Atomic movements in plagioclase feldspars: Kinetic interpretation

The diffraction, n.q.r. and optical data on plagioclase feldspars are used to derive kinetic interpretations of structural changes induced by laboratory heat treatment and by geological processes. For anorthite, the Si, Al configuration is essentially ordered except for unusual transient processes. Cooperation between Ca atoms, and random nucleation, produces a domain texture in the primitive structure which is highly sensitive to temperature. The rapid inversion from the primitive to the body-centered structure is explained by increasingly rapid “rattling” of the Ca ions in the interstices of the semi-flexible alumino-silicate framework. The weakening of “b” reflections at higher temperatures is ascribed to incipient Si, Al disorder associated with irregular vibration of the alumino-silicate framework and the Ca atoms. Quenching phenomena are explained by variation of the domain boundary texture inherited from disorder at high temperature. For albite, the Si, Al configuration changes sluggishly from an ordered to a disordered pattern, and vice versa. Kinetic data are reinterpreted using a model in which the cell dimensions depend on local rather than distant order: the major change in distant order is deduced to occur at 450–600° C. Sodic plagioclase grown at high temperature shows distant disorder of the atoms, but cell dimensions suggest development of strong local order for calcic compositions. Low-entropy plagioclases of intermediate composition show complex intergrowths and domain structures because of kinetic barriers to atomic diffusion. X-ray diffraction data for slowly-cooled specimens are consistent with nucleation of albite- and anorthite-like regions from a high-temperature disordered phase. Electrostatic energy calculations show that Na and Ca atoms, although they face smaller energy barriers for diffusion, cannot form domains until the Si and Al atoms have moved jointly. The Si, Al ordering patterns of low albite and anorthite are topologically incompatible in a continuous framework if oxygen is not to be bonded to two Al. Therefore domains of low-albite and anorthite must be separated by disordered boundaries. For intermediate compositions, An₁₅-An₇₅, domains remain small. The anorthite-like domains probably form at higher temperatures than the albite-like domains. The latter tend to be about the same size for all bulk compositions. The atomic positions are influenced by neighboring atoms. Upon heating rapidly, Si and Al atoms remain in position and provide a memory for reformation of an identical structure upon cooling. The framework changes shape, and some Na, Ca atoms inter-diffuse to yield a quasi-homogeneous structure with a diffraction pattern which qualitatively approaches that of high albite. Upon prolonged heating at high temperature, Si, Al atoms inter-diffuse producing nonquenchable changes to the high-albite structure. At Na-rich bulk compositions, some domains of low albite grow into large lamellae while others remain small in contact with anorthite domains producing alternate lamellae of intermediate structure type; hence the peristerite intergrowth. A similar but opposite process could cause an intergrowth of lamellae of anorthite structure interposed with an intermediate type structure. A unique low plagioclase series is not expected. Plagioclases of intermediate composition trend towards slightly different endproducts depending on the details of the cooling history. Breaks and bends in plots of physical properties, and intergrowths for certain specimens, depend on special compositional, growth and annealing factors. The intergrowth responsible for iridescence of intermediate plagioclase is ascribed to Na, K segregation prior to development of the complex domain structure. Prolonged annealing at high temperature in a dry environment is suggested. It is futile to attempt to describe low entropy plagioclases in terms of classical thermodynamics: only a kinetic interpretation based on atomic and sub-microscopic textural factors can be viable.     

Thermodynamics of plagioclases I: Theory of the I\bar 1 - P\bar 1 phase transition in anorthite and Ca-rich plagioclases

Landau theory of the \(P\bar 1 - I\bar 1\) phase transition in Ca-rich plagioclases reveals the sensitivity of the phase transition behaviour to a) Al, Si disorder, b) structural replacement of Ca by Na, and c) inhomogeneities of lattice strains. The following effects are predicted:

1. A tricritical phase transition exists in fully ordered anorthite. Al, Si disorder and Na, Ca exchange lead to second order phase transitions.
2. The transition temperatures depend sensitively on the degree of Al, Si disorder and the chemical composition of the Ca-rich plagioclases. Increasing Na-content decreases the transition temperatures.
3. The thermal evolution of c and d reflections depends on the homogeneity of the crystal and do not necessarily reflect the temperature evolution of the macroscopic lattice strain. A simple quadratic dependence of the X-ray scattering intensity on the order parameter exists only for fully ordered, homogeneous anorthite.

The role of inhomogeneous Al, Si distributions and lattice relaxations are discussed including possible structural modulations.     

