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     

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.     

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.     

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     

Multipole-refined charge density study of diopside at ambient conditions

The experimental multipole electron density, ρ(r), of diopside was derived from high-resolution single-crystal diffraction at room temperature. Its topological analysis revealed predominantly ionic Si–O bonding, as found in electron density studies of other silicates. In particular, the non-bridging Si–O bonds are slightly less ionic in character than the bridging Si–O bonds. The Ca–O and Mg–O bonds are classified as pure closed-shell ionic interactions. An analysis of –∇²ρ(r) showed the presence of maxima around the oxygen atoms, associated to lone pairs domains that are involved in bonds with the surrounding ions. Calculation of atomic basins gave net charges of –1.56(12), 3.11(17), 1.79(13) and 1.88(18) e for O (averaged), Si, Ca and Mg atoms, respectively. O···O interactions between the O atoms at the vertices of the SiO₄ tetrahedron were also detected from the topological analysis of ρ(r), and indicate a cooperative interaction among the lone pairs of neighbouring oxygen atoms. All these results were also confirmed by periodic restricted Hartree–Fock (RHF) calculations. Electronic Supplementary Material Supplementary material is available for this article at and is accessible for authorized users.     

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 crystal chemical study of protoanthophyllite: orthoamphiboles with the protoamphibole structure

Two new protoamphibole-type amphiboles with space group type Pnmn, have been found in nature: protoferro-anthophyllite (Fe_0.80Mn_0.20)₂ (Fe_0.98Mg_0.02)₅ (Si₄O₁₁)₂(OH)₂, and protomangano-ferro-anthophyllite, (Mn_0.70Fe_0.30)₂ (Fe_0.82Mg_0.18)₅ (Si₄O₁₁)₂(OH)₂. Protoferro-anthophyllite (PFA) occurs in pegmatites at both Gifu Prefecture, Japan and at Cheyenne Mountain, El Paso County, Colorado, USA. Protomangano-ferro-anthophyllite, (PMFA) occurs in pegmatites at Fukushima Prefecture and in a Mn mine at Tochigi Prefecture, Japan. Structure determinations of the two amphiboles show that both are isostructural with the synthetic fluorian-amphibole, protoamphibole (= protofluorian-lithian-anthophyllite). A calculation of the procrystal electron density distributions, the bond paths and the bond critical point properties of PFA, PMFA, grunerite and protoamphibole indicates that the M4 cation in these amphiboles is 4-coordinated. A calculation of the electron density distributions at the Becke3LYP/6-311G(2d,p) level for model silicate tetrahedra for these amphiboles and anthophyllite reveals that the value of the electron density at the bond critical points, ρ(r _c ), for the SiO(nbr) bonds is larger, on average (0.93 e/ų), than that for the SiO(br) bonds (0.90 e/ų). The observed SiO bond lengths decrease linearly with increasing ρ(r _c ) while the magnitudes of the curvatures of ρ(r _c ) both perpendicular and parallel to the bonds and the Laplacian of ρ(r _c ) each increases. These trends are associated with an increase in the electronegativity of the Si cation, a possible increase in the covalent character of the SiO bond and a tendency for SiO(nbr) bonds to be involved in wider OSiO angles than SiO(br) bonds. It is possible, if not likely, that protoanthophyllite has often been misidentified as anthophyllite.     

Power law relationships between bond length, bond strength and electron density distributions

The strength of a bond, defined as p=s/r, where s is the Pauling bond strength and r is the row number of an M cation bonded to an oxide anion, is related to a build-up of electron density along the MO bonds in a relatively large number of oxide and hydroxyacid molecules, three oxide minerals and three molecular crystals. As p increases, the value of the electron density is observed to increase at the bond critical points with the lengths of the bonds shortening and the electronegativities of the M cations bonded to the oxide anion increasing. The assertion that the covalency of a bond is intrinsically connected to its bond strength is supported by the electron density distribution and its bond critical point properties. A connection also exists between the properties of the electron density distributions and the connectivity of the bond strength network formed by the bonded atoms of a structure. Received: 20 August 1997 / Revised, accepted: 3 November 1997     

