Experimental multipole-refined and theoretical charge density study of LiGaSi<Subscript>2</Subscript>O<Subscript>6</Subscript> clinopyroxene at ambient conditions

The synthetic LiGaSi₂O₆ clinopyroxene is monoclinic C2/c at room-T. Its experimental electron density, ρ(r), has been derived starting from accurate room-T single-crystal diffraction data. Topological analysis confirms an intermediate ionic-covalent character for Si–O bonding, as found by previous electron-density studies on other silicates such as diopside, coesite and stishovite. The non-bridging Si–O bonds have more covalent character than the bridging ones. The Ga–O bonds have different bonding characters, the Ga–O2 bond being more covalent than the two Ga–O1 bonds. Li–O bonds are classified as pure closed-shell ionic interactions. Similar to spodumene (LiAlSi₂O₆), Li has sixfold coordination, but the bond critical points associated to the two longest bonds are characterized by very low electron density values. Similar to what previously found in spodumene and diopside, O···O interactions were detected from the topological analysis of ρ(r), and indicate a cooperative interaction among the lone pairs of neighbouring oxygen atoms. In particular, this kind of interaction has been obtained for the O1···O1 edge shared between two Ga octahedra. Integration over the atomic basins gives net charges of −1.39(10), 2.82(10), 1.91(10) and 0.82(8) e for O (averaged), Si, Ga and Li atoms, respectively. Periodic Hartree–Fock and DFT calculations confirm the results obtained by multipole refinement of the experimental data. Moreover, the theoretical topological properties of the electron density distribution on the Si₂O₆ group are very similar to those calculated for spodumene. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

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 (γ-Mg₂SiO₄), the topological analysis of the electron density ρ(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 mantel boundary. The topological results show that the decomposition of the ringwoodite at high pressures is caused by a conflict catastrophe. Furthermore, topological evidences of the central role played by the oxygen atoms to facilitate the pressure-induced ringwoodite decomposition and the subsequent phase transition have been noticed.     

Critical point properties of electron density distributions for oxide molecules containing first and second row cations

 Minimum energy geometries and electron density distributions, ϱ(r), for ∼40 polyatomic oxide molecules containing first and second row M-cations have been calculated at the Hartree-Fock level with a 6-311++G** basis set. The nature of the bonded interactions in these molecules is examined in terms of the relative electronegativities, χ _M , of the M-cations and the properties of the electron density distribution, ϱ(r _c ), evaluated at the bond critical points, r _c , along each MO bond. As ϱ(r _c ) and the Laplacian of ϱ(r _c ) increase, χ _M increases indicating an increase in the covalent character of the bonded interactions between M and O. The ratios of the curvatures of ϱ(r _c ) indicate that the NO bond is predominantly covalent, that the CO and SO bonds are of intermediate type and that the remaining MO bonds are indicated to be predominantly ionic in character. A comparison of the critical point properties of ϱ(r _c ) and χ _M indicates that the minimum energy MO bond length is an important determinate of the properties of ϱ(r _c ) and the character of the MO bonds. On the other hand, values of the local energy density, H(r _c ), indicate that the LiO, BeO, NaO, MgO and AlO bonds are predominantly ionic and that the BO, CO, NO, SiO, PO and SO bonds are predominantly covalent in character. The χ _M -values provided by the properties of ϱ(r _c ) indicate that the covalent component of a bond increases with decreasing bond length, coordination number and increasing bond strength. Each MO bond seems to represent a unique entity and to possess a distinct set of ϱ(r _c ) properties, the distinction being greater for the more electronegative cations. The bonded radius of the oxide ion, r _b (O), and the χ _M -values determined from ϱ(r _c ) correlate with values determined from promolecule electron density distributions. In addition, r _b (O) and χ _M -values determined from experimental electron density distributions for crystals correlate with values determined from procrystal electron density distributions. The number of critical points and bond paths are modeled rather faithfully by procrystal and promolecule electron density distributions, despite the neglect of the binding forces in their constructions. Received: October 15, 1996/Revised, accepted: February 10, 1997     

Electron density distributions and bonded interactions for the fibrous zeolites natrolite, mesolite and scolecite and related materials