Theoretical approach to evaluating plagioclase dissolution mechanisms

The more rapid dissolution of Ca-rich feldspars relative to Na, K-rich feldspars has been attributed to the preferential leaching of Al deep within the feldspar structure. Evidence from surface microanalysis (e.g., Hellmann et al., 2003), however, shows that preferential dissolution of Al is confined to the top layers of the feldspar lattice and that the amorphous surface layer most likely results from precipitation versus dissolution. It is thus critical to examine the extent of preferential Al removal. Here we present a theoretical study of plagioclase dissolution behavior using parameterized Monte Carlo simulations. Two different dissolution mechanisms, a mechanism involving preferential leaching of Al and an interfacial dissolution-reprecipitation mechanism, are tested using compositions representing the entire plagioclase solid solution series. Our modeling results indicate that under the control of the preferential Al leaching mechanism, the influence of (Al, Si) disorder on the dissolution rate is significant. At a fixed composition, an increase in the degree of (Al, Si) disorder yields an increased dissolution rate, with an 8-fold increase in dissolution rate observed for highly disordered albite (An₀) compared to low albite. Increasing anorthite content tends to decrease the variation in the dissolution rate due to disorder. The difference in the dissolution rate of 293 tested oligoclase configurations with a composition of An₂₀ is 3-fold, and the difference is reduced to 2-fold among 107 andesine configurations of An₃₀. Furthermore, feldspar configurations with completely disordered (Al, Si) distributions yield a consistent log-linear dependence of dissolution rate on the anorthite content (An), while other feldspar configurations with modest degrees of (Al, Si) disorder exhibit rates less than this trend. In contrast, when Al removal is confined to the top surface layers, a variety of feldspar configurations with different (Al, Si) disorder but a single fixed composition have similar dissolution rates; and the dissolution rate of Ca-rich feldspars departs positively from its log-linear relationship with anorthite content. This departure occurs around An₈₀ and is in good agreement with previous experimental studies. Subsequent modeling results of aluminum inhibition, ΔG dependence, and formation of altered surface layers in the framework of the interfacial dissolution-reprecipitation mechanism are all comparable with experimental investigations, and these results suggest that an interfacial dissolution-reprecipitation mechanism governs the dissolution of plagioclase feldspars.     

Thermodynamics of mixing in diopside–jadeite,CaMgSi<Subscript>2</Subscript>O<Subscript>6</Subscript>–NaAlSi<Subscript>2</Subscript>O<Subscript>6</Subscript>, solid solution from static lattice energy calculations

Static lattice energy calculations (SLEC), based on empirical interatomic potentials, have been performed for a set of 800 different structures in a 2 × 2 × 4 supercell of C2/c diopside with compositions between diopside and jadeite, and with different states of order of the exchangeable Na/Ca and Mg/Al cations. Excess static energies of these structures have been cluster expanded in a basis set of 37 pair-interaction parameters. These parameters have been used to constrain Monte Carlo simulations of temperature-dependent properties in the range of 273–2,023 K and to calculate a temperature–composition phase diagram. The simulations predict the order–disorder transition in omphacite at 1,150 ± 20°C in good agreement with the experimental data of Carpenter (Mineral Petrol 78:433–440, 1981). The stronger ordering of Mg/Al within the M1 site than of Ca/Na in the M2 site is attributed to the shorter M1–M1 nearest-neighbor distance, and, consequently, the stronger ordering force. The comparison of the simulated relationship between the order parameters corresponding to M1 and M2 sites with the X-ray refinement data on natural omphacites (Boffa Ballaran et al. in Am Mineral 83:419–433, 1998) suggests that the cation ordering becomes kinetically ineffective at about 600°C.     

Dehydration and partial melting of tremolitic amphibole coexisting with zoisite, quartz, anorthite, diopside, and water in the system H2O-CaO-MgO-Al2O3-SiO2