Electron density distribution of FeTiO<Subscript>3</Subscript> ilmenite under high pressure analyzed by MEM using single crystal diffraction intensities

Many of ilmenites ABO₃ compounds bearing transition elements have semiconductive, ferroelectric and antiferromagnetic properties. The high-pressure diffraction studies of FeTiO₃ have been conducted up to 8.2 GPa using synchrotron radiation in KEK at Tsukuba with diamond anvil cell. The compression mechanism of FeTiO₃ ilmenite has been investigated by the structure refinements converged to the reliable factors R = 0.05. The deformations of the FeO₆ and TiO₆ octahedra were reduced with increasing pressure. In order to elucidate the electric conductivity change with pressure, electron density distribution of ilmenite have been executed by maximum entropy method (MEM) using single-crystal diffraction intensity data. MEM based on F _obs(hkl) of FeTiO₃ clearly shows electron density in comparison with the difference Fourier synthesis based on F _obs(hkl) − F _calc(hkl). The radial distribution of the electron density indicates electron localization around the cation positions. The bonding electron density found in bond Fe–O and Ti–O is lowered with pressure. The isotropic temperature factors B _iso become smaller with increasing pressure. Nevertheless the thermal vibration is considerably restrained by the compression, the electric conductivity is enhanced with pressure. Neither charge transfer nor electron hopping between Fe and Ti along the c axis in FeTiO₃ is plausible under high pressure. But the electric conductivity due to electron super-exchange in Fe–Fe and Ti–Ti has been clarified by the MEM electron density distribution. The anisotropy in the electric conductivity has been clarified.     

Pauling bond strength, bond length and electron density distribution

The power law regression equation, <R(M–O)> = 1.46(<ρ(r _c)>/r)^?0.19, relating the average experimental bond lengths, <R(M–O)>, to the average accumulation of the electron density at the bond critical point, <ρ(r _c)>, between bonded pairs of metal and oxygen atoms (r is the row number of the M atom), determined at ambient conditions for oxide crystals, is similar to the regression equation R(M–O) = 1.41(ρ(r _c)/r)^?0.21 determined for three perovskite crystals at pressures as high as 80 GPa. The pair are also comparable with the equation <R(M–O)> = 1.43(<s>/r)^?0.21 determined for oxide crystals at ambient conditions and <R(M–O)> = 1.39(<s>/r)^?0.22 determined for geometry-optimized hydroxyacid molecules that relate the geometry-optimized bond lengths to the average Pauling bond strength, <s>, for the M–O bonded interactions. On the basis of the correspondence between the equations relating <ρ(r _c)> and <s> with bond length, it seems plausible that the Pauling bond strength might serve a rough estimate of the accumulation of the electron density between M–O bonded pairs of atoms. Similar expressions, relating bond length and bond strength hold for fluoride, nitride and sulfide molecules and crystals. The similarity of the expressions for the crystals and molecules is compelling evidence that molecular and crystalline M–O bonded interactions are intrinsically related. The value of <ρ(r _c)> = r[(1.41)/<R(M–O)>]^4.76 determined for the average bond length for a given coordination polyhedron closely matches the Pauling’s electrostatic bond strength reaching each the coordinating anions of the coordinated polyhedron. Despite the relative simplicity of the expression, it appears to be more general in its application in that it holds for the bulk of the M–O bonded pairs of atoms of the periodic table.     