 For the fibrous zeolites natrolite, Na₂[Al₂Si₃O₁₀]·2H₂O, mesolite, Na₂Ca₂[Al₂Si₃O₁₀]₃·8H₂O, and scolecite, Ca[Al₂Si₃O₁₀]·3H₂O, with topologically identical aluminosilicate framework structures, accurate single-crystal X-ray diffraction data have been analyzed by least-squares refinements using generalized scattering factor (GSF) models. The final agreement indices were R(F ) = 0.0061, 0.0165, and 0.0073, respectively. Ensuing calculations of static deformation [Δρ(r)], and total, [ρ(r)], model electron density distributions served to study chemical bonding, in particular by topological electron density analyses yielding bond critical point (bcp) properties and in situ cation electronegativities. The results for 32 SiO, 24 AlO, 14 CaO, and 12 NaO unique bonds are compiled and analyzed in terms of both mean values and correlations between bond lengths, bonded oxygen radii, bcp densities, curvatures at the bcps, and electronegativities. Comparison with recent literature data obtained from both experimental electron density studies on minerals and model calculations for geometry-optimized molecules shows that the majority of the present findings conforms well with chemical expectation and with the trends observed from molecular modeling. For the SiO bond, the shared interaction is indicated to increase with decreasing bond length, whereas the AlO bond is of distinctly more polar nature, as is the NaO bond compared to CaO. Also, the observed ranges of the Si and Al in situ electronegativities and their mean electronegativities agree well with both Pauling's values and model calculation results, and statistically significant correlations are obtained which are consistent with trends described for oxide and nitride molecules. Received: 10 May 1999 / Revised, accepted: 14 September 1999     

Ab initio Hartree–Fock study and charge density analysis of beryl (Al4Be6Si12O36)

 An ab initio Hartree–Fock calculation on beryl structure has been performed and the wave function has been used for an analysis of the electron density. The equilibrium geometry, determined by minimizing the energy with respect to cell parameters and fractional coordinates, is in good agreement with structural experimental measurements; small differences in length between the various Si–O bonds of the structure are well reproduced by the calculation. The two non-equivalent oxygen atoms (O1 and O2) of beryl show different electron distributions. In particular, the valence shell charge concentration (VSCC) of O1 (the bridge between two Si ions) has a torus-like shape, showing a bulge on the external side of the Si–O–Si angle and a thinning on the internal side of it; by contrast O2 has two lone pairs which are approximately located on the line for O2, normal to the plane passing, on average, through the atoms O2, Si, Be and Al. The electron density of each oxygen is strongly polarized toward the Si ions and much less polarized towards the other cations. Such features of the VSCC of the oxygens can be recast in terms of the valence bond theory, to explain the observed differences in bond lengths. By calculating the potential inside the channels of the beryl structure, predictions could be made about the positions occupied by alkali cations, which are often found in natural minerals belonging to the beryl group: results agree in general with experimental findings, but foresee a shift of such cations off the central positions located on the six fold symmetry axis. Additionally, calculations of position and orientation of H₂O inside the channel, in the alkali-free beryl, locate the molecule close to the basal plane, with the H⋯H axis parallel to [001] or oriented at 40^∘ from it. Received: 12 December 2001 / Accepted: 6 April 2002     

A physical basis for Pauling's definition of bond strength

 The average strength, s, of the bonded interactions comprising a cation containing oxide anion coordination polyhedron and the value of the electron density, ρ(r _c ), at the bond-critical points are inversely correlated with bond length. In each case, the observed bond lengths, R, were modeled with power-law expressions defined in terms of s/r and ρ(r _c )/r, respectively, where r is the Periodic Table row number of the cation involved in the bonded interaction. On the basis of the close connection between bond strength and the value of the electron density at the bond-critical point, we conclude that bond strength is a direct measure of bond type; the greater its value, the greater the localization of electron density in the binding region and the greater the shared–electron covalent character of the bonded interaction. Received: 15 October 2002 / Accepted: 17 February 2003 Present address:G. V. Gibbs in care of M. Spackman Department of Chemistry, University of New England, Armidale 2351, Australia Acknowledgements The NSF is thanked for supporting this study with grant EAR–9627458. The paper was written while GVG was a Visiting NSF Scholar at The University of Arizona. The faculty and graduate students of the Department of Geosciences and Bob Downs and Marelina Stimpf in particular are thanked for making the visit great fun.     

