Kinetic rate laws derived from order parameter theory III: Al,Si ordering in sanidine

The time dependence of the ordering and disordering of Al and Si in sanidine is described within the framework of the kinetic rate laws developed in papers I and II of this series. It was found that the relevant order parameter Q _t is homogeneous and non-conserved. The rate law is:

Maximum entropy and shear strain of shear zone

The principle of maximum entropy can be used to determine the shear strain in natural shear zones. When the margin of a shear zone is assumed, the principle leads to the truncated exponential distribution of the shear strain. Ifx is the distance remote from the shear zone center, which possesses the maximum shear strain, the shear strain (x) is given by

The crystal structure of a triclinic roscherite

Summary The crystallography of roscherite is more complicated than previously thought. Single crystal X-ray work on material from Foote Mine (California) gave triclinic symmetry. The unit cell corresponding to the one adopted for monoclinic roscherite hasa=15.921,b=11.965,c=6.741 Å, =91°04, =94°21, =89°59 1/2, space group . The least-squares refinement of the structure using 2380 non zero reflections with anisotropic temperature factors resulted in a conventional reliability factorR=0.060.The X-ray study indicates the formula while that proposed for monoclinic roscherite is The atomic arrangements of both varieties of roscherite are very similar. The lowering of symmetry is caused by the segregation of the trivalent cations into only half of the sites of a monoclinic point position. Crystallochemical considerations suggest that the symmetry of roscherite does not depend on the kind of trivalent cations occupying the 6-coordinated position, but rather by the ratio between trivalent and divalent metal ions.

---

Die Kristallstruktur eines triklinen Roscherites

Zusammenfassung Die Kristallographie des Roscherites ist komplizierter als man bisher annahm. Einkristall-Röntgenuntersuchungen an Material von Foote Mine (Kalifornien) ergaben trikline Symmetrie. Die Elementarzelle, welche der für monoklinen Roscherit angenommenen entspricht, hata=15,921,b=11,965,c=6,741 Å, =91°04, =94°21, =89°59 1/2, Raumgruppe . Die Verfeinerung der Struktur mit der Methode der kleinsten Quadrate ergab unter Verwendung anisotroper Temperaturfaktoren für 2380 beobachtete Reflexe einen konventionellen ZuverlässigkeitsindexR=0,060.Die Röntgenuntersuchung weist auf die Formel , während für monoklinen Roscherit vorgeschlagen wurde. Die Atomanordnungen beider Abarten des Roscherites sind sehr ähnlich. die Symmetrieerniedrigung wird dadurch hervorgerufen, daß die dreiwertigen Kationen nur die Hälfte der Positionen einer monoklinen Punktlage besetzen. Kristallchemische Überlegungen weisen darauf hin, daß die Symmetrie nicht von der Art der dreiwertigen Kationen, welche eine 6-koordinierte Punktlage besetzen, abhängt, sondern vielmehr von dem Mengenverhältnis zwischen 3-wertigen und 2-wertigen Metallionen.

---

---

With 1 Figure     

High-temperature creep and kinetic decomposition of Ni2SiO4

To investigate high-temperature creep and kinetic decomposition of nickel orthosilicate (Ni₂SiO₄), aggregates containing 3 vol% amorphous SiO₂ have been deformed in uniaxial compression at a total pressure of one atomsphere. Twenty-three samples with grain sizes (d) from 9 to 30 m were deformed at temperatures (T) from 1573 to 1813 K, differential stresses () from 3 to 20 MPa, and oxygen fugacities (f o ₂) from 10^-1 to 10⁵ Pa. At temperatures up to 1773 K, the steady-state creep rate () can be described by the flow law

Opening and resetting temperatures in heating geochronological systems

We present a theoretical model for diffusive daughter isotope loss in radiochronological systems with increasing temperature. It complements previous thermochronological models, which focused on cooling, and allows for testing opening and resetting of radiochronometers during heating. The opening and resetting temperatures are, respectively,

Reversed experimental calibration of the garnet-clinopyroxene Fe — Mg exchange thermometer

The temperature-sensitive Fe,Mg exchange equilibrium,

Crustal Growth Rate of the North China Platform：a Method of Estimating Mass Equilibrium between Crust and Mantle

The following equation is proposed in this paper to estimate the crustal growth rate of the North China Platform on the basis of mass equilibrium between the crust and the mantle:

