by-pixel and critical points) to assess the ability of MEM to retrieve EDs, on the b…

Bader’s topological analysis of the electron density in the pressure-induced phase transitions/amorphization in α-quartz from the catastrophe theory viewpoint

In this work, the Bader's topological analysis of the electron density, coupled with Thom's catastrophe theory, was used to characterize the pressure-induced transformations in α-quartz. In particular, ab initio calculations of the α-quartz structures in the range 0-105 Gpa have been performed at the HF/DFT exchange-correlation terms level, using Hamiltonians based on a WC1LYP hybrid scheme. The electron densities calculated throughout the ab initio wave functions have been analysed by means of the Bader's theory, seeking for some catastrophic mechanism in the sense of Thom's theory. The analysis mainly showed that there is a typical fold catastrophe feature involving an O-O interaction at …

(2004) Struttura, natura del legame e proprietà elettroniche di SrTiO3 e Sr1-3x/2LaxTiO3

MEM reconstruction of the experimental electron density: limits and possible applications

Fe-periclase reactivity at Earth's lower mantle conditions: Ab-initio geochemical modelling

Intrinsic and extrinsic stability of the (Mg, Fe) O solid mixture in the Fe-Mg-Si-O system at high P, T conditions relevant to the Earth's mantle is investigated by the combination of quantum mechanical calculations (Hartree-26 Fock/DFT hybrid scheme), cluster expansion techniques and statistical thermodynamics. Iron in the (Mg, Fe) O binary mixture is assumed to be either in the low spin (LS) or in the high spin (HS) state. Un-mixing at solid state is observed only for the LS condition in the 23-42 GPa pressure range, whereas HS does not give rise to un-mixing. LS (Mg, Fe) O un-mixings are shown to be able to incorporate iron by subsolidus reactions with a reservoir of a virtual bridgmanit…

Melting temperature prediction by thermoelastic instability: An ab initio modelling, for periclase (MgO)

Abstract Melting temperature (TM) is a crucial physical property of solids and plays an important role for the characterization of materials, allowing us to understand their behavior at non-ambient conditions. The present investigation aims i) to provide a physically sound basis to the estimation of TM through a “critical temperature” (TC), which signals the onset of thermodynamic instability due to a change of the isothermal bulk modulus from positive to negative at a given PC-VC-TC point, such that (∂P/∂V)VC,TC = -(∂2F/∂V2) VC,TC = 0; ii) to discuss the case of periclase (MgO), for which accurate melting temperature observations as a function of pressure are available. Using first princip…

Modelling of thermo-chemical properties over the sub-solidus MgO–FeO binary, as a function of iron spin configuration, composition and temperature

Thermo-chemical properties and T–X phase relations diagram of the (Mg,Fe)O solid solution are modelled using mixing Helmholtz energy, ΔF(T,x)mixing, calculated by quantum mechanical and semi-empirical techniques. The sub-solidus MgO–FeO binary has been explored as a function of composition, with iron either in high-spin (HS) or low-spin (LS) configuration. Only the HS model provides physically sound results at room pressure, yielding a correct trend of cell edge versus composition, whereas LS’s issues are at variance with observations. Mixing Helmholtz energy has been parametrized by the following relationship: ΔF(T,x)mixing = x × y × [U0(T) + U1(T) × (x – y) + U2(T) × (x − y)2]−T × S(x,y)c…

A Bader’s topological approach for the investigation of the high pressure stability field of the Mg-perovskite phase

Calculation of the effective charges of the atomic basins from ab initio Hartree-Fock electron densities in NaAlSi2O6 and NaTiSi2O6 pyroxenes

Bader's topologycal analysis of the electron density and the laplacian in TOT Phyllosilicates: the case of pyrophyllite and talc

Iteratively reweighted least squares in crystal structure refinements

The use of robust techniques in crystal structure multipole refinements of small molecules as an alternative to the commonly adopted weighted least squares is presented and discussed. As is well known, the main disadvantage of least-squares fitting is its sensitivity to outliers. The elimination from the data set of the most aberrant reflections (due to both experimental errors and incompleteness of the model) is an effective practice that could yield satisfactory results, but it is often complicated in the presence of a great number of bad data points, whose one-by-one elimination could become unattainable. This problem can be circumvented by means of a robust least-squares regression that…