The greenschist to amphibolite transition as modeled by the reaction zoisite+tremolite + quartz= anorthite+diopside+water has been experimentally investigated in the chemical system H₂O−CaO− MgO−Al₂O₃−SiO₂ over the range of 0.4–0.8 GPa. This reaction is observed to lie within the stability fields of anorthite + water and of zoisite + quartz, in accord with phase equilibrium principles, and its position is in excellent agreement with the boundary calculated from current internally-consistent data bases. The small dP/dT slope of 0.00216 GPa/K (21.6 bars/K) observed for this reaction supports the pressure-dependency of this transition in this chemical system. Experimental reversals of the Al content in tremolitic amphibole coexisting with zoisite, diopside, quartz, and water were obtained at 600, 650, and 700^°C and indicated Al total cations (atoms per formula unit, apfu) of only up to 0.5±0.08 at the highest temperature. Thermodynamic analysis of these and previous compositional reversal data for tremolitic amphibole indicated that, of the activity/composition relationships considered, a two-site-coupled cation substitution model yielded the best fit to the data and a S ⁰ (1 bar, 298 K) of 575.4±1.6 J/K · mol for magnesio-hornblende. The calculated isopleths of constant Al content in the amphibole are relatively temperature sensitive with Al content increasing with increasing temperature and pressure. Finally, several experiments in the range of 1.0–1.3 GPa were conducted to define the onset of melting, and thus the upper-thermal limit, for this mineral assemblage, which must involve an invariant point located at approximately 1.05 GPa and 770^°C. Received: 24 January 1997 / Accepted: 2 October 1997     

苏鲁造山带东部荣成榴辉岩中蓝晶石及绿辉石的分解——一种可能的新成因解释

在麻粒岩相条件下，荣成含蓝晶石榴辉岩发生退变质，其中的绿辉石退变质成透辉石＋中长石组成的后成合晶，蓝晶石大部分被冠状体取代，基于详细探针分析结果的成分迁移估算显示，冠状体的形成需要从绿辉石的分解中获取CaO,MgO,FeO，绿辉石的分解包含两个反应：一个为绿辉石中的硬玉分子与石英结合形成钠长石；另一个发生在绿辉石内部各端员组分之间，后者不但形成后成合晶，而且为蓝晶石周围冠状体的形成提供CaO,MgO,FeO，蓝晶石的分解未能给后成合晶的形成提供SiO2，绿辉石与蓝晶石在分解时并冰形成一个封闭体系，它们均从周围环境中获取SiO2。     

TEM evidence of perovskite–brownmillerite coexistence in the Ca(AlxFe1−x)O2.5 system with minor amounts of titanium and silicon

Observations by transmission electron microscopy (TEM) of the submicrometer phases present in calcium aluminate cements have shown that Ca-Al-Fe oxides coexist in two forms with brownmillerite (b) and perovskite (p) structures, respectively. Homogeneous single crystals of both brownmillerite and perovskite have been observed but exsolved lamellae also occur on the scale of tens of nanometers. Perovskite lamellae in brownmillerite exhibit coherent interfaces with an almost perfect [1 0 1]_b = {1 0 0}_p topotactic relationship. Energy-dispersive X-ray spectroscopy (EDXS) measurements show that perovskite lamellae are enriched in Ti and Si relative to the brownmillerite lamellae. The perovskite phase may accommodate up to 0.17 Si atoms per formula unit, but the exsolution process seems mainly to concern the Ti content. It is estimated that the solvus width ranges between concentrations of 0.06 < Ti < 0.13 atoms per formula unit. O K and Fe L _2,3 edges collected by electron energy loss spectrometry (EELS) confirm that both phases are mainly composed of Fe³⁺, requiring that the perovskite is highly oxygen-deficient. Al K and Si K EELS spectra have features comparable with those of fourfold-co-ordinated Al and Si sites, suggesting that they are probably located close to oxygen-vacant sites. Received: 23 June 1999 / Accepted: 18 February 2000     

Cation ordering in BaAl2Ge2O8-feldspar: implications for the phase transition in anorthite

BaAl₂Ge₂O₈-Feldspar undergoes an order-disorder phase transition I2/c↔C2/m at T _tr ≈1690 K. The thermodynamics of the Al,Ge cation ordering process is described in terms of the compressible Ising model in mean field approximation. The mean field potential predicts a first order character of the phase transition. This is compared to antiferromagnetic ordering in a two-dimensional square Ising model with NN-pair interactions and four-spin interactions on alternating squares. Calculated order parameters and short range ordering are in good agreement with the corresponding properties observed in BaAl₂Ge₂O₈-feldspar by means of X-ray diffraction, hard mode infrared spectroscopy and TEM. Using known calorimetric data a similar model is postulated for Al,Si ordering in anorthite, CaAl₂Si₂O₈, for which the derived potential describes a transition with slightly stronger first order character at T _tr ≈1928 K. Received: 30 January 1998 / Revised, accepted: 29 August 1998     

Radiation-induced defects in quartz. III. Single-crystal EPR,ENDOR and ESEEM study of a peroxy radical