Potential protonation sites in the Al<Subscript>2</Subscript>SiO<Subscript>5</Subscript> polymorphs based on polarized FTIR spectroscopy and properties of the electron density distribution

Potential protonation sites for, kyanite, sillimanite, and andalusite, located in a mapping of the (3, −3) critical points displayed by their L(r) = −∇²ρ(r) distributions, are compared with polarized single-crystal FTIR spectra of kyanite and sillimanite determined earlier and with andalusite measured in this study. For andalusite, seven peaks were observed when the electric vector, E, is parallel to [100]: four intense ones at 3,440, 3,460, 3,526, and 3,597 cm⁻¹ and three weaker ones at 3,480, 3,520, and 3,653 cm⁻¹. Six peaks, three intense ones at 3,440, 3,460, and 3,526 cm⁻¹ and three weaker ones at 3,480, 3,520, and 3,653 cm⁻¹ when E parallels [010]. No peaks were observed when E is parallel to [001]. The concentration of water in andalusite varies between 110 and 168 ppm by weight % H₂O. Polarized FTIR spectra indicate that the OH vector is parallel to (001) in andalusite and sillimanite and in kyanite. Examination of the L(r) (3, −3) critical points in comparison with the polarized FTIR indicates that H prefers to bond to the oxygen atoms O1 and O2 in andalusite and O2 and O4 in sillimanite which correspond to the underbonded oxygen atoms and those with the largest L(r) maxima. In kyanite, comparison of the FTIR spectrum and the critical points indicates that H will preferentially bond to the two 4-coordinated O2 and O6 atoms.     

A study of the bonded interactions in nitride molecules in terms of bond critical point properties and relative electronegativities

Bond critical point properties calculated for the MN bonds in a number of geometry optimized nitride molecules containing first- and second-row M cations are compared with those calculated for a number of oxide molecules. As reported for the oxides, the value of the electron density, ρ(r _c ), at the bond critical points, r _c , increases with decreasing bond length while for the more electronegative cations, the local energy density, H(r _c ) decreases nonlinearly in value as the relative electronegativities of the M-cations, χ _M , tend to increase. In the majority of cases, χ_M, |λ₁|/λ₃ and ∇²ρ(r _c ) increase with decreasing minimum energy bond lengths. The bond lengths adopted by the molecules are indicated to be an important determinant of the critical point properties of the electron density distributions. The relative electronegativities derived from the electron density distributions of the nitrides agree with those derived for the oxides and Pauling’s electronegativities to within ∼5%, on average. Received: 3 February 1997 / Revised, accepted: 11 July 1997     

Shear modulus, heat capacity, viscosity and structural relaxation time of Na2O–Al2O3–SiO2 and Na2O–Fe2O3–Al2O3–SiO2 melts