SiO bonded interactions in coesite: a comparison of crystalline, molecular and experimental electron density distributions

Bond critical point properties of electron density distributions calculated for representative Si₅O₁₆ moieties of the structure of coesite are compared with those observed and calculated for the bulk crystal. The values calculated for the moieties agree with those observed to within ∼5%, on average, whereas those calculated for the crystal agree to within ∼10%. As the SiOSi angles increase and the SiO bonds shorten, there is a progressive build-up in the calculated electron density along the bonds. This is accompanied by an increase in both the curvatures of the electron density, both perpendicular and parallel to each bond, and the Laplacian of the electron density distribution at the bond critical points. The cross sections of the bonds at the critical points become more circular as the angle approaches 180o. Also, the bonded radius of the oxide anion decreases about twice as much as that of the Si cation as the SiO bond length decreases and the fraction of s-character of the bond is indicated to increase. A knowledge of electron density distributions is central to our understanding of the forces that govern the structure, properties, solid state reactions, surface reactions and phase transformations of minerals. The software (CRYSTAL95 and TOPOND) used in this study to calculate the bond critical properties of the electron density and Laplacian distributions is bound to promote a deeper understanding of crystal chemistry and properties. Received: 23 February 1998 / Revised, accepted: 16 July 1998     

The single-crystal,polarized-light,FTIR spectrum of stoppaniite,the Fe analogue of beryl

We report here a single-crystal polarized-light study of stoppaniite, ideally (Fe,Al,Mg)₄(Be₆Si₁₂O₃₆)(H₂O)₂(Na,□), from Capranica (Viterbo). Polarized-light FTIR spectra were collected on an oriented (hk0) section, doubly polished to 15 μm. The spectrum shows two main bands at 3,660 and 3,595 cm⁻¹; the former is strongly polarized for E ⊥c, while the latter is polarized for E //c. A sharp and very intense band at 1,620 cm⁻¹, plus minor features at 4,000 and 3,228 cm⁻¹ are also polarized for E //c. On the basis of literature data and considering the pleochroic behavior of the absorptions, the 3,660 cm⁻¹ band is assigned to the ν₃ stretching mode and the 1,620 cm⁻¹ (associated with an overtone 2*ν₂ at 3,230 cm⁻¹) band to the ν₂ bending mode of “type II” water molecules within the structural channels of the studied beryl. The sharp band at 3,595 cm⁻¹ is not associated with a corresponding ν₂ bending mode; thus it is assigned to the stretching vibration of O–H groups in the sample. The minor 4,000 cm⁻¹ feature can be assigned to the combination of the O–H bond parallel to c with a low-frequency metal-oxygen mode such as the Na–O stretching mode. The present results suggest that the interpretation of the FTIR spectrum of Na-rich beryl needs to be carefully reconsidered.     

The crystal structure of arsentsumebite, Pb2Cu[(As, S)O4]2(OH)

Summary The crystal structure of arsentsumebite, ideally, Pb₂Cu[(As, S)O₄]₂(OH), monoclinic, space group P2₁/m, a = 7.804(8), b = 5.890(6), c = 8.964(8) ?, β = 112.29(6)°, V = 381.2 ?³, Z = 2, d_calc. = 6.481 has been refined to R = 0.053 for 898 unique reflections with I> 2σ(I). Arsentsumebite belongs to the brackebuschite group of lead minerals with the general formula Pb₂ Me(XO₄)₂(Z) where Me = Cu²⁺, Mn²⁺, Zn²⁺, Fe²⁺, Fe³⁺; X = S, Cr, V, As, P; Z = OH, H₂O. Members of this group include tsumebite, Pb₂Cu(SO₄)(PO₄)(OH), vauquelinite, Pb₂Cu(CrO₄)(PO₄)(OH), brackebuschite, Pb₂ (Mn, Fe)(VO₄)₂(OH), arsenbracke buschite, Pb₂(Fe, Zn)(AsO₄)₂(OH, H₂O), fornacite, Pb₂Cu(AsO₄)(CrO₄)(OH), and feinglosite, Pb₂(Zn, Fe)[(As, S)O₄]₂(H₂O). Arsentsumebite and all other group members contain M = M–T chains where M = M means edge-sharing between MO₆ octahedra and M–T represents corner sharing between octahedra and XO₄ tetrahedra. A structural relationship exists to tsumcorite, Pb(Zn, Fe)₂(AsO₄)₂ (OH, H₂O)₂ and tsumcorite-group minerals Me(1)Me(2)₂(XO₄)₂(OH, H₂O)₂. Received June 24, 2000; revised version accepted February 8, 2001     