The X- and W-band single-crystal electron paramagnetic resonance spectra of an electron-irradiated natural quartz permit quantitative analysis of a ²⁹Si hyperfine structure (A ~12.6 MHz) and an ²⁷Al hyperfine structure (A ≤ 0.8 MHz) for a previously reported hole-like center. The ²⁹Si hyperfine structure arises from interaction with two equivalent Si atoms and is characterized by the direction of the unique A axis close to a Si–O bond direction. The ²⁷Al hyperfine structure, confirmed by pulsed electron nuclear double resonance and electron spin echo envelope modulation spectra, is characterized by the unique A axis approximately along a twofold symmetry axis. These ²⁹Si and ²⁷Al hyperfine data, together with published theoretical results on peroxy radicals in SiO₂ as well as our own density functional theory (DFT) calculations on model peroxy centers, suggest this hole-like center to have the unpaired spin on a pair of oxygen atoms linked to two symmetrically equivalent Si atoms and a substitutional Al³⁺ ion across the c-axis channel, a first peroxy radical in quartz. The nuclear quadrupole matrix P also suggests that the Al³⁺ ion corresponds closely to the diamagnetic precursor to the [AlO₄]⁰ center. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Oxygen deficient perovskites in the system CaSiO3–CaAlO2.5 and implications for the Earth’s interior

Oxygen deficient perovskites of the system CaSiO₃–CaAlO_2.5 have been synthesised at high-pressure and -temperature conditions relevant to the Earth’s transition zone in order to investigate their stabilities in the Earth’s mantle and determine structural properties associated with vacancy incorporation. Two polysomes of thermodynamically stable defect perovskites with Ca(Al_0.4Si_0.6)O_2.8 and Ca(Al_0.5Si_0.5)O_2.75 stoichiometry have been identified. The ordering of oxygen defects into pseudo-cubic (111) layers results in well-ordered ten- or eightfold superstructures, respectively. At all other compositions examined, a metastable formation of perovskites has been observed instead, which are assumed to grow initially disordered. These are now characterised by tiny domains, formed due to subsequent ordering of vacancies along various pseudo-cubic {111} layers. Both ordered defect perovskites show a large P–T stability field ranging from about 9–18 GPa and 4–12 GPa, respectively. Microstructural TEM analyses revealed the presence of growth and ferroelastic twins, which indicate a phase transition from rhombohedral to monoclinic symmetry during quenching. Electron energy loss spectroscopy of Si and Al K edges point at the presence of tetrahedral, octahedral and maybe some pentacoordinated silicon, whereas aluminium is predominantly octahedrally coordinated with minor fractions in lower coordination. Observed properties are interpreted in terms of a new structural model, explaining the observed phase transition and formation of different twin laws as well as giving reasons for the development of such large superstructures. With respect to phase relations of the transition zone, the potential occurrence of such defect perovskites in the Earth’s interior is discussed.     

Diffusion Gradients in an Eclogite Xenolith from the Roberts Victor Kimberlite Pipe: 1. Mechanism and Evolution of Garnet Exsolution in Al2O3-rich Clinopyroxene