The configurational heat capacity, shear modulus and shear viscosity of a series of Na₂O–Fe₂O₃–Al₂O₃–SiO₂ melts have been determined as a function of composition. A change in composition dependence of each of the physical properties is observed as Na₂O/(Na₂O + Al₂O₃) is decreased, and the peralkaline melts become peraluminous and a new charge-balanced Al-structure appears in the melts. Of special interest are the frequency dependent (1 mHz–1 Hz) measurements of the shear modulus. These forced oscillation measurements determine the lifetimes of Si–O bonds and Na–O bonds in the melt. The lifetime of the Al–O bonds could not, however, be resolved from the mechanical spectrum. Therefore, it appears that the lifetime of Al–O bonds in these melts is similar to that of Si–O bonds with the Al–O relaxation peak being subsumed by the Si–O relaxation peak. The appearance of a new Al-structure in the peraluminous melts also cannot be resolved from the mechanical spectra, although a change in elastic shear modulus is determined as a function of composition. The structural shear-relaxation time of some of these melts is not that which is predicted by the Maxwell equation, but up to 1.5 orders of magnitude faster. Although the configurational heat capacity, density and shear modulus of the melts show a change in trend as a function of composition at the boundary between peralkaline and peraluminous, the deviation in relaxation time from the Maxwell equation occurs in the peralkaline regime. The measured relaxation times for both the very peralkaline melts and the peraluminous melts are identical with the calculated Maxwell relaxation time. As the Maxwell equation was created to describe the timescale of flow of a mono-structure material, a deviation from the prediction would indicate that the structure of the melt is too complex to be described by this simple flow equation. One possibility is that Al-rich channels form and then disappear with decreasing Si/Al, and that the flow is dominated by the lifetime of Si–O bonds in the Al-poor peralkaline melts, and by the lifetime of Al–O bonds in the relatively Si-poor peralkaline and peraluminous melts with a complex flow mechanism occurring in the mid-compositions. This anomalous deviation from the calculated relaxation time appears to be independent of the change in structure expected to occur at the peralkaline/peraluminous boundary due to the lack of charge-balancing cations for the Al-tetrahedra.     

ELF isosurface maps for the Al2SiO5 polymorphs

This study examines the electron localization function (ELF) isosurfaces of the Al₂SiO₅ polymorphs kyanite, sillimanite, and andalusite to see how differences in coordination and geometry of the cations and anions affect the ELF isosurfaces. Examination of the ELF isosurfaces indicates that their shapes are dependent on the coordination and geometry of the oxygen atoms and are not sensitive to coordination of the surrounding cations. Of the 18 crystallographically distinct oxygen atoms in the Al₂SiO₅ polymorphs, 13 are bonded to two aluminum atoms and one silicon atom (Al₂–O–Si) and are associated with two different ELF isosurface shapes. The shape of the ELF isosurface is dependent on the distance at which the oxygen atom lies from a plane defined by the three surrounding cations: at a distance greater than 0.2 Å the ELF can be defined as horseshoe-shaped and at a distance less then 0.2 Å it can be described as concave hemispherical. This feature is also seen in the ELF isosurfaces for the oxygens bonded to three aluminum atoms (Al₃–O) where the isosurfaces can be defined as trigonally toroidal and uniaxially trigonally toroidal. The changes in the ELF isosurfaces for the three coordinated oxygens are also indicative of changes in hybridization. The ELF isosurface for the two-fold coordinated oxygen (Al–O–Si) has a large mushroom-shaped isosurface along the Al–O bond and a concave hemispherical isosurface along the Si–O. The four-fold coordinated oxygen (Al₄–O) contains two concave hemispherical isosurfaces along the shorter Al–O bonds and a banana-shaped isosurface, which encompasses the longer Al–O bonds. In addition, this study shows the homeomorphic relationship between the ELF isosurfaces and electron density difference maps with respect to number and arrangement of domains.     

An X-ray diffraction study of shock-wave-densified SiO<Subscript>2</Subscript> glasses

 The densification and structural changes in SiO₂ glass compressed up to 43.4 GPa by shock experiments are investigated quantitatively by the X-ray diffraction technique. Direct structural data (average Si–O and Si–Si distances and Si–O–Si angles, coordination number of the Si atom) of these shock-densified SiO₂ glasses have been obtained by analyzing the radial distribution function curves, RDF(r), calculated with X-ray diffraction data. The coordination number of all densified glasses is about 4 and shows almost no pressure variation. The SiO₂ glass has shown density increase of 11% at a shock compression of 26.3 GPa. This density evolution could not be explained by the coordination change. The reduction of the average Si–O–Si angle (144° at 0 GPa to 136° at 26.3 GPa) obtained from RDF(r) data may account for this density increase. This Si–O–Si angle change may be caused by shrinkage of the network structure and the increase of small rings of SiO₄ tetrahedra. For higher shock pressure, a decrease in the Si–O–Si angle to 140° was observed. This is consistent with the decrease in density at 32.0 and 43.2 GPa. This decrease in the Si–O–Si angle and density could be attributed to an annealing effect due to high after-shock residual temperature. This pressure dependence of average Si–O–Si angles in shock-densified SiO₂ glass agrees with the results of our previous Raman spectroscopic study. On the other hand, the pressure variation for the first sharp diffraction peak (FSDP) was analyzed to estimate the evolution of intermediate range structures. It is suggested that the mean d value (d _m ) obtained from the position of FSDP strongly depends on the shock and residual temperature, as well as shock pressure. Received: 29 June 2001 / Accepted: 14 November 2001     