Garnet in silicic liquids and its possible use as a P-T indicator

Melting experiments on a model pelitic composition yield low-spessartine garnet as an important residual phase at pressures above 7 kb. The K _D values for distribution of iron and magnesium between coexisting garnet and liquid in the pelitic composition are mainly sensitive to temperature, but also have a small pressure dependence. At temperatures above 950 ° C garnet has a higher value than coexisting liquid, but below 950 ° C the garnet value is lower than that of the coexisting liquid. Thus at temperatures below 950 ° C silicic magmas may fractionate garnet and produce more magnesian derivative liquids.Reconnaissance experiments with added MnO content in the model pelite demonstrate that spessartine-rich garnets are stable in silicic liquids to pressures as low as 3 kb. The MnO and CaO contents of the experimentally crystallized garnets show an antipathetic relation. Also, the grossular content of near-liquidus garnets crystallizing from a range of compositions increases with increasing pressure. The spessartine and grossular contents of most natural garnets in eastern Australian granitic rocks suggest that these garnets formed at pressures greater than 5 kb. Increased spessartine content allows crystallization of garnet in equilibrium with a silicic magma well within the pressure limit of stability of cordierite, provided the garnet contains 10 mol.% spessartine. Thus the depth range over which garnet and cordierite may coexist in a silicic melt is broadened, subject to the availability of MnO. The effect of increased Mn content on the low-pressure stability limit of garnet may also explain the lack of resorption of some garnets in granitic magmas, as these magmas rise to shallower levels. These euhedral garnets characteristically show zoning from an Mn-poor core (typically <4 % MnO) to an Mn-richer rim (typically >4 % MnO) and may reflect continued growth of the garnet in a low pressure regime, stabilized by Mn concentrated in the residual liquid fractions of the crystallizing magma.     

Empirical estimation of isostatic uplift using the lake-tilting method at lake Fegen and lake S?ven, southwestern Sweden

A nonuniform glacio-isostatic uplift results in differential uplift for different parts of a lake. If the lake outlet is situated in the area with the greatest rate of uplift, then the lake will be continuously transgressed. Ancient lake levels can be estimated by dating transgressed peat at different depths in such a lake. Two lakes in southwestern Sweden have been investigated by this method and the course of glacio-isostatic uplift has been determined empirically. The uplift can be expressed by an exponential function through the following formula

A Coupled Riverine-Marine Fractionation Model for Dissolved Rare Earths and Yttrium

Fractionation of yttrium (Y) and the rare earth elements (REEs) begins in riverine systems and continues in estuaries and the ocean. Models of yttrium and rare earth (YREE) distributions in seawater must therefore consider the fractionation of these elements in both marine and riverine systems. In this work we develop a coupled riverine/marine fractionation model for dissolved rare earths and yttrium, and apply this model to calculations of marine YREE fractionation for a simple two-box (riverine/marine) geochemical system. Shale-normalized YREE concentrations in seawater can be expressed in terms of fractionation factors ( _ij ) appropriate to riverine environments ( ) and seawater ( ):

Equations of state of Plagioclase Feldspars

The volume variation with pressure of seven intermediate plagioclase feldspars has been determined by high-pressure single-crystal X-ray diffraction. The bulk moduli of plagioclases for a 3rd-order Birch-Murnaghan EoS can be described by the following pair of equations:

The experimental investigation of the reactions MnCO3+SiO2=MnSiO37#x002B;CO2 and MnSiO3+MnCO3=Mn2SiO4+CO2 in CO2/H2O gasmixtures at a total pressure of 500 bars

The equilibrium constants for the reaction (2) Rhodochrosite + Quartz=Pyroxmangite+CO₂ obtained are:logK(₂)(bars)= $$\begin{gathered}{\text{log}}f_{co_2 } = - \frac{{(9862 \pm 102)}}{T} \hfill \\+ (15.887 \pm 0.220) + (0.1037 \pm 0.0020)\frac{{P - 1}}{T} \hfill \\\end{gathered} $$ and for the reaction (3) Rhodochrosite+Pyroxmangite=Tephroite+CO₂: logK(₃)(bars)= $$\begin{gathered}{\text{log}}f_{co_2 } = - \frac{{(6782 \pm 205)}}{T} \hfill \\+ (11.296 \pm 0.304) + (0.0835 \pm 0.0030)\frac{{P - 1}}{T} \hfill \\\end{gathered} $$ The present data lie within reasonable limits of error of the values calculated from previous experimental results at P _tot = 2000 bars.     

