The origin of space group violations in a lunar orthopyroxene

The space group of an orthopyroxene (En₈₆) from a deep crustal lunar rock (sample 76535) that was previously reported as having space group P2₁ ca has been re-examined on an automated X-ray diffractometer. In addition to diffractions violating the b-glide of the conventional space group, Pbca (0kl,k-odd) reported in the earlier study, diffractions violating the a-glide of Pbca are also present. Careful examination of both the a-glide- and b-glide-violations shows them to be sharp, with no evidence of diffuse streaks parallel to a ^*, and with consistent intensities at several rotations about ψ. Diffractions violating the b-glide are in registry with the host, however, those violating the a-glide appear to be out of registry and result from a cell with a slightly longer a of about 18.4 Å, consistent with previous electron diffraction studies. The most reasonable explanation for the observed space group violations is that both the a- and b-glide violations result from ordering of Ca into (100) Guinier-Preston (G-P) zones that possess orthopyroxene topology, but have space group P2₁/c and a cell of a=18.4 Å, b=8.83 Å, c=5.18 Å, and β=90.0°; whereas the Cadepleted host has space group Pbca and a cell of a= 18.230(6) Å, b = 8.828(2) Å, and c=5.1946(9) Å. In addition to the G-P zones which may compose 12% or more of the sample, the crystal contains (100) lamellae of pigeonite, and other samples from the same rock contain lamellae of augite.     

The spin-forbidden absorption spectrum of Fe2+ in orthopyroxene

In this article, we have established the energy matrices of the strong-field terms SΓ of the d ⁴ (d ⁶) electron configuration in a crystal-field with C _2v symmetry. When we used this procedure to calculate the spin-forbidden absorption bands of Fe²⁺ in the M(2) site in orthopyroxene, we substituted the single-electron crystal-field energy levels (determined by the experimental results of the spinallowed spectrum) into the energy matrices instead of the single-electron crystal-field matrix elements. Thus, by means of only one parameter B (C=4B), most of the spin-forbidden bands of Fe²⁺ have been determined. Furthermore, when a similar treatment was made of the M(1) site of O _h symmetry, the entire spin-forbidden spectrum of Fe²⁺ in orthopyroxenes could be semiquantitatively explained. This shows that the method is particularly useful for the calculation of spin-forbidden spectra of complexes with the d ⁴ (d ⁶) configuration in a low-symmetry site.     

The solubility of alumina in orthopyroxene coexisting with garnet

The solubility of alumina in complex orthopyroxenes crystallised in equilibrium with garnet has been determined over the pressure-temperature range 8–30 Kb and 800–1250° C. The results are in good agreement with predictions made using the simple thermodynamic model of Wood and Banno (1973). The model has been refined using a combination of the new data on orthopyroxenes of about En₆₀Fs₄₀ (with variable calcium content) and previously published data on more magnesian systems. Given analyses of coexisting Orthopyroxene and garnet in natural assemblages it is possible to calculate a P-T curve for the rock which should, in most cases, be accurate to within 2 or 3 kbar.     

Structure of Cu-bearing orthopyroxene, Mg(Cu.56,Mg.44)Si2O6, and behavior of Cu2+ in the orthopyroxene structure

Cu-bearing pyroxene, Mg(Cu.₅₆,Mg.₄₄)Si₂O₆, has been synthesized by a flux method and crystal structure refinement has been performed by single crystal X-ray diffraction. It is found that the crystal structure is orthorhombic (space group Pbca) with unit cell dimensions of a=18.221(4), b=8.890(1), c=5.2260(7)Å and the cell volume of 846.5( )3ų. In the M2-site one of the M-O bonds(M-O3B) is extremely expanded from 2.444(2) in enstatite to 2.732(2), thus the coordination polyhedron around M2-site is regarded as square pyramidal rather than square planar or octahedral. It is also found that the M1-site in the pyroxene structure is occupied almost exclusively by Mg, while the M2-site is almost evenly occupied by Mg and Cu. The observed extreme site preference shown by Cu²⁺ is unusual among the divalent cations with similar ionic sizes.     