Visualization-based analysis of structural and dynamical properties of simulated hydrous silicate melt

We have explored first-principles molecular dynamics simulation data for hydrous MgSiO₃ liquid (with 10 wt% water) to gain insight into its structural and dynamical behavior as a function of pressure (0–150 GPa) and temperature (2,000–6,000 K). By visualizing/analyzing a number of parameters associated with short- and mid-range orders, we have shown that the melt structure changes substantially on compression. The speciation of the water component at low pressures is dominated by the isolated structures (with over 90% hydrogen participated) consisting of hydroxyls, water molecules, O–H–O bridging and four-atom (O–H–O–H and H–O–H–O) groups, where every oxygen atom may be a part of polyhedron or free (i.e., bound to only magnesium atom). Hydroxyls favor polyhedral sites over magnesium sites whereas molecular water is almost entirely bound to magnesium sites, and also interpolyhedral bridging (Si–O–H–O–Si) dominates other types of bridging. Water content is shown to enhance and suppress, respectively, the proportions of hydroxyls and molecular water. As compression increases, these isolated structures increasingly combine with each other to form extended structures involving a total of five or more O and H atoms and also containing threefold coordination species, which together consume over 80% hydrogen at the highest compression studied. Our results show that water lowers the mean coordination numbers of different types including all cation–anion environments. The hydrous melt tends to be more tetrahedrally coordinated but with the Si–Si network being more disrupted compared to the anhydrous melt. Protons increase the content of non-bridging oxygen and decrease the contents of bridging oxygen as well as oxygen triclusters (present at pressures above 10 GPa). The calculated self-diffusion coefficients of all atomic species are enhanced in the presence of water compared to those of the anhydrous melt. This is consistent with the prediction that water depolymerizes the melt structure at all pressures. Our analysis also suggests that proton diffusion involves two processes—the transfer of H atoms (requiring the rupture and formation of O–H bonds) and the motion of hydroxyls as hydrogen carriers (requiring the rupture and formation of Si–O and/or Mg–O bonds). Both the processes are operative at low compression whereas only the first process is operative at high compression.     

Charge-density analysis of spodumene (LiAlSi<Subscript>2</Subscript>O<Subscript>6</Subscript>), from ab initio Hartree–Fock calculations

An ab initio Hartree–Fock study of spodumene structure has been performed, and the wave function was used for a topological analysis of the electron density. The three non-equivalent oxygen atoms (O1, O2 and O3) of spodumene differed mainly in their valence shell charge concentration (VSCC). In particular, O1 shows a maximum of charge concentration along the Si–O bond path, and two other maxima, which can be regarded as lone pairs, point in the opposite direction with respect to the silicon position. O2 shows a torus of local charge concentration, whose axis is parallel to the Al–Si direction, with a bulge on the external side of the Si–O2–Al angle; even if no maximum exists in the Si direction, the valence shell of O2 appears to be strongly polarized toward the silicon; a slight polarization also exists along the Al–O bond path. A similar situation is displayed by O3, whose charge concentration has a torus-like shape, with the axis parallel to the Si–Si direction, and a bulge on the external side of the Si–O3–Si angle; as in the case of O2, a significant polarization of the valence shell of O3 is observed, towards the two Si directions. By recasting the calculated electron distribution in terms of the valence bond theory, a correlation has been found between structural details (bond lengths) and the hybridization state of the oxygen atoms.     