Xenolith JJG41 is from the Roberts Victor kimberlite and isa bimineralic eclogite which is striking for its Al- and Ca-richclinopyroxene crystals showing garnet exsolution lamellae. Thedevelopment of the exsolution has been interpreted as a resultof a slow cooling at depth from near-solidus conditions (c.1400?C) towards normal mantle lithosphere temperatures (Harte& Gurney, 1975). The clinopyroxene retains marked compositionalgradients adjacent to the garnet lamellae and the present paperis concerned with the generation and preservation of these diffusiongradients within a rock from the Earth's mantle In order to understand the mechanism of exsolution reactiona re-examination has been made of the microtexture and chemistryof the garnet lamellae in relation to the compositional gradientsin adjacent clinopyroxene. Three sets of garnet lamellae, whichappear to have crystallized in sequence, may be recognised:type A, large lamellae, nucleated first and closest to the transformationtemperature; type B of intermediate size and age; and type C,small lamellae, nucleated last and with the greatest overstepof the transformation temperature. The major compositional zoning in JJG41 clinopyroxene, a decreaseof Al as Si and Mg increase, is consistent with the garnet growthreaction 2Diop+Al₂Si^–1Mg^–1=2Gros, 1Py.Ca, unlikemost of the elements, shows very flat composition profiles,but with a higher concentration than the initial Ca contentof the unexsolved clinopyroxene. Garnet lamellae are individuallyhomogeneous, but Ca contents vary between lamellae as a functionof lamellae size. In contrast the Fe/Mg distribution coefficientsat interfaces between garnet and clinopyroxene are relativelyconstant irrespective of garnet size. The redistribution of the principal cations—Ca, Fe, Mg,Al, Si—between and within the clinopyrox ene and garnet,during garnet exsolution and cooling, obviously proceeded differentlyfor different elements. Two principal stages in the coolinghistory may be identified: (1) The growth of the sets of garnetlamellae controlled by Al₂Mg^–1Si^–1 redistributionin clinopyroxene. This redistribution was both part of the nettransfer reaction creating garnet, and an exchange reactionin clinopyroxene essential for the diffusional transport ofAl to the growing garnet. Al diffusion in clinopyroxene wasprobably the rate-limiting step, and all other cations, Ca andFe as well as Mg and Si, were mobile during this stage. (2)The occurrence, after the cessation of garnet growth, of diffusionof Fe, Mg and Ca in garnet and interdiffusion of Fe-Mg in clinopyroxene.This resulted in the setting of the KD Fe-Mg at the Cpx-Gt interfacesto a roughly constant value equivalent to approximately 1000?C,which is taken to be the final (‘freezing-in’) temperaturefor redistribution of any elements. During this post garnet-growthstage Ca also became homogenized within individual garnet lamellae,but there is no evidence of Ca equilibration with the clinopyroxene.Under the P-T conditions operating, the initial clinopyroxenecomposition probably resulted in a maximum (M2 site fully occupied)Ca content in clinopyroxene during the stage of garnet growth,and this was maintained during the post-growth stage.     

Mode of formation of hibonite (CaAl12O19) within the U-Th skarns from the granulites of S-E Madagascar

 In Madagascar, hibonite occurs as a rather frequent mineral within thorianite-bearing skarns which are widespread in the Pan African granulitic formations constituting the S-E part of the Island (Tranomaro area). In these skarns, leucocratic segregations made up of CO₃-scapolite to meionite (An_equivalent=89–95% which implies T≥850° C), spinel and corundum were formed at stage 1 of metasomatism in a titanite-bearing matrix consisting of scapolite (An_eq=77–88) and aluminous diopside. During stage 2 of metasomatism, scapolite from the lenses were altered to anorthite+calcite while the less calcic scapolite remained stable which indicates T≈800° C. Hibonite crystallized at the expense of corundum and spinel. Expressed as mol% of the CaAl₁₂O₁₉/Ca(Al₁₀TiR²⁺)O₁₉/REE(Al₁₁R²⁺)O₁₉ [+Th (Al₁₀R²⁺ ₂)O₁₉] end-members (R ²⁺=Mg, Fe²⁺, Zn²⁺; Al=Al, Fe³⁺; Ti=Ti, Si), its composition varies from 26/72/2 to 50/23/27. The ideal activity of the CaAl₁₂O₁₉ component is about 0.25. Fluid inclusions in corundum, hibonite and anorthite are composed of nearly pure CO₂. In corundum, the isochores for primary inclusions are in agreement with the P-T estimates for regional metamorphism and stage 1 metasomatism (T≈850° C, P≈5 kbar). Inclusions with the highest density in hibonite and anorthite constrain P to about 3–3.5 kbar for T=800° C. Thermodynamic calculations indicate that, in addition to a low activity of CaAl₁₂O₁₉, stability of hibonite in equilibrium with anorthite and calcite implies an extremely low activity of silica (below the zircon-baddeleyite buffer). By contrast the activity of CO₂ may be high, in agreement with the observed fluid compositions. These results are corroborated by a short comparison with the other granulite occurrences of hibonite in Tanzania and South India. Received: 18 August 1994 / Accepted: 12 October 1995     

Aluminum substitution mechanisms in perovskite-type MgSiO<Subscript>3</Subscript>: an investigation by Rietveld analysis