The composition,structure, and stability of guinier-preston zones in lunar and terrestrial orthopyroxene

Lunar and terrestrial orthopyroxenes (Mg,Fe,Ca)₂Si₂O₆ contain varying abundances of coherent, Ca-enriched Guinier-Preston (G.P.) zones. G.P. zones 5–6 unit cells thick have been found in one lunar sample whereas all other examples (lunar and terrestrial) are only one unit-cell-thick. Electron diffraction maxima from the larger lunar G.P. zones indicate that d ₁₀₀=18.52 Å whereas, d ₁₀₀=18.2 Å for the host. This increase in the a direction corresponds to an increase in calcium content in the G.P. zones over that of the host of ～25 mol% Ca₂Si₂O₆. Diffraction patterns of the hk0 net from an area containing G.P. zones show extra spots (h=2n+1) not observed in the host orthopyroxene (Pbca), that violate the a-glide of the host. The G.P. zones, therefore, have space group Pbc2₁ if it is assumed that the c-glide of pyroxene is retained and the space group of the G.P. zone is a subgroup of Pbca. The loss of the a-glide in the G.P. zones results in 4 distinct silica chains and 4 distinct cation sites M1A, M1B, M2A, M2B; by symmetry, equivalent M2A or M2B sites are clustered together in only one-half of the unit cell. As one-fourth of the divalent cations in the G.P. zones are calcium, ordering of Ca on M2A or M2B would produce a zone 9 Å thick extended parallel to (100) with the composition of Ca(Mg,Fe)Si₂O₆, but constrained by the host to the structure of orthopyroxene. This zone and the Ca-poor half-unit-cell then constitute an 18 Å thick G.P. zone. Heating experiments of varying duration indicate that the zones become unstable with respect to the host orthopyroxene at ～950°C for Wo_0.6 and ～1,050°C for Wo_2.5. The zones are interpreted in terms of the pyroxene subsolidus as a metastable phase having either a solvus relationship with orthopyroxene or originating as a distinct phase. The size, distribution, composition and structure of G.P. zones may be an important indicator of the low-temperature thermal history of orthopyroxene.     

The influence of multiple diffraction on the space group determination of orthopyroxene,spodumene, low omphacite and pigeonite

Forbidden reflections of some pyroxenes described as having a lower symmetry than Pbca or C2/c have been examined, mainly using the detailed ψ-scanning method of the four-circle automated diffractometer. All reflections violating the systematic absences of Pbca orthopyroxene, C2/c spodumene, P2/n omphacite and P2₁/c pigeonite were found to be due to the Umweganregung process of multiple diffraction; the Umweganregung peaks observed for the ψ azimuth were indexed in terms of a four-circle geometry. Thus, the space groups of orthopyroxene, α spodumene, low omphacite and low pigeonite were confirmed to be Pbca, C2/c, P2/n and P2₁/c, respectively.     

The reversed alumina contents of orthopyroxene in equilibrium with spinel and forsterite in the system MgO-Al2O3-SiO2