Clay-biosurfactant materials as functional drug delivery systems: Slowing down effect in the in vitro release of cinnamic acid

Abstract The main objectives of the present paper were the preparation and characterization of new surfactant-modified clays and the evaluation of their potential applicability as drug delivery systems for the oral administration of the cinnamic acid (CA) drug. The organoclays (OC) were prepared by loading different amounts of the biocompatible nonionic polyoxyethylene sorbitan monolaurate surfactant (Tween20) onto K10 montmorillonite (Mt) clay and characterized through the construction of the adsorption isotherms by means of the spectrophotometric method. The performance of the prepared material was verified by gathering the adsorption isotherms of the cinnamic acid onto the Mt/Tween20 org…

Pressure stability field of Mg-perovskite under deep mantle conditions: A topological approach based on Bader's analysis coupled with catastrophe theory

Abstract The pressure stability field of the Mg-perovskite phase was investigated by characterizing the evolution of the electron arrangement in the crystal. Ab initio calculations of the perovskite structures in the range 0–185 GPa were performed at the HF/DFT (Hartree-Fock/Density Functional Theory) exchange–correlation terms level. The electron densities, calculated throughout the ab-initio wave functions, were analysed by means of the Bader's theory, coupled with Thom's catastrophe theory. To the best of our knowledge the approach is used for the first time. The topological results show the occurrence of two topological anomalies at P~20 GPa and P~110 GPa which delineate the pressure ra…

ADSORPTION OF WATER MOLECULES ONTO 1:1 DIOCTAHEDRAL CLAY MINERALS: A BADER'S TOPOLOGICAL ANALYSIS OF THE AB-INITIO ELECTRON DENSITIES

Trace element fractionation through halite crystallisation: Geochemical mechanisms and environmental implications

Halite is an important mineral for industry, agriculture and food production. It crystallises after water evaporation, while the progressive growth of dissolved metal ions in brines is occurring. Then, halite exploitation may provide the delivery of metal ions in the environment and the mechanism of this trace element accumulation should be studied. In this work we investigate the distribution of lanthanides and Y (hereafter named Rare Earth Elements, REE), Zr and Hf between crystallising halite and brines in the Dead Sea as geochemical tools for recognising the mechanism of metal ion removal from brines and accumulation in halite. Halite forms cubic crystals where octahedral planes sometim…

(2004) Miglioramento della mappa di densità elettronica ottenuta con il Maximum Entropy Method

SYNTHESIS OF 3-SUBSTITUTED DIHYDRO-1-1PHENYLAMINO-1H-PYRROLO[1,2-A]IMIDAZOLE-2,5(3H,6H)-DIONES FROM A-AMINO ACID PHENYLHYDRAZIDES AND LEVULINIC ACID

α-N-Protected amino acid hydrazides (1) readily reacted with NaBH4 to afford 5-substituted 4,5-dihydro-1,2,4-triazin- 3(2H)-one derivatives 2 in good yields. Unfortunately, the reaction caused partial racemization at the α-amino acidic carbon atom of the starting hydrazide. A mechanism, supported by experimental evidence, has been proposed in an attempt to explain this to date unprecedented reaction. The structure of compounds 2 was confirmed by X-ray structural analysis.

Negative thermal expansion in cuprite-type compounds: A combined synchrotron XRPD, EXAFS, and computational study of Cu2O and Ag2O

Cuprite-type oxides (Cu2O and Ag2O) are framework structures composed by two interpenetrated networks of metal-sharing M4O tetrahedra (M = Cu, Ag). Both compounds exhibit a peculiar negative thermal expansion (NTE) behaviour over an extended temperature range (9 240 K for Cu2O, 30-470 K for Ag2O). High-accuracy synchrotron powder diffraction and EXAFS measurements were performed from 10 K up to the decomposition temperature to understand the nature of the NTE effects. The critical comparison of the diffraction and absorption results concerning the temperature dependence of the interatomic distances and of the atomic vibrational parameters proves to be fundamental in defining the local dynam…

Getting reliable experimental electron density maps of pure compounds and solid solution by Maximum Entropy Method

ELECTRONIC, MAGNETIC AND STRUCTURAL PROPERTIES OF NIO AND FEO THIN FILMS EPITAXIALLY GROWN ON SURFACES OF CU(001) : AN AB-INITIO DENSITY FUNCTIONAL STUDY