OH in zoned amphiboles of eclogite from the western Tianshan,NW-China

Chemically-zoned amphibole porphyroblast grains in an eclogite (sample ws24-7) from the western Tianshan (NW-China) have been analyzed by electron microprobe (EMP), micro Fourier-transform infrared (micro-FTIR) and micro-Raman spectroscopy in the OH-stretching region. The EMP data reveal zoned amphibole compositions clustering around two predominant compositions: a glaucophane end-member ( ^B Na₂ ^C M²⁺ ₃ M³⁺ ₂ ^T Si₈(OH)₂) in the cores, whereas the mantle to rim of the samples has an intermediate amphibole composition ( ^A _0.5 ^B Ca_1.5Na_0.5 ^C M ²⁺ _4.5 M _0.5^{3+ T} Si_7.5Al_0.5(OH)₂) (A = Na and/or K; M ²⁺ = Mg and Fe²⁺; M ³⁺ = Fe³⁺ and/or Al) between winchite (and ferro-winchite) and katophorite (and Mg-katophorite). Furthermore, we observed complicated FTIR and Raman spectra with OH-stretching absorption bands varying systematically from core to rim. The FTIR/Raman spectra of the core amphibole show three lower-frequency components (at 3,633, 3,649–3,651 and 3,660–3,663 cm⁻¹) which can be attributed to a local O(3)-H dipole surrounded by ^{M(1) M(3)}Mg₃, ^{M(1) M(3)}Mg₂Fe²⁺ and ^{M(1) M(3)} Fe²⁺ ₃, respectively, an empty A site and ^T Si₈ environments. On the other hand, bands at higher frequencies (3,672–3,673, 3,691–3,697 and 3,708 cm⁻¹) are observable in the rims of the amphiboles, and they indicate the presence of an occupied A site. The FTIR and Raman data from the OH-stretching region allow us to calculate the site occupancy of the A, M(1)–M(3), T sites with confidence when combined with EPM data. By contrast M(2)- and M(4) site occupancies are more difficult to evaluate. We use these samples to highlight on the opportunities and limitations of FTIR OH-stretching spectroscopy applied to natural high pressure amphibole phases. The much more detailed cation site occupancy of the zoned amphibole from the western Tianshan have been obtained by comparing data from micro-chemical and FTIR and/or Raman in the OH-stretching data. We find the following characteristic substitutions Si(T-site) (Mg, Fe)[M(1)–M(3)-site] → Al(T-site) Al[M(1)–M(3)-site] (tschermakite), Ca(M4-site)□ (A-site) → Na(M4-site) Na + K(A-site) (richterite), and Ca(M4-site) (Mg, Fe) [M(1)–M(3)-site] → Na(M4-site) Al[M(1)–M(3)-site] (glaucophane) from the configurations observed during metamorphism.     

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 [ρ(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 synthesis, but free of the uncertainties due to the abrupt truncation of the series. The charge distribution is investigated by means of the notion of ‘‘site basin’’, i.e., those site-centered volumes delimited by a surface such as ∇ρ·n = 0. In particular, we observe: (1) the overall partitioning of the basin total charge between cation and anion sites, and the interlayer site charge seems to depend on sample composition, and (2) the apical-oxygen plane total basin charge and hydroxyl basin charge are presumably related to the polytype. The MEM-determined electron density does not allow full exploration of the critical points for very complex structures as micas, insofar as conventional room temperature experimental diffraction data are used.     