Equilibrium alumina contents of orthopyroxene coexisting with spinel and forsterite in the system MgO-Al₂O₃-SiO₂ have been reversed at 15 different P-T conditions, in the range 1,030–1,600° C and 10–28 kbar. The present data and three reversals of Danckwerth and Newton (1978) have been modeled assuming an ideal pyroxene solid solution with components Mg₂Si₂O₆ (En) and MgAl₂SiO₆ (MgTs), to yield the following equilibrium condition (J, bar, K): $$\begin{gathered} RT{\text{ln(}}X_{{\text{MgTs}}} {\text{/}}X_{{\text{En}}} {\text{) + 29,190}} - {\text{13}}{\text{.42 }}T + 0.18{\text{ }}T + 0.18{\text{ }}T^{1.5} \hfill \\ + \int\limits_1^P {\Delta V_{T,P}^{\text{0}} dP = 0,} \hfill \\ \end{gathered} $$ where $$\begin{gathered} + \int\limits_1^P {\Delta V_{T,P}^{\text{0}} dP} \hfill \\ = [0.013 + 3.34 \times 10^{ - 5} (T - 298) - 6.6 \times 10^{ - 7} P]P. \hfill \\ \end{gathered} $$ The data of Perkins et al. (1981) for the equilibrium of orthopyroxene with pyrope have been similarly fitted with the result: $$\begin{gathered} - RT{\text{ln(}}X_{{\text{MgTs}}} \cdot X_{{\text{En}}} {\text{) + 5,510}} - 88.91{\text{ }}T + 19{\text{ }}T^{1.2} \hfill \\ + \int\limits_1^P {\Delta V_{T,P}^{\text{0}} dP = 0,} \hfill \\ \end{gathered} $$ where $$\begin{gathered} + \int\limits_1^P {\Delta V_{T,P}^{\text{0}} dP} \hfill \\ = [ - 0.832 - 8.78{\text{ }} \times {\text{ 10}}^{ - {\text{5}}} (T - 298) + 16.6{\text{ }} \times {\text{ 10}}^{ - 7} P]{\text{ }}P. \hfill \\ \end{gathered} $$ The new parameters are in excellent agreement with measured thermochemical data and give the following properties of the Mg-Tschermak endmember: $$H_{f,970}^0 = - 4.77{\text{ kJ/mol, }}S_{298}^0 = 129.44{\text{ J/mol}} \cdot {\text{K,}}$$ and $$V_{298,1}^0 = 58.88{\text{ cm}}^{\text{3}} .$$ The assemblage orthopyroxene+spinel+olivine can be used as a geothermometer for spinel lherzolites, subject to a choice of thermodynamic mixing models for multicomponent orthopyroxene and spinel. An ideal two-site mixing model for pyroxene and Sack's (1982) expressions for spinel activities provide, with the present experimental calibration, a geothermometer which yields temperatures of 800° C to 1,350° C for various alpine peridotites and 850° C to 1,130° C for various volcanic inclusions of upper mantle origin.     

Thermochemistry of (Fe2+, Mg)SiO3 orthopyroxene

Enthalpies of solution in eutectic (Li, Na)₂B₂O₄ melts at 1023 K were measured for five synthetic orthopyroxenes on the join MgSiO₃-FeSiO₃. The pyroxenes were synthesized at 1120°C and 20 kbar and thus were presumed to be highly disordered. The measurements indicate a small positive enthalpy of mixing, with W_H = 950 cal/MSiO₃.Enthalpy of solution measurements were made on a natural, well-ordered orthopyroxene near the composition En_52.5Fs_47.5 and on this material after heat-treatment at 1150°C and 20 kbar. Irreversible expansion of the unit-cell constants of the natural pyroxene after heat-treatment at various temperatures was used to characterize the degree of M-site disorder. The observed enthalpy of solution decrement of 0.85 kcal/MSiO₃ between the natural En_52.5 and the same material heated at 1150° corresponds to about half of the maximum possible disordering, or ΔX_Fe^M1? 0.25, which leads to a ΔH of 7.5 kcal/M₂Si₂O₆, for the exchange reaction: Fe(M2) + Mg(Ml) = Fe(Ml) + Mg(M2) if M-site interaction energy terms are ignored. This ΔH is larger than inferred from any of the analyses of site-occupancy data except that of Besancon (1981), who gave a very similar value. The measured ΔH of disorder and the W_H of mixing together indicate a large ΔH as great as 3.2 kcal for the reciprocal reaction: Fe₂Si₂O₆ + Mg₂Si₂O₆ = Fe(M2)Mg(M1)Si₂O₆ + Fe(M1)Mg(M2)Si₂O₆ as anticipated by Sack (1980).As a consequence of the inferred magnitudes of ΔHof the exchange and reciprocal reactions, departures from ideality of Gibbs energy of mixing of orthopyroxene are very small at 700°–1000°C. Activities of MgSiO₃ and FeSiO₃ may be replaced by their mol fractions at all temperatures in most petrologic calculations.     