Ab initio calculation at DFT level of NaGaSi2O6 and LiAlSi2O6 pyroxenes: a comparison from the Bader's topology viewpoint

In situ analysis of garnet inclusion in diamond using single-crystal X-ray diffraction and X-ray micro-tomography

A single crystal of garnet enclosed in a diamond from the Jericho kimberlite (Slave Craton, Canada) has been investigated using X-ray diffraction and X-ray micro-tomography. The novel experimental approach allowed us to determine the crystal structure of the garnet. The unit-cell edge a and fractional atomic coordinates of oxygen were used to determine the composition via an updated Margules model for garnets. The composition is Pyr(0.41(5))Alm(0.36(7))Gro(0.22(1))Uva(0.01(1)), which is indistinguishable from the eclogitic garnets found in other Jericho diamonds. We also demonstrated that residual pressures on the inclusion of up to 1 GPa do not affect significantly the determination of the…

Montmorillonite nanodevices for the colon metronidazole delivery.

The adsorption profiles of the antibiotic metronidazole (MNE) into the K10-montmorillonite (MMT-K10) clay and the subsequent release have been investigated as a function of pH and MNE/MMT-K10 ratio, in order to evaluate the potential of the MNE/MMT-K10 hybrids as controlled drug delivery system. The adsorption mechanism has been first elucidated by performing complementary equilibrium and kinetic studies and through the X-ray diffractometry (XRD) characterization of the obtained composite materials. The gathered results allowed us to propose a mechanism consisting of a multi-step pathway involving the neutral and the cationic form of the drug, which interact with different sites of the clay…

5-Substituted 4,5-Dihydro-1,2,4-triazin-3(2H)-ones from the Unprecedented Reaction between α-N-Protected Amino Acid Hydrazides and NaBH4

α-N-Protected amino acid hydrazides (1) readily reacted with NaBH4 to afford 5-substituted 4,5-dihydro-1,2,4-triazin-3(2H)-one derivatives 2 in good yields. Unfortunately, the reaction caused partial racemization at the α-amino acidic carbon atom of the starting hydrazide. A mechanism, supported by experimental evidence, has been proposed in an attempt to explain this to date unprecedented reaction. The structure of compounds 2 was confirmed by X-ray structural analysis. (© Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2006)

Aluminium distribution in an Earth's non–primitive lower mantle

The aluminium incorporation mechanism of perovskite was explored by means of quantum mechanics in combination with equilibrium/off-equilibrium thermodynamics under the pressure-temperature conditions of the Earth's lower mantle (from 24 to 80 GPa). Earth's lower mantle was modelled as a geochemically non-primitive object because of an enrichment by 3 wt% of recycled crustal material (MORB component). The compositional modelling takes into account both chondrite and pyrolite reference models. The capacity of perovskite to host Al was modelled through an Al2O3 exchange process in an unconstrained Mg-perovskite + Mg-Al-perovskite + free-Al2O3(corundum) system. Aluminium is globally incorporate…

Investigating structural properties of crystal at high pressures: a contribution from the Bader analysis of the electron density

Synthesis and characterization of taylor-made organo-clays for biotechnological applications

Bader's topologycal analysis of teh electron density and the laplacian in kaolinite and dikite.

Regression diagnostics applied in kinetic data processing: outlier recognition and robust weighting procedures

An efficient protocol, based on advanced statistical diagnostics and robust fitting techniques applied to the least-squares processing of kinetic data of chemical reactions, is here presented and discussed. The procedure, which is aimed at obtaining highly accurate estimation of the fitting parameters, consists in the identification of the outliers that remarkably impair the fitting by means of the so called 'leverage analysis' and some related diagnostics, allowing the elimination of the actually aberrant observations from the data set and/or their robust weighting to inhibit the negative effects induced on the data fitting and to reduce the bias introduced into the parameter estimates. It…

(2004) Ottimizzazione del raffinamento strutturale con i minimi quadrati mediante riconoscimento ed eliminazione degli outlier attraverso la combinazione di «leverage analysis» e «Cook’s distance»

Low-pressure ferroelastic phase transition in rutile-type AX2 minerals: cassiterite (SnO2), pyrolusite (MnO2) and sellaite (MgF2)