Al-containing MgSiO₃ perovskites of four different compositions were synthesized at 27 GPa and 1,873 K using a Kawai-type high-pressure apparatus: stoichiometric compositions of Mg_0.975Si_0.975Al_0.05O₃ and Mg_0.95Si_0.95Al_0.10O₃ considering only coupled substitution Mg²⁺ + Si⁴⁺ = 2Al³⁺, and nonstoichiometric compositions of Mg_0.99Si_0.96Al_0.05O_2.985 and Mg_0.97Si_0.93Al_0.10O_2.98 taking account of not only the coupled substitution but also oxygen vacancy substitution 2Si⁴⁺ = 2Al³⁺ + V_O¨. Using the X-ray diffraction profiles, Rietveld analyses were performed, and the results were compared between the stoichiometric and nonstoichiometric perovskites. Lattice parameter–composition relations, in space group Pbnm, were obtained as follows. The a parameters of both of the stoichiometric and nonstoichiometric perovskites are almost constant in the X _Al range of 0–0.05, where X _Al is Al number on the basis of total cation of two (X _Al = 2Al/(Mg + Si + Al)), and decrease with further increasing X _Al. The b and c parameters of the stoichiometric perovskites increase linearly with increasing Al content. The change in the b parameter of the nonstoichiometric perovskites with Al content is the same as that of the stoichiometric perovskites within the uncertainties. The c parameter of the nonstoichiometric perovskites is slightly smaller than that of the stoichiometric perovskites at X _Al of 0.10, though they are the same as each other at X _Al of 0.05. The Si(Al)–O1 distance, Si(Al)–O1–Si(Al) angle and minimum Mg(Al)–O distance of the nonstoichiometric perovskites keep almost constant up to X _Al of 0.05, and then the Si(Al)–O1 increases and both of the Si(Al)–O1–Si(Al) angle and minimum Mg(Al)–O decrease with further Al substitution. These results suggest that the oxygen vacancy substitution may be superior to the coupled substitution up to X _Al of about 0.05 and that more Al could be substituted only by the coupled substitution at 27 GPa. The Si(Al)–O1 distance and one of two independent Si(Al)–O2 distances in Si(Al)O₆ octahedra in the nonstoichiometric perovskites are always shorter than those in the stoichiometric perovskite at the same Al content. These results imply that oxygen defects may exist in the nonstoichiometric perovskites and distribute randomly.     

Nature of the chemical heterogeneity of the continental lithospheric mantle

The paper reports data on the chemical composition of mantle peridotite xenoliths from kimberlites and alkaline basalts that represent the continental lithospheric mantle (CLM) beneath Early Precambrian and Late Proterozoic-Cenozoic structures, respectively. In order to identify compositional trends during the melting of primitive material and propose the most reliable criteria for constraining the conditions of this process and its degree, we analyzed literature data on the melting of spinel and garnet peridotites within broad temperature and pressure ranges. It was determined that the degree of melting (F%) of pristine peridotite of composition close to that of the primitive mantle (PM) can be deduced from the Mg/Si and Al/Si ratios in the residue; an equation was proposed for evaluating F from the Mg/Si ratio. The Ca/Al ratio of residues at low (1–1.5 GPa) pressures and degrees of melting from 2–3 to 20–25% increases several times but decreases with increasing F at pressures higher than 3 GPa. The Na partition coefficient between melt and residue decreases at increasing pressure and approaches one at a pressure close to 20 GPa. Residues after low-degree melting are strongly depleted in Ti, Zr, Y, and Nb but are enriched in Cr. The application of these criteria to the composition of xenoliths brought to the surface from the mantle occurring beneath tectonic structures of various age led us to conclude that compositional heterogeneities of CLM (particularly the variations in the concentrations of major and certain siderophile elements) are controlled, first of all, by the melting of the mantle source material. These processes occurred under various thermodynamic conditions (T, P, and $ f_{O_2 } $ f_{O_2 } ) and differed in their intensity, and this predetermined the compositional diversity of the residual mantle material (its concentrations of Mg, Al, Si, Ca, Na, K, Ni, Co, V, and Cr). Our results are principally consistent with the hypothesis of the global magmatic ocean. It is thought that the early phases of its consolidation were variably controlled by the fractionation of minerals, for example, majorite. Moreover, heterogeneities in the distribution of siderophile elements could be partly predetermined by changes in the properties of these elements at ultrahigh temperatures and pressures. The processes of partial melting were the most intense during the early evolution of the mantle (perhaps, in the Early Precambrian), and hence, the mantle has different chemical composition beneath Archean cratons and Phanerozoic foldbelts.     