The Blomskog granite — a possible diapiric structure

A group of granitic intrusions occurs in western Sweden, showing a regular spacing between consecutive intrusions. Their spacing suggests solid-state doming of granitic material. However the textures of the rock are most easily interpreted in terms of crystallization from a magma. This interpretation is also consistent with contact observations and chemical characteristics of the rock. A hypothesis simultaneously explaining the textures and the spacing is presented, where doming of a light layer of potassium-rich migmatite is suggested to be followed by partial melting of the same rock. The magma collects at the top of the thus-formed sinusoidal waves and later intrudes into the country rock, where it crystallizes before reaching the surface.     

Xanes analysis on pyroxenes with different ca concentration in M2 site

X-ray Absorption Near-Edge Structure (XANES) analysis of the calcium K-edge of a series of natural pyroxenes is reported. The samples belong to the solid solution series diopside (CaMgSi₂O₆) — jadeite (NaAlSi₂O₆). In diopside, the M2 site is occupied by Ca only, but along the join Na substitutes Ca in this position. From XANES analysis of different samples we found a distortion of the polyhedron around the M2 site varying as a function of Ca content. This is probably due to compression of the site in a selected direction with an unchanged average distance, so that the coordination around the Ca atom changes from the 4-2-2 configuration typical of the diopside structure to the 6-2 configuration typical of Na in the jadeite structure. Intermediate pyroxenes exhibit both configurations, and acquire therefrom the structural order as already detected by X-ray diffraction techniques.     

The reaction forsterite+cordierite=aluminous orthopyroxene+spinel in the system MgO-Al2O3-SiO2

Reversal experiments at 1,150–1,300°C on the reaction forsterite+cordierite=aluminous orthopyroxene+spinel in the system MgO-Al₂O₃-SiO₂ show the equilibrium to have a negativedT/dP. The slope andT-P location of this equilibrium have been modelled using available heat capacity data and various structural models which explore the configurational entropy contributions to the totalΔS. The experimental data are consistent with the aluminous orthopyroxene model of Ganguly and Ghose (1979) where limited Al disorder occurs between theM1 andM2 sites, Al-Si mixing occurs on the tetrahedralB site with the ‘aluminum avoidance’ principle maintained, and Mg-Al disorder occurs in spinel with an interchange enthalpy of 9–12 kcal mol^?1. Additionally, Al-Si disordering which occurs in the indialite structure of cordierite is inconsistent with the experimental data and all pyroxene and spinel mixing models; consequently, Si and Al in anhydrous cordierites to 1,300°C in the system MgO-Al₂O₃-SiO₂ must be largely ordered.     

Electrical conductivity of H-bearing orthopyroxene single crystals measured with impedance spectroscopy

In this study, the electrical conductivity of synthetic and natural orthopyroxene single crystals containing various amounts of hydrogen and cation impurities (i.e., Al, Fe) was investigated using impedance spectroscopy. A new cell was developed to measure conductivities of submillimeter-sized oriented single crystals with impedances up to 10¹⁰?Ohm. In contrast to previous studies on olivine and orthopyroxene, results from this study do not show a simple correlation of the concentration of protons and the electrical conductivity. Instead, the electrical conductivity appears to be a complex function of iron content, hydrogen content, crystal orientation and concentration of other impurity cations and shows similar activation energies to hydrogen diffusion. Model calculations considering proton conduction rather exclude than suggest orthopyroxene as responsible phase for high-conductivity regions in the Earth’s upper mantle.     