The structural behaviour of cassiterite (SnO2), pyrolusite (MnO2) and sellaite (MgF2), i.e. AX2-minerals, has been investigated at room temperature by in situ high-pressure single-crystal diffraction, up to 14 GPa, using a diamond anvil cell. Such minerals undergo a ferroelastic phase transition, from rutile-like structure (SG: P42/mnm) to CaCl2-like structure (SG: Pnnm), at ≈ 10.25, 4.05 and 4.80 GPa, respectively. The structural evolution under pressure has been described by the trends of some structure parameters that are other than zero in the region of the low-symmetry phase’s stability. In particular, three tilting-angles (ω, ω′, ABS) and the metric distortion of the cation-centred oc…

New tailor-made bio-organoclays for the remediation of olive mill waste water

A systematic study aimed at obtaining new organoclays for the treatment of Olive Mill Waste water (OMW) has been performed. Several organoclays have been prepared by loading different amounts of the biocompatible surfactant Tween20 onto the K10 montmorillonite (MMT). Complementary kinetic and equilibrium studies on the adsorption of the Tween20 onto the MMT have been carried out and the characterization of the new tailor-made bio-materials has been performed by means of the XRD and FT-IR measurements. Finally the prepared bio-organoclays have been successfully applied for the OMW remediation and they proved to be highly effective in decreasing the organic content (OC) to an extent that depe…

Modified Montmorillonite as Drug Delivery Agent for Enhancing Antibiotic Therapy

The appealing properties of surfactant-intercalated Montmorillonites (Organo-montmorillonite, OMt) were successfully investigated to propose an effective drug delivery system for metronidazole (MNE) antibiotic therapy. This represents a serious pharmaceutical concern due to the adverse drug reactions and the low targeting ability of MNE. The non-ionic surfactant Tween 20 was used to functionalize montmorillonite, thus accomplishing the two-fold objective of enhancing the stability of clay dispersion and better controlling drug uptake and release. The adsorption process was performed under different experimental conditions and investigated by constructing the adsorption isotherms through hig…

Preparation and characterization of bio-organoclays using nonionic surfactant

The present study was aimed at the preparation and characterization of tailor made hybrid materials, whose peculiar hosting capability could be exploited in biotechnological applications. With this purpose, the modification of K10 montmorillonite by intercalation of Tween 20 surfactant, was accomplished. The influence of two internal parameters, namely pH and surfactant/clay ratio, on the surfactant uptake ability by clay was investigated. The adsorption mechanism was elucidated on the basis of complementary kinetic and equilibrium studies and, then, corroborated by the useful information provided by the FT-IR, TGA and XRD characterization. The gathered results allow to draw the conclusion …

Electron-density critical points analysis and catastrophe theory to forecast structure instability in periodic solids

The critical points analysis of electron density,i.e. ρ(x), fromab initiocalculations is used in combination with the catastrophe theory to show a correlation between ρ(x) topology and the appearance of instability that may lead to transformations of crystal structures, as a function of pressure/temperature. In particular, this study focuses on the evolution of coalescing non-degenerate critical points,i.e. such that ∇ρ(xc) = 0 and λ1, λ2, λ3≠ 0 [λ being the eigenvalues of the Hessian of ρ(x) atxc], towards degenerate critical points,i.e. ∇ρ(xc) = 0 and at least one λ equal to zero. The catastrophe theory formalism provides a mathematical tool to model ρ(x) in the neighbourhood ofxcand allo…

Characterization of the pressure induced Ringwoodite toMg-perovskite and Mg-wüstite phase transition by Catastrophe Theory

The pressure-induced ringwoodite to Mg-perovskite and periclase post-spinel phase transition: a Bader’s topological analysis of the ab initio electron densities

In order to characterize the pressure-induced decomposition of ringwoodite (c-Mg2SiO4), the topological analysis of the electron density q(r), based upon the theory of atoms in molecules (AIM) developed by Bader in the framework of the catastrophe theory, has been performed. Calculations have been carried out by means of the ab initio CRYSTAL09 code at the HF/DFT level, using Hamiltonians based on the Becke- LYP scheme containing hybrid Hartree– Fock/density functional exchange–correlation terms. The equation of state at 0 K has been constructed for the three phases involved in the post-spinel phase transition (ringwoodite -> Mg-perovskite + periclase) occurring at the transition zone–lower…