Pressure dependence on partition coefficients for trace elements between olivine and the coexisting melts

Partition coefficients between olivine and melt at upper mantle conditions, 3 to 14 GPa, have been determined for 27 trace elements (Li, Be, B, Na, Mg, Al, Si, P, K, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Rb, Sr, Y, Zr, Cs, Ba, La and Ce) using secondary-ion mass-spectrometry (SIMS) and electron-probe microanalysis (EPMA). The general pattern of olivine/melt partitioning on Onuma diagrams resembles those reported previously for natural systems. This agreement strongly supports the argument that partitioning is under structural control of olivine even at high pressure. The partition coefficients for mono- and tri-valent cations show significant pressure dependence, both becoming larger with pressure, and are strongly correlated with coupled substitution into cation sites in the olivine structure. The dominant type of trace element substitution for mono- and tri-valent cations into olivine changes gradually from (Si, Mg)↔(Al, Cr) at low pressure to (Si, Mg)↔(Al, Al) and (Mg, Mg)↔(Na, Al) at high pressure. The change in substitution type results in an increase in partition coefficients of Al and Na with pressure. An inverse correlation between the partition coefficients for divalent cations and pressure has been observed, especially for Ni, Co and Fe. The order of decreasing rate of partition coefficient with pressure correlates to strength of crystal field effect of the cation. The pressure dependence of olivine/melt partitioning can be attributed to the compression of cation polyhedra induced by pressure and the compensation of electrostatic valence by cation substitution. Received: March 6, 1997 / Revised, accepted: March 12, 1998     

Mechanical twinning and slip in experimentally deformed plagioclases

Mechanical albite and pericline twins were induced in seven feldspars, (Na, Ca) (Al, Si)₄O₈, in triaxial compression tests at 800° C, 8 to 10 kb confining pressure. Two were initially in a high temperature structural state (disordered) (An₁, An₅₉). Three (An₃₂, An₃₉, and An₅₃) were slightly disordered, and two (An₇₆ and An₉₅) had the transitional and primitive anorthite structure, respectively. No microscopic twinning was detected in comparable tests on ordered albite and oligoclase (An₁, An₂₀), feldspars in the peristerite range (An₁₁ An₁₄) or in a low structural state labradorite (An₅₁). Other deformational features include lamellae 60 to 80° from the c axis and (010) slip in the opposite sense for (010) twinning.Work performed under the auspices of the U. S. Atomic Energy Commission.     

Thermal expansion and structural transformations of stuffed derivatives of quartz along the LiAlSiO4–SiO2 join: a variable-temperature powder synchrotron XRD study

 The structural behavior of stuffed derivatives of quartz within the Li_{1− x} Al_{1− x} Si_{1+ x} O₄ system (0 ≤ x ≤ 1) has been studied in the temperature range 20 to 873 K using high-resolution powder synchrotron X-ray diffraction (XRD). Rietveld analysis reveals three distinct regimes whose boundaries are defined by an Al/Si order-disorder transition at x=∼0.3 and a β–α displacive transformation at x=∼0.65. Compounds that are topologically identical to β-quartz (0 ≤ x < ∼0.65) expand within the (0 0 1) plane and contract along c with increasing temperature; however, this thermal anisotropy is significantly higher for structures within the regime 0 ≤ x < ∼0.3 than for those with compositions ∼0.3 ≤ x < ∼0.65. We attribute this disparity to a tetrahedral tilting mechanism that occurs only in the ordered structures (0 ≤ x < ∼0.3). The phases with ∼0.65 ≤ x ≤ 1 adopt the α-quartz structure at room temperature, and they display positive thermal expansion along both a and c from 20 K to their α–β transition temperatures. This behavior arises mainly from a rotation of rigid Si(Al)-tetrahedra about the <100> axes. Landau analysis provides quantitative evidence that the charge-coupled substitution of Li+Al for Si in quartz dampens the α–β transition. With increasing Li+Al content, the low-temperature modifications exhibit a marked decrease in spontaneous strain; this behavior reflects a weakening of the first-order character of the transition. In addition, we observe a linear decrease in the α–β critical temperature from 846 K to near 0 K as the Li+Al content increases from x=0 to x=∼0.5. Received: 26 June 2000 / Accepted: 1 December 2000     

Radiation-induced defects in quartz. II. Single-crystal W-band EPR study of a natural citrine quartz