The reaction garnet+clinopyroxene+quartz =2 orthopyroxene+anorthite: A potential geobarometer for granulites

A mineralogic geobarometer based on the reaction garnet+clinopyroxene+quartz=2 orthopyroxene+anorthite is proposed. The geobarometric formulations for the Fe- and Mg- end member equilibria are $$\begin{gathered} P_{({\text{Fe}})} {\text{ }}({\text{bars}}){\text{ = 32}}{\text{.097 }}T{\text{ }} - {\text{ 26385 }} - {\text{ 22}}{\text{.79 (}}T - 848 - T1{\text{n(}}T/848{\text{))}} \hfill \\ {\text{ }} - (3.655 + 0.0138T){\text{ }}\left( {\frac{{{\text{(}}T - 848{\text{)}}^{\text{2}} }}{T}} \right) \hfill \\ {\text{ }} - {\text{(3}}{\text{.123) }}T1{\text{n }}\frac{{(a_{a{\text{n}}}^{{\text{Plag}}} )(a_{{\text{fs}}}^{{\text{P}}\ddot u{\text{x}}} )^2 }}{{(a_{{\text{alm}}}^{{\text{Gt}}} )(a_{{\text{hed}}}^{{\text{Opx}}} )}} \hfill \\ P_{({\text{Mg}})} {\text{ (bars) = 9}}{\text{.270 }}T + 4006 - 0.9305{\text{ }}(T - 848 - T1{\text{n (}}T/848{\text{)}}) \hfill \\ {\text{ }} - (1.1963{\text{ }} - {\text{ }}6.0128{\text{ x 10}}^{ - {\text{3}}} T)\left( {\frac{{(T - 848)^2 }}{T}} \right) \hfill \\ {\text{ }} - 3.489{\text{ }}T1{\text{n }}\frac{{(a_{an}^{{\text{Plag}}} ){\text{ }}(a_{{\text{ens}}}^{{\text{Opx}}} )}}{{{\text{(}}a_{{\text{pyr}}}^{{\text{Gt}}} {\text{) (}}a_{{\text{diop}}}^{{\text{Cpx}}} {\text{)}}}}. \hfill \\ \end{gathered}$$ The end member thermodynamic data have been taken from the data base of Helgeson et al. (1978) and Saxena and Erikson (1983). The activities of pyroxene components and anorthite in plagioclase have been modelled after Wood and Banno (1973) and Newton (1983) respectively. The activities of pyrope and almandine are calculated from the binary interaction parameters for garnet solid solutions proposed by Saxena and Erikson (1983). Pressures computed from these equations for fifty sets of published mineral data from several granulite areas are comparable with those obtained from dependable geobarometers. The pressure values determined from the Fe-end member equilibrium appear to be more reasonable than those from the Mg-end member reaction. It is likely that the difference in pressures computed from the Fe- and Mg-end members, ΔP ^*, have been caused by non-ideal mixing in the phases, especially in garnets.     

The crystal chemistry of lithium and Fe3+ in synthetic orthopyroxene

Lithian ferrian enstatite with Li₂O = 1.39 wt% and Fe₂O₃ 7.54 wt% was synthesised in the (MgO–Li₂O–FeO–SiO₂–H₂O) system at P = 0.3 GPa, T = 1,000°C, fO₂ = +2 Pbca, and a = 18.2113(7), b = 8.8172(3), c = 5.2050(2) Å, V = 835.79(9) Å³. The composition of the orthopyroxene was determined combining EMP, LA-ICP-MS and single-crystal XRD analysis, yielding the unit formula ^M2(Mg_0.59Fe _0.21 ²⁺ Li_0.20) ^M1(Mg_0.74Fe _0.20 ³⁺ Fe _0.06 ²⁺ ) Si₂O₆. Structure refinements done on crystals obtained from synthesis runs with variable Mg-content show that the orthopyroxene is virtually constant in composition and hence in structure, whereas coexisting clinopyroxenes occurring both as individual grains or thin rims around the orthopyroxene crystals have variable amounts of Li, Fe³⁺ and Mg contents. Structure refinement shows that Li is ordered at the M2 site and Fe³⁺ is ordered at the M1 site of the orthopyroxene, whereas Mg (and Fe²⁺) distributes over both octahedral sites. The main geometrical variations observed for Li-rich samples are actually due to the presence of Fe³⁺, which affects significantly the geometry of the M1 site; changes in the geometry of the M2 site due to the lower coordination of Li are likely to affect both the degree and the kinetics of the non-convergent Fe²⁺-Mg ordering process in octahedral sites.     