Computational study of defects in ideal phengite

Phengite is the name of a series designating the “potassic dioctahedral micas between, or close to, the joins muscovite-aluminoceladonite and muscovite-celadonite” (Rieder et al. 1998). These micas play a important role in most petrogenetic reactions occurring in high-pressure (HP) metamorphic environments; they are useful geothermobarometers and participate in reactions as H2O carriers in the subduction zone. In this work we have employed atomistic simulations techniques to model defects, evaluate the most stable defect species and determine the most likely diffusion mechanism in crystals. We have calculated the defect formation energies for vacancies, impurities and interstitials, Frenkel…

The formation of silica high temperature polymorphs from quartz: Influence of grain size and mineralising agents

Abstract The formation of high-temperature silica polymorphs in presence of Na and K has been studied at various temperatures and soaking times, starting from quartzes of different grain size, ex situ as well as in situ. The results show that cristobalite and tridymite formation is strongly influenced by the nature and the amount of mineraliser added. In particular, K seems to discriminate more between the two structures, as it produces the largest observed amount of cristobalite. The disappearance of quartz can be controlled by the proper combination of mineraliser/temperature/time, which in turn control the amount and the type of polymorph formed, together with the amount of amorphous mat…

Effect of the Biopolymer Charge and the Nanoclay Morphology on Nanocomposite Materials

This work represents a contribution to the design, preparation, and characterization of nanocomposite materials based on biocompatible components. The effects of composition, filler geometry, and polymer charge were highlighted, and their role on the final properties of the nanocomposites was revealed. We combined some biopolymers (methylcellulose, alginate, chitosan) with two nanoclays (kaolinite sheets and halloysite nanotubes) to prepare nanocomposites by means of the casting method from water. The thermal stability, the surface wettability, and the mechanical properties of the obtained films were studied. SEM micrographs highlighted the surface morphology of the biocomposite materials. …

Experimental and robust modeling approach for lead(II) uptake by alginate gel beads: influence of the ionic strength and medium composition.

Abstract Systematic kinetic and equilibrium studies on the lead ions removal ability by Ca-alginate gel beads have been performed by varying several internal parameters, namely, number of gel beads, nature and composition of the ionic medium and pH, which allowed us to model a wastewater in order to closely reproduce the composition of a real sample. Moreover, the effects brought about the different ionic species present in the reacting medium have been evaluated. Differential Pulse Anodic Stripping Voltammetry (DP-ASV), has been systematically used to perform kinetic and equilibrium measurements over continuous time in a wide range of concentration. Kinetic and equilibrium data have been q…

Kinetic and equilibrium studies for the adsorption of acid nucleic bases onto K10 montmorillonite

Abstract The kinetic of the adsorption of two nucleic acid bases, namely adenine (A) and cytosine (C), on K10 montmorillonite (MMT) clay has been investigated over a wide range of nitrogenous bases concentrations, by using the spectrophotometric method. The measurements have been performed at T = 25.0 °C and pH = 4.0 where adenine and cytosine exist both in their protonated and neutral forms. Preliminary to the kinetic data treatment, the adsorption isotherms have been gathered and, then, analyzed by using the Freundlich and the Dubinin–Radushkevich model. The obtained results allow to draw the conclusion that physisorption of adenine and cytosine on MMT occurs and the process is mainly gov…

OUTLIER RECOGNITION AND ROBUST WEIGHTING PROCEDURES APPLIED IN CATION ORDERING-DISORDERING KINETIC DATA PROCESSING

Simultaneous Removal and Recovery of Metal Ions and Dyes from Wastewater through Montmorillonite Clay Mineral

The main objective of this work was to evaluate the potential of Montmorillonite nanoclay (Mt), readily and inexpensively available, for the simultaneous adsorption (and removal) of two classes of pollutants: metal ions and dyes. The attention was focused on two &ldquo

Lower mantle hydrogen partitioning between periclase and perovskite : a quantum chemical modelling