Thermal expansion and decomposition of jarosite: a high-temperature neutron diffraction study

The structure of deuterated jarosite, KFe₃(SO₄)₂(OD)₆, was investigated using time-of-flight neutron diffraction up to its dehydroxylation temperature. Rietveld analysis reveals that with increasing temperature, its c dimension expands at a rate ~10 times greater than that for a. This anisotropy of thermal expansion is due to rapid increase in the thickness of the (001) sheet of [Fe(O,OH)₆] octahedra and [SO₄] tetrahedra with increasing temperature. Fitting of the measured cell volumes yields a coefficient of thermal expansion, α = α₀ + α₁ T, where α₀ = 1.01 × 10⁻⁴ K⁻¹ and α₁ = −1.15 × 10⁻⁷ K⁻². On heating, the hydrogen bonds, O1···D–O3, through which the (001) octahedral–tetrahedral sheets are held together, become weakened, as reflected by an increase in the D···O1 distance and a concomitant decrease in the O3–D distance with increasing temperature. On further heating to 575 K, jarosite starts to decompose into nanocrystalline yavapaiite and hematite (as well as water vapor), a direct result of the breaking of the hydrogen bonds that hold the jarosite structure together.     

The combined inelastic neutron scattering and solid state DFT study of hydrogen atoms dynamics in a highly ordered kaolinite

The dynamics of the hydrogen atoms in the highly ordered kaolinite was studied by vibrational spectroscopy based on inelastic neutron scattering method with the focus on the spectral region of 100–1,250 cm⁻¹. The experimental spectrum was interpreted by means of the solid state density functional theory calculations covering both normal mode analysis and molecular dynamics going beyond the harmonic approximation. The Al–O–H bending modes were found to be spread over the large interval of 100–1,100 cm⁻¹, with the dominant contributions located between 800 and 1,100 cm^-1. The shapes of the individual hydrogen spectra depend on the strengths of the individual interlayer O–H···O hydrogen bonds involving the inner surface hydroxyl groups. The modes assigned to the in-plane movements of the respective hydrogen atoms are well-defined and always appear on the top of the intervals of energy transfer. In contrast, the modes generated by the out-of-plane movements are spread over large intervals of energies spanning down to the region of external (lattice) modes.     

Compression mechanisms of coesite

 The structure of coesite has been determined at ten pressures up to a maximum of 8.68 GPa by single-crystal X-ray diffraction. The dominant mechanism of compression is the reduction of four of the five independent Si–O–Si angles within the structure. There is no evidence of the fifth linkage, Si1–O1–Si1, deviating from 180°. Some Si–O bond distances also decrease by up to 1.6% over the pressure range studied. The pattern of Si–O–Si angle reduction amounts to a rotation of the Si2 tetrahedron around the [001] direction. This rotation induces significant internal deformation of the Si1 tetrahedron. Comparison of the experimental data with rigid-unit distance least-squares simulations of coesite suggests that this pattern of compression, the anomalous positive values of both s₂₃ and K′′ in the equation of state of coesite, its high elastic anisotropy and the unusual straight Si1–O1–Si1 linkage within the structure are all consequences of the connectivity of the tetrahedral framework. Received: 11 July 2002 / Accepted: 14 January 2003 Acknowledgements The help of Christian Baerlocher of ETH Zurich in providing both the DLS-76 software and advice in its use is gratefully acknowledged, as are discussions with Paul Ribbe of Virginia Tech and the comments of two anonymous reviewers. The data analysis was supported by the National Science Foundation under grant EAR-0105864 to N.L. Ross and R.J. Angel.     

The charge-density distribution, its multipole refinement and the antiferromagnetic structure of dioptase, Cu6[Si6O18]·6H2O