Single-crystal electron paramagnetic resonance (EPR) spectra of a natural citrine quartz without any artificial irradiation, measured at W-band frequencies (∼94 GHz) and temperatures of 77, 110 and 298 K, allow better characterization of three previously-reported Centers (#6, #7 and B) and discovery of three new defects (B′, C′ and G′). The W-band EPR spectra reveal that Centers #6 and #7 do not reside on twofold symmetry axes, contrary to results from a previous X-band EPR study. The W-band spectra also show that the previously reported Center B is a mixture of two defects (B and B′) with similar g matrices but different-sized ²⁷Al hyperfine structures. Center C′ has similar principal g values to the previously reported Center C but is distinct from the latter by a larger ²⁷Al hyperfine structure with splittings from 0.10 to 0.22 mT. Also, Center G′ has a similar g matrix to the previously reported Center G but a different ²⁷Al hyperfine structure with splittings from 0.41 to 0.53 mT. These spin-Hamiltonian parameters, together with observed thermal properties and microwave-power dependence, suggest that Centers #6 and #7 probably represent O₂³⁻ type defects. Centers B and B′ are probably superoxide radicals (O₂⁻) with the unpaired spin localized on the same pair of oxygen atoms around a missing Si atom but linked to a substitutional Al³⁺ ion each at different neighboring tetrahedral sites. Similarly, Centers G and G′ are most likely superoxide radicals with the unpaired spin localized on another pair of oxygen atoms around a missing Si atom and linked to a substitutional Al³⁺ ion each at different neighboring tetrahedral sites. Center C′ is probably an ozonide radical associated with a missing Si atom and linked to a substitutional Al³⁺ ion at the neighboring tetrahedral site. This study exemplifies the value of  high-frequency EPR for discrimination of  similar defect centers and determination of  small local structural distortions that are often difficult to resolve in conventional  X- and Q-band EPR studies.     

The superstructure of plagioclase feldspars

A modulation function representing the position and density of (Na, Ca) atoms in the superstructure of the e-plagioclase has been derived from the average structures of different plagioclase and a general modulation theory. Based on this function the superstructure of bytownite (An₇₃) has been studied with the single crystal X-ray method. The cell dimensions by Megaw's axes are a=7.946(3)A, b=67.09(2)A, c=12.236(4)A, α=39.03(1)°, β=45.63(1)° and γ=59.63(1)°. Z=18(Na, Ca) Al(Al, Si)Si₂O₈. The initial phase factor of the modulation function for bytownite has been obtained from the intensity data of the satellite reflections. This modulation function indicates a coherent small-scale alternation of the Na-rich and Ca-rich bands in the superstructure. This superstructure has been refined by applying the albite and anorthite structures to the Na-rich and Ca-rich bands, respectively. The change of the superstructure of the e-plagioclase due to the compositional change has been described based on the movements of the satellites in reciprocal space. The direction of the coherent small-scale intergrowth of the anorthite-like and albite-like bands is perpendicular to the t vector. The thickness of the intergrowth is 1/|t|. Both direction and thickness change regularly from An₇₅ to An₂₅.     

A comment on diffusion and the displacement of atoms in metamorphic transformations

Experimental data on diffusion in olivine , are used to define certain terms – diffusion coefficient, jump frequency, characteristic distance, random walk – that are useful in a discussion of atom displacements under natural conditions. Examples of atom displacements in two metamorphic terranes of the Canadian Precambrian Shield are then examined, as follows. (i) In a high‐grade metamorphic terrane in the Mid‐Proterozoic Grenville Province (Otter Lake Area), Mg concentration gradients about dolomite microcrystals in calcite and Na gradients about albite microcrystals in K‐feldspar are viewed as stranded Mg–Ca and Na–K interdiffusion gradients, formed by exsolution during slow cooling from ~700 to ~400 °C. (ii) In the Archean Slave Province (Yellowknife area), the crystallization of sillimanite, near andalusite but within crystals of quartz, possibly occurred by coupled Al–Si and oxygen–vacancy interdiffusion in quartz at ~550 °C. And the crystallization of garnet from chlorite occurred by the two‐way crystal‐boundary diffusion of several kinds of atoms across distances ranging to 3 mm. (iii) In the Otter Lake area, the crystallization of orthopyroxene–hornblende–spinel reaction zones at boundaries between crystals of olivine and plagioclase in metagabbro, evidently occurred by the mechanism of interstitial diffusion, that transported Mg, Fe, Mn and O atoms across the reaction zone from olivine to the plagioclase–(hornblende+spinel) boundary, and Si, Al, Ca and Na atoms from plagioclase to the olivine–orthopyroxene boundary, accompanied by NaSi–CaAl interdiffusion in plagioclase, and the addition of hydrogen and minor Ti, Zn, F, Cl and K from beyond the reaction zone. Also, centimetric reaction zones, with abundant biotite and plagioclase, at boundaries between K‐feldspar gneiss and deformed amphibolite dykes, evidently formed by the reaction, strained hornblende (in amphibolite) + K‐feldspar (in gneiss)→biotite (in amphibolite) + plagioclase (in gneiss), with crystal‐boundary diffusion of (Na + Ca) atoms and of K atoms across the reaction zone.