The Reaction Titanite+Kyanite=Anorthite+Rutile and Titanite-Rutile Barometry in Eclogites

Titanite and rutile are a common mineral pair in eclogites, and many equilibria involving these phases are potentially useful in estimating pressures of metamorphism. We have reversed one such reaction,

The electrical conductivity of upper-mantle rocks: water content in the upper mantle

The electrical conductivity of upper-mantle rocks—dunite, pyroxenite, and lherzolite—was measured at ∼2–3 GPa and ∼1,273–1,573 K using impedance spectra within a frequency range of 0.1–10⁶ Hz. The oxygen fugacity was controlled by a Mo–MoO₂ solid buffer. The results indicate that the electrical conductivity of lherzolite and pyroxenite are approximately half and one order of magnitude higher than that of dunite, respectively. A preliminary model involving water and iron content effects on the electrical conductivity was derived and is summarized by the relation:

Water in microcrystalline quartz of volcanic origin: Agates

Agates of volcanic origin, containing the different quartz species, fibrous, length-fast chalcedony (CH), granular fine quartz (FQ), and fibrous, length-slow, to lepidospheric quartzine (QN), have been investigated to evaluate possible relations between microstructure, i.e. crystallite size and texture, refractive indices, densities, contents of trace elements and of water, as well as dehydration behaviour. By means of near infrared spectroscopy, total water contents , could be differentiated quantitatively into contents of molecular water, , and silanole-group water, . Despite the low total water contents of the agates studied ( between 1 and 2 wt.%), near infrared spectroscopy results in reliable data on and .Wall-layering CH consists of fibrous quartz crystals and exhibits higher C-ratios, , than horizontally layered FQ which consists predominantly of granular quartz crystals (C _CH=0.45±0.11 (N=6), C _FQ=0.36±0.10 (N=4). This result is interpreted to be due to analogy with the behaviour of C-ratios in fluid phase-deposited opals-AN (hyalithe) and liquid phase-deposited opals-AG (non-crystalline opal) or -CT (common opal) (Langer and Flörke 1974).Translucent layers of CH show mostly lower refractive indices, when measured parallel than when measured perpendicular to the axes of the quartz fibers. The same is true for milky layers of CH. Crystallite sizes are smaller in the latter than in the former.For all samples studied, exists a positive correlation between at% (1/2Ca+1/2Mg+Na+K+Li) and at% (Al³⁺+Fe³⁺). This indicates that at least parts of (A1³⁺+ Fe³⁺) substitute for Si in the quartz structure. The charge is balanced by incorporation of di- and mono-valent cations in structural interstices. When the quantity at % H⁺, as obtained from , is included into the sum at% (1/2 Me²⁺+Me⁺), the above correlation is destroyed. This result could be indicative for a strong concentration of the Si-OH groups in the surface of the quartz microcrystallites.     

Über p-Veatehit,eine neue Veatehit-Varietät aus dem Zechsteinsalz

Zusammenfassung Im Älteren Steinsalz von Reyershausen bei Göttingen wurde eine neue Veatchit-Varietät gefunden mita ₀ = 6,721 Å,b ₀ = 20,81 Å,c ₀ = 6,64₇ Å, = 119° 4; Raumgruppe oderP2₁,Z = 4[(Sr, Ca) O · 3 B₂O₃ · 2 H₂O]. (010) ist die Ebene der vollkommenen Spalt-barkeit. Die Polymorphie der Veatehit-Minerale wird geometrisch durch geringfügige Deformationen der rhombischen Raumgruppe (bzw.A2₁ a m) erklärt.Der neue Vertreter wirdp-Veatehit (mit einfach-primitivem Raumgitter) genannt im Unterschied zum Original-Veatehit, der in die Raumgruppe gehört und dessen Symametrieebene senkrecht auf der vollkommenen Spaltebene steht.     

The effect of liquid composition on the partitioning of Ni between olivine and silicate melt

