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1.
A unifying theory of kinetic rate laws, based on order parameter theory, is presented. The time evolution of the average order parameter is described by $$\langle Q\rangle \propto \smallint P(x)e^{^{^{^{^{^{^{ - xt} } } } } } } dx = L(P)$$ where t is the time, x is the effective inverse susceptibility, and L indicates the Laplace transformation. The probability function P(x) can be determined from experimental data by inverse Laplace transformation. Five models are presented:
  1. Polynomial distributions of P(x) lead to Taylor expansions of 〈Q〉 as $$\langle Q\rangle = \frac{{\rho _1 }}{t} + \frac{{\rho _2 }}{{t^2 }} + ...$$
  2. Gaussian distributions (e.g. due to defects) lead to a rate law $$\langle Q\rangle = e^{ - x_0 t} e^{^{^{^{^{\frac{1}{2}\Gamma t^2 } } } } } erfc\left( {\sqrt {\frac{\Gamma }{2}} t} \right)$$ where x 0 is the most probable inverse time constant, Γ is the Gaussian line width and erfc is the complement error integral.
  3. Maxwell distributions of P are equivalent to the rate law 〈Q〉∝e?k√t .
  4. Pseudo spin glasses possess a logarithmic rate law 〈Q〉∝lnt.
  5. Power laws with P(x)=x a lead to a rate law: ln〈Q〉=-(α + 1) ln t.
The power spectra of Q are shown for Gaussian distributions and pseudo spin glasses. The mechanism of kinetic gradient coupling between two order parameters is evaluated.  相似文献   

2.
Widely extended, cation stacking faults in experimentally deformed Mg2GeO4 spinel have been studied using transmission electron microscopy (TEM). The faults lie on {110} planes. The displacement vector is of the form \(\frac{1}{4}\left\langle {1\bar 10} \right\rangle \) and is normal to the fault plane. The partial dislocations which bound the stacking fault have colinear Burgers vectors of the form \(\frac{1}{4}\left\langle {1\bar 10} \right\rangle \) which are normal to the fault plane.  相似文献   

3.
The partitioning of Fe and Mg between garnet and aluminous orthopyroxene has been experimentally investigated in the pressure-temperature range 5–30 kbar and 800–1,200° C in the FeO-MgO-Al2O3-SiO2 (FMAS) and CaO-FeO-MgO-Al2O3-SiO2 (CFMAS) systems. Within the errors of the experimental data, orthopyroxene can be regarded as macroscopically ideal. The effects of Calcium on Fe-Mg partitioning between garnet and orthopyroxene can be attributed to non-ideal Ca-Mg interactions in the garnet, described by the interaction term:W CaMg ga -W CaFe ga =1,400±500 cal/mol site. Reduction of the experimental data, combined with molar volume data for the end-member phases, permits the calibration of a geothermometer which is applicable to garnet peridotites and granulites: $$T(^\circ C) = \left\{ {\frac{{3,740 + 1,400X_{gr}^{ga} + 22.86P(kb)}}{{R\ln K_D + 1.96}}} \right\} - 273$$ with $$K_D = {{\left\{ {\frac{{Fe}}{{Mg}}} \right\}^{ga} } \mathord{\left/ {\vphantom {{\left\{ {\frac{{Fe}}{{Mg}}} \right\}^{ga} } {\left\{ {\frac{{Fe}}{{Mg}}} \right\}}}} \right. \kern-\nulldelimiterspace} {\left\{ {\frac{{Fe}}{{Mg}}} \right\}}}$$ and $$X_{gr}^{ga} = (Ca/Ca + Mg + Fe)^{ga} .$$ The accuracy and precision of this geothermometer are limited by largerelative errors in the experimental and natural-rock data and by the modest absolute variation inK D with temperature. Nevertheless, the geothermometer is shown to yield reasonable temperature estimates for a variety of natural samples.  相似文献   

4.
The linear thermal expansions of åkermanite (Ca2MgSi2O7) and hardystonite (