The structure of urban space, movement and co-presence: The case of Atlanta

Urban areas in Atlanta are analyzed using a computer based technique known as ‘space syntax’ to reveal an underlying systematic and consistent relationship between pedestrian or vehicular movement and spatial configuration. This provides a framework for discussing how far different urban morphologies are characterized by similar regular patterns; how design choices can affect the social use of space; and how methodological and theoretical issues, such as the study of the effects of scale, can be formulated with greater clarity.     

Transmission electron microscope study of dislocations in orthopyroxene (Mg,Fe)2Si2O6

The orthopyroxene crystal structure can be viewed as the stacking of alternating tetrahedral and octahedral layers parallel to the (100) plane. Easy glide occurs in the (100) plane at the level of the octahedral layer to prevent breakage of the strong Si-O bonds. Dislocations with c and b Burgers vectors have been activated in (100) by room temperature indentation in an orthoenstatite gem quality single crystal. Investigations in transmission electron microscopy show that the b dislocations (b?9 Å) are not dissociated while the c's (c=5.24 Å) are dissociated into four partials. This result is interpreted by considering the oxygen sublattice as a distorted FCC one. The four c partials are thus Shockley partials bounding three stacking faults. For the two outer ones, synchroshear of the cations is necessary to keep unchanged their sixfold coordination; the oxygen sublattice is locally transformed into a HCP lattice. This accounts for the observed low splitting (?100 Å) of these faults as compared to the median one (?500 Å) which does not affect the oxygen sublattice and does not require cation synchroshear. In a Fe rich orthopyroxene (eulite), semi coherent exsolution lamellae have been studied. Either only c edge dislocations or both b and c edge dislocations occur in the phase boundaries depending upon the thickness of the lamellae. Only the c dislocations are dissociated. From the observed spacing between these mismatch dislocations a crude estimate of the exsolution temperature is proposed T _ex ? 700° C.     

X-ray diffraction study of Fe2+-Mg order-disorder in orthopyroxene. Some kinetic results

Kinetic rates of Fe²⁺-Mg disordering in three orthopyroxenes (mean value of X_Fe = Fe²⁺/(Fe²⁺+Mg) = 0.175,0.482,0.770 respectively) have been determined employing heating experiments and single crystal X-ray structural refinements. Disordering rate constants \((\vec K)\) (550800° C) for two pyroxenes are given by: ln \((\vec K)\) = 27.107(±5.177)?32062(±783)T^?1(X_Fe = 0.175) ln \((\vec K)\) = 16.142(±0.057)?18227(±423)T^?1(X_Fe = 0.770) The distribution coefficients K_D (representing a steady state of disordering Fe_M2 + Mg_M1 ? Fe_M1 + Mg_M2) are given by: ln K_D = 5.016(±0.223)-7033(±1473) T^?1(X_Fe = 0.175) ln K_D = 1.988(±0.122)-3809(±913)T^?1(X_Fe = 0.770) These distribution coefficients provide the constraint of the disordering reaction on the value of the equilibrium constant for Fe²⁺-Mg order-disorder. Until the low temperature dependence of K_D is well constrained, the calculation of cooling rates of pyroxenes and host rocks cannot be done reliably.