Electron density distribution and bond critical point properties for forsterite, Mg2 SiO4, determined with synchrotron single crystal X-ray diffraction data

A generalized X-ray scattering factor model experimental electron density distribution has been generated for the orthosilicate forsterite, using an essentially extinction and absorption free set of single crystal diffraction data recorded with intense, high energy synchrotron X-ray radiation (E=100.6 keV). A refinement of the model converged with an R(F)=0.0061. An evaluation of the bond critical point, bcp, properties of the distribution at the (3, –1) stationary points for the SiO and MgO bonded interactions, yielded values that agree typically within ~5%, on average, with theoretical values generated with quantum chemical computational strategies, using relatively robust basis sets. On the basis of this result, the modeling of the experimental distribution is considered to be adequate. As the bcp properties increase in magnitude, the MgO and SiO bonds decrease in length as calculated for a number of rock forming silicates. As asserted by Coppens (X-ray charge densities and chemical bonding. Oxford University Press, Oxford, 1997), large negative ²(r_c) values, characteristic of shared interactions involving first row atoms, may not be characteristic of closed shell covalent bonded interactions involving second row Si, P and S atoms bonded to O. This study adds new evidence to the overall relatively good agreement between theoretical bcp properties generated with computational quantum strategies, on the one hand, and experimental properties generated with single crystal high energy synchrotron diffraction data on the other. The similarity of results not only provides a basis for using computational strategies for studying and modeling structures, defects and the reactivity of representative structures, but it also provides a basis for improving our understanding of the crystal chemistry of earth materials and the character of the SiO bonded interaction.     

On the Ratios between Elastic Modulus and Uniaxial Compressive Strength of Heterogeneous Carbonate Rocks

The ratios M _R = E/σ _c for 11 heterogeneous carbonate (dolomites, limestones and chalks) rock formations collected from different regions of Israel were examined. Sixty-eight uniaxial compressive tests were conducted on weak-to-strong (5 MPa < σ _c < 100 MPa) and very strong (σ _c > 100 MPa) rock samples exhibiting wide ranges of elastic modulus (E = 6100–82300 MPa), uniaxial compressive strength (σ _c = 14–273.9 MPa), Poisson's ratio (ν = 0.13–0.49), and dry bulk density (ρ = 1.7–2.7 g/cm³). The observed range of M _R = 60.9–1011.4 and mean value of M _R = 380.5 are compared with the results obtained by Deere (Rock mechanics in engineering practice, Wiley, London, pp 1–20, 1968) for limestones and dolomites, and the statistical analysis of M _R distribution is performed. Mutual relations between E, σ _c, ρ, M _R for all studied rocks, and separately for concrete rock formations are revealed. Linear multiple correlations between E on the one hand and σ _c and ρ on the other for Nekorot and Bina limestone and Aminadav dolomite are obtained. It is established that the elastic modulus and M _R in very strong carbonate samples are more correlated with ρ−σ _c combination and ε _a max, respectively, than in weak to strong samples. The relation between M _R and maximum axial strain (ε _a max) for all studied rock samples (weak-to-strong and very strong) is discussed.     

H2O activity in concentrated NaCl solutions at high pressures and temperatures measured by the brucite-periclase equilibrium

