Outlier recognition in the 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 outliers and the elimination of those that impair the least-squares fit. In this paper, a procedure for filtering data points based on this kind of analysis for crystallographic X-ray data is presented and discussed

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 leastsquares 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 minimizes the influence of outliers. This work is aimed at showing the capability of a robust regression to achieve an higher reliability of the least-squares estimates with respect to the traditional weighted least-squares crystal structure refinement in terms of both accuracy and precision. The results can be considered encouraging and represent a starting point for future developments

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 incorporated principally via an increase in the amount of Al bearing perovskite [Mg-Al-pv(80 GPa)/Mg-Al-pv(24 GPa)1.17], rather than by an increase in the Al2O3 content of the average chemical composition which changes little (0.11-0.13, mole fraction of Al2O3) and tends to decrease in Al. The Al2O3 distribution in the lower mantle was described through the probability of the occurrence of given compositions of Al bearing perovskite. The probability of finding Mg-Al-perovskite is comparable to Mg-perovskites. Perovskite with Al2O3 mole fraction up to 0.15 has an occurrence probability of ~28% at 24 GPa, increasing up to ~43% at 80 GPa; on the contrary, perovskite compositions in the range 0.19-0.30 Al2O3 mole fraction drop their occurrence probability from 9.8 to 2.0%, over the same P-range. In light of this, the distribution of Al in the lower mantle shows that, among the possible Al bearing perovskite phases, the (Mg0.89Al0.11)(Si0.89Al0.11)O3 composition is the likeliest, providing from 5 to 8% of the bulk perovskite in the pressure range from 24 to 80 GPa. The occurrence of the most Al rich composition, i.e. (Mg0.71Al0.29)(Si0.71Al0.29)O3, is a rare event (probability of occurrence < 1.7%). This study predicts that perovskite may globally host Al2O3 in terms of 4.3 and 4.8 wt% (with respect to the non-primitive lower mantle mass), thus accounting for ~ 90% and 100% of the bulk Al2O3 estimated in the framework of pyrolite and chondrite reference models, respectively. A calcium-ferrite type phase (on the MgAl2O4-NaAlSiO4 join) seems to be the only candidate that can compensate for the 10% gap of the perovskite Al incorporation capacity, in the case of a pyrolite non-primitive lower mantle model

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)config, where y = 1−x and Uj(T) are polynomials in T of the second order. ΔF(T,x)mixing exhibits a quasi-symmetric behaviour and allows one to build the T–X phase relations diagram over the MgO–FeO join. The HS model including vibrational contribution to the Helmholtz energy predicts a solid solution’s critical temperature of some 950 K, remarkably larger than olivine’s and Mg–Fe garnet’s. All this points to a more difficult Mg–Fe mixing in periclase-like structure than olivine and garnet, which, in turn, provide more structure degrees of freedom for atomic relaxation. From ΔF(T,x)mixing, we have then derived ΔH(T,x)excess and ΔS(T,x)excess. The former, characterized by a quasi-regular behaviour, has been parametrized through W × x × (1−x), obtaining WH,Mg–Fe of 17.7(5) kJ/mol. ΔS(T,x)excess, in turn, increases as a function of temperature, showing absolute figures confined within 0.1 J/mol/K. Mixing Gibbs energy, calculated combining the present issues with earlier theoretical determinations of the magnesio-wüstite’s elastic properties, has shown that the HS configuration is stable and promote Mg–Fe solid solution up to ≈15 GPa

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 binding constant values classically evaluated and those estimated by the deconvolution protocol unveiled that overall binding values perfectly match with the mean values of the local binding sites. This result suggests that deconvolution procedure provides more precise and reliable values, which are more representative of drug confinement

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

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\u2013185 GPa were performed at the HF/DFT (Hartree-Fock/Density Functional Theory) exchange\u2013correlation 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 range where Mg-perovskite is stable. The paper accomplishes the twofold objectives of providing a contribution in shading light into the behaviour of the dominant component of the Earth's lower mantle across the D\u2019\u2019 layer and of proposing a novel approach in predicting the stability of a compound at extreme conditions

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

none9A 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 garnet composition by structure refinement.noneFABRIZIO NESTOLA;M. MERLI;PAOLO NIMIS;M. PARISATTO;M. KOPYLOVA;A. DE;M. LONGO;L. ZIBERNA;M. MANGHNANINestola, Fabrizio; M., Merli; Nimis, Paolo; Parisatto, Matteo; M., Kopylova; A., De; Longo, Micaela; Ziberna, Luca; M., Manghnan