 The chemical bonding in the ring silicate mineral dioptase is investigated on the basis of accurate single-crystal X-ray diffraction data. A multipole model is used in the refinements. Static deformation electron density is mapped for the silicon tetrahedron, Cu-octahedron and water molecule in different sections. The silicon tetrahedron exhibits peaks resulting from σ-bonds between Si–sp³ hybrid orbitals and O–p orbitals. The excess density is located on bonds between the Si atom and bridge (in ring) O(1)-, O(1′)-oxygens and across the interior of the Si–O–Si angle. In the Jahn-Teller distorted Cu octahedron, in addition to peaks which result from single Cu–O σ-bonds, there are peaks which are due to 3d electrons. The analysis of crystal-field influence on the Cu charge distribution is made using the tetragonal D _{4 d} approximation for the low-symmetry (C1) Cu octahedron. The calculation of the occupancies of the 3d atomic orbitals shows that the Cu non-bonding orbitals are most populated (˜20%) and the bonding orbitals least populated (14%), as is typical for the Jahn-Teller octahedron. The effective atomic charge on the Cu atom in dioptase determined from the multipoles is +1.23e: closer to the Cu⁺¹ than to the Cu⁺² state. The charge on the Si atom has a value +1.17e, which is in the range typical for Si atoms already determined by this method. The accumulation of density on bridge oxygens and across the interior of the Si–O–Si angle may be explained by additional strain in the bond with the decrease of the Si–O–Si angle in dioptase to 132°. The same effect was found earlier in coesite. A single-crystal neutron diffraction study shows that dioptase becomes antiferromagnetic below a Néel temperature of 15.9(1) K, in contrast to the previously reported specific heat anomaly at 21 K. The magnetic propagation vector is (0, 0, 3/2) on the hexagonal triple cell or (1/2, 1/2, 1/2) in rhombohedral indices. The relation between the antiferromagnetic and the charge-density models for dioptase is discussed. The less occupied Cu d _x2−y2 orbitals are responsible for the magnetic properties. These lie in the Cu–O squares, which are approximately perpendicular to c _hex, but which are alternately inclined to it by a small angle. The magnetic moments of 0.59(1)μ _B on the Cu ions in the same level are ordered ferromagnetically, but between ions in alternate levels the coupling is antiferromagnet. Within experimental error the magnetic moments are perpendicular to the square planes, which make an angle ±13(3)° to the triad axis. Received: 8 June 2001 / Accepted: 10 January 2002     

Plastic deformation of wadsleyite: III. Interpretation of dislocations and slip systems

 Linear anisotropic elasticity has been applied to interpret the dislocation stability and ease of slip in wadsleyite. It is shown that wadsleyite is very isotropic from the elastic point of view. The influence of crystal chemistry and bonding on the choice of the slip plane is discussed. It is shown that slip is predominantly achieved on planes that do not shear Si–O bonds. It is suggested that dissociation of dislocations is essential in determining the ease of slip among the various slip systems. Received: 15 July 2002 / Accepted: 14 February 2003 Acknowledgements High-pressure experiments were performed at the Bayerisches Geoinstitut under the EU IHP – Access to Research Infrastructures Programme (Contract no. HPRI-1999-CT-00004 to D.C. Rubie). Enlightening discussions with A. Coujou and J. Rabier are gratefully acknowledged.     

Radiation-damage-induced defects in quartz. I. Single-crystal W-band EPR study of hole centers in an electron-irradiated quartz

Single-crystal W-band electron paramagnetic resonance (EPR) spectra of an electron-irradiated quartz, measured at room temperature, 110 and 77 K, disclose three previously reported hole centers (#1, G and an ozonide radical). The W-band EPR spectra of these three centers clearly resolve six magnetically nonequivalent sites each, whereas previous X- and Q-band EPR studies reported Centers #1 and the ozonide radical to consist of only three symmetry-related components and interpreted them to reside on twofold symmetry axes in the quartz structure. The calculated g matrices of Center #1 and the ozonide radical show that deviations from twofold symmetry axes are <10°, which are probably attributable to distortion related to neighboring charge compensating ions. The W-band EPR spectra of Center G not only result in improved g matrices but also allow quantitative determination of the nuclear hyperfine (A) and quadrupole (P) matrices of its ²⁷Al hyperfine structure that was incompletely resolved before. In particular, the g-maximum and g-minimum principal axes of Center G are approximately along two pairs of O–O edges of the SiO₄ tetrahedron, while the unique A principal axis is approximately along a Si–Si direction. These new spin-Hamiltonian parameters suggest that Center G most likely involves trapping of a hole between two oxygen atoms related to a silicon vacancy and stabilized by an Al³⁺ ion in the neighboring tetrahedron (hence an O₂ⁿ⁻–Al³⁺ defect, where n is either 1 or 3).