 H₂O activities in concentrated NaCl solutions were measured in the ranges 600°–900° C and 2–15 kbar and at NaCl concentrations up to halite saturation by depression of the brucite (Mg(OH)₂) – periclase (MgO) dehydration equilibrium. Experiments were made in internally heated Ar pressure apparatus at 2 and 4.2 kbar and in 1.91-cm-diameter piston-cylinder apparatus with NaCl pressure medium at 4.2, 7, 10 and 15 kbar. Fluid compositions in equilibrium with brucite and periclase were reversed to closures of less than 2 mol% by measuring weight changes after drying of punctured Pt capsules. Brucite-periclase equilibrium in the binary system was redetermined using coarsely crystalline synthetic brucite and periclase to inhibit back-reaction in quenching. These data lead to a linear expression for the standard Gibbs free energy of the brucite dehydration reaction in the experimental temperature range: ΔG° (±120J)=73418–134.95T(K). Using this function as a baseline, the experimental dehydration points in the system MgO−H₂O−NaCl lead to a simple systematic relationship of high-temperature H₂O activity in NaCl solution. At low pressure and low fluid densities near 2 kbar the H₂O activity is closely approximated by its mole fraction. At pressures of 10 kbar and greater, with fluid densities approaching those of condensed H₂O, the H₂O activity becomes nearly equal to the square of its mole fraction. Isobaric halite saturation points terminating the univariant brucite-periclase curves were determined at each experimental pressure. The five temperature-composition points in the system NaCl−H₂O are in close agreement with the halite saturation curves (liquidus curves) given by existing data from differential thermal analysis to 6 kbar. Solubility of MgO in the vapor phase near halite saturation is much less than one mole percent and could not have influenced our determinations. Activity concentration relations in the experimental P-T range may be retrieved for the binary system H₂O-NaCl from our brucite-periclase data and from halite liquidus data with minor extrapolation. At two kbar, solutions closely approach an ideal gas mixture, whereas at 10 kbar and above the solutions closely approximate an ideal fused salt mixture, where the activities of H₂O and NaCl correspond to an ideal activity formulation. This profound pressure-induced change of state may be characterized by the activity (a) – concentration (X) expression: a _{H 2}O=X _{H 2}O/(1+αX _NaCl), and a _NaCl=(1+α)^(1+α)[X _NaCl/(1+αX _NaCl)]^(1+α). The parameter α is determined by regression of the brucite-periclase H₂O activity data: α=exp[A–B/ϱ_{H 2}O ]-CP/T, where A=4.226, B=2.9605, C=164.984, and P is in kbar, T is in Kelvins, and ϱ_{H 2}O is the density of H₂O at given P and T in g/cm³. These formulas reproduce both the H₂O activity data and the NaCl activity data with a standard deviation of ±0.010. The thermodynamic behavior of concentrated NaCl solutions at high temperature and pressure is thus much simpler than portrayed by extended Debye-Hückel theory. The low H₂O activity at high pressures in concentrated supercritical NaCl solutions (or hydrosaline melts) indicates that such solutions should be feasible as chemically active fluids capable of coexisting with solid rocks and silicate liquids (and a CO₂-rich vapor) in many processes of deep crustal and upper mantle metamorphism and metasomatism. Received: 1 September 1995 / Accepted: 24 March 1996     

High-<Emphasis Type="Italic">T</Emphasis> behaviour of gedrite: thermoelasticity,cation ordering and dehydrogenation

The thermoelastic behaviour of a natural gedrite having the crystal-chemical formula ^ANa_0.47 ^B(Na_0.03 Mg_1.05 Fe_0.86²⁺ Mn_0.02 Ca_0.04) ^C(Mg_3.44 Fe_0.36²⁺ Al_1.15 Ti_0.05⁴⁺) ^T(Si_6.31 Al_1.69)O₂₂ ^W(OH)₂ has been studied by single-crystal X-ray diffraction to 973 K (Stage 1). After data collection at 973 K, the crystal was heated to 1,173 K to induce dehydrogenation, which was registered by significant changes in unit-cell parameters, M1–O3 and M3–O3 bond lengths and refined site-scattering values of M1 and M4 sites. These changes and the crystal-chemical formula calculated from structure refinement show that all Fe²⁺ originally at M4 migrates into the ribbon of octahedrally coordinated sites, where most of it oxidises to Fe³⁺, and there is a corresponding exchange of Mg from the ribbon into M4. The resulting composition is that of an oxo-gedrite with an inferred crystal-chemical formula ^ANa_0.47 ^B(Na_0.03 Mg_1.93 Ca_0.04) ^C(Mg_2.56 Mn_0.02²⁺ Fe_0.10²⁺ Fe_1.22³⁺ Al_1.15 Ti_0.05⁴⁺) ^T(Si_6.31 Al_1.69) O₂₂ ^W[O_1.12²⁻ (OH)_0.88]. This marked redistribution of Mg and Fe is interpreted as being driven by rapid dehydrogenation at the H3A and H3B sites, such that all available Fe in the structure orders at M1 and M3 sites and is oxidised to Fe³⁺. Thermoelastic data are reported for gedrite and oxo-gedrite; the latter was measured during cooling from 1,173 to 298 K (Stage 2) and checked after further heating to 1,273 K (Stage 3). The thermoelastic properties of gedrite and oxo-gedrite are compared with each other and those of anthophyllite.