Abstract Partitioning of hydrogen (often referred to as H2O) between periclase (pe) and perovskite (pvk) at lower mantle conditions (24–80 GPa) was investigated using quantum mechanics, equilibrium reaction thermodynamics and by monitoring two H-incorporation models. One of these (MSWV) was based on replacements provided by Mg2+ ↔ 2H+ and Si4+ ↔ 4H+; while the other (MSWA) relied upon substitutions in 2Mg2+ ↔ Al3+ + H+ and Si4+ ↔ Al3+ + H+. H2O partitioning in these phases was considered in the light of homogeneous (Bulk Silicate Earth; pvk: 75%–pe:16% model contents) and heterogeneous (Layered Mantle; pvk:78%–pe:14% modal contents) mantle geochemical models, which were configured for lower…

Deconvolution procedure of the UV-vis spectra. A powerful tool for the estimation of the binding of a model drug to specific solubilisation loci of bio-compatible aqueous surfactant-forming micelle

UV-vis-spectra evolution of Nile Red loaded into Tween 20 micelles with pH and [Tween 20] have been analysed in a non-conventional manner by exploiting the deconvolution method. The number of buried sub-bands has been found to depend on both pH and bio-surfactant concentration, whose positions have been associated to Nile Red confined in aqueous solution and in the three micellar solubilisation sites. For the first time, by using an extended classical two-pseudo-phases-model, the robust treatment of the spectrophotometric data allows the estimation of Nile Red binding constant to the available loci. Hosting capability towards Nile Red is exalted by the pH enhancement. Comparison between bin…

About the reliability of the Maximum Entropy Method in reconstructing electron density: the case of MgO

Abstract The reliability of the Maximum Entropy Method (MEM) to reconstruct finite temperature electron density (ED) is here discussed, investigating the case of periclase (MgO). A theoretical electron density has been generated by quantum mechanic calculations and folded with a function simulating atomic thermal motion, in order to produce a reference errorless ED [ρ(r)REF]. The Fourier coefficients of ρ(r)REF have been calculated, and used as “observed” diffraction intensities to reconstruct via MEM the original ED. The electron density attained by MEM [ρ(r)MEM] and ρ(r)REF have been compared with each other (pixel-by-pixel and critical points) to assess the ability of MEM to retrieve EDs…

Maximum entropy method : an unconventional approach to explore observables related to the electron density in phengites

The maximum entropy method (MEM) is used here to get an insight into the electron density [rho(r)] of phengites 2M (1) and 3T, paying special attention to the M1-formally empty site and charge distribution. Room temperature single crystal X-ray diffraction data have been used as experimental input for MEM. The results obtained by MEM have been compared with those from conventional structure refinement which, in turn, has provided the prior-electron density to start the entropy maximization process. MEM reveals a comparatively non-committal approach, able to produce information related to the M1-site fractional occupancy, and yields results consistent with those from the difference Fourier s…

La ricostruzione della densità elettronica sperimentale mediante il metodo di massimizzazione della entropia: il caso delle fengiti

Beyond the Vegard's law: solid mixing excess volume and thermodynamic potentials prediction, from end-members

Abstract A method has been developed, herein presented, to model binary solid solutions' volume, enthalpy and Gibbs energy using the energy state functions, E ( V , S ) , of the end-members only. The E ( V , S ) s are expanded around an unknown mixing volume, V Mix , and the fundamental equilibrium equation − ( ∂ E / ∂ V ) S = P is used to determine V Mix . V Mix allows us to model enthalpy, straightforwardly. The same argument holds using Helmholtz energy, F ( V , T ) , in place of E ( V , S ) , and the equilibrium equation becomes − ( ∂ F / ∂ V ) T = P . One can readily determine the Gibbs free energy, too. The method presented remarkably simplifies computing of solid mixings' thermodynam…

Bader's analysis of the electron density in the Pbca enstatite - Pbcn protoenstatite phase transition

The Bader’s topological analysis of the electron density obtained via ab initio quantum mechanical simulation at Hartree–Fock and DFT level has been performed for experimentally in situ heated structures of enstatite–protoenstatite MgSiO 3 . The measurements have been performed in the temperature range 1200–1400 K. The work was aimed at characterizing both the evolution of the electron arrangement in the crystal and that of the crystal-structure at the enstatite–protoenstatite phase transition in terms of topology of the electron density, with particular care about the Mg–O and the O–O bonds. The observed breaking of some chemical bonds with increasing temperature and/or due to the phase tr…

Metronidazole/montmorillonite nanodevices for controlled drug delivery

Ab initio quantum-mechanical simulation of the adsorption process of Ti, Ca, Na by a corundum crystal: inferences on defects of industrial glass