We report the results of experiments designed to separate the effects of temperature and pressure from liquid composition on the partitioning of Ni between olivine and liquid, \(D_{\text{Ni}}^{\text{ol/liq}}\). Experiments were performed from 1300 to 1600 °C and 1 atm to 3.0 GPa, using mid-ocean ridge basalt (MORB) glass surrounded by powdered olivine in graphite–Pt double capsules at high pressure and powdered MORB in crucibles fabricated from single crystals of San Carlos olivine at one atmosphere. In these experiments, pressure and temperature were varied in such a way that we produced a series of liquids, each with an approximately constant composition (~12, ~15, and ~21 wt% MgO). Previously, we used a similar approach to show that \(D_{\text{Ni}}^{\text{ol/liq}}\) for a liquid with ~18 wt% MgO is a strong function of temperature. Combining the new data presented here with our previous results allows us to separate the effects of temperature from composition. We fit our data based on a Ni–Mg exchange reaction, which yields \(\ln \left( {D_{\text{Ni}}^{\text{molar}} } \right) = \frac{{ -\Delta _{r(1)} H_{{T_{\text{ref}} ,P_{\text{ref}} }}^{ \circ } }}{RT} + \frac{{\Delta _{r(1)} S_{{T_{\text{ref}} ,P_{\text{ref}} }}^{ \circ } }}{R} - \ln \left( {\frac{{X_{\text{MgO}}^{\text{liq}} }}{{X_{{{\text{MgSi}}_{ 0. 5} {\text{O}}_{ 2} }}^{\text{ol}} }}} \right).\) Each subset of constant composition experiments displays roughly the same temperature dependence of \(D_{\text{Ni}}^{\text{ol/liq}}\) (i.e.,\(-\Delta _{r(1)} H_{{T_{\text{ref}} ,P_{\text{ref}} }}^{ \circ } /R\)) as previously reported for liquids with ~18 wt% MgO. Fitting new data presented here (15 experiments) in conjunction with our 13 previously published experiments (those with ~18 wt% MgO in the silicate liquid) to the above expression gives \(-\Delta _{r(1)} H_{{T_{\text{ref}} ,P_{\text{ref}} }}^{ \circ } /R\) = 3641 ± 396 (K) and \(\Delta _{r(1)} S_{{T_{\text{ref}} ,P_{\text{ref}} }}^{ \circ } /R\) = ? 1.597 ± 0.229. Adding data from the literature yields \(-\Delta _{r(1)} H_{{T_{\text{ref}} ,P_{\text{ref}} }}^{ \circ } /R\) = 4505 ± 196 (K) and \(\Delta _{r(1)} S_{{T_{\text{ref}} ,P_{\text{ref}} }}^{ \circ } /R\) = ? 2.075 ± 0.120, a set of coefficients that leads to a predictive equation for \(D_{\text{Ni}}^{\text{ol/liq}}\) applicable to a wide range of melt compositions. We use the results of our work to model the melting of peridotite beneath lithosphere of varying thickness and show that: (1) a positive correlation between NiO in magnesian olivine phenocrysts and lithospheric thickness is expected given a temperature-dependent \(D_{\text{Ni}}^{\text{ol/liq}} ,\) and (2) the magnitude of the slope for natural samples is consistent with our experimentally determined temperature dependence. Alternative processes to generate the positive correlation between NiO in magnesian olivines and lithospheric thickness, such as the melting of olivine-free pyroxenite, are possible, but they are not required to explain the observed correlation of NiO concentration in initially crystallizing olivine with lithospheric thickness.     

The concept of geochemical potential field exemplified by ore formation field

Geochemical potential field is defined as the scope within the earth’s space where a given component in a certain phase of a certain material system is acted upon by a diffusion force, depending on its spatial coordinatesX, Y andZ. The three coordinates follow the relations: $$NF_{ix} = - \frac{{\partial \mu }}{{\partial x}}, NF_{iy} = - \frac{{\partial \mu }}{{\partial y}}, NF_{iz} = - \frac{{\partial \mu }}{{\partial z}}$$ The characteristics of such a field can be summarized as: (1) The summation of geochemical potentials related to the coordinatesX, Y, Z, or pseudo-velocity head, pseudo-pressure head and pseudo-potential head of a certain component in the earth is a constant as given by $$\mu _x + \mu _y + \mu _z = c$$ or $$\mu _{x2} + \mu _{y2} + \mu _{z2} = \mu _{x1} + \mu _{y1} + \mu _{z1} $$ Derived from these relations is the principle of geochemical potential conservation. The following relations have the same physical significance: $$\mu _k + \mu _u + \mu _p = c$$ or $$\mu _{k2} + \mu _{u2} + \mu _{p2} = \mu _{k1} + \mu _{u1} + \mu _{p1} $$ (2) Geochemical potential field is a vector field quantified by geochemical field intensity which is defined as the diffusion force applied to one molecular volume (or one atomic volume) of a certain component moving from its higher concentration phase to lower concentration phase. The geochemical potential field intensity is given by $$\begin{gathered} E = - grad\mu \hfill \\ E = \frac{{RT}}{x}i + \frac{{RT}}{y}j + \frac{{RT}}{z}K \hfill \\ \end{gathered} $$ The present theory has been inferred to interpret the mechanism of formation of some tungsten ore deposits in China.     

Kinetic rate laws as derived from order parameter theory I: Theoretical concepts

A theoretical concept is outlined, which links the kinetics of structural transformations with thermodynamic theories of structural phase transitions. Starting from Landau theory and Markovian processes, the general rate laws for crystals with long correlation lengths are derived. The rate laws in Ginzburg-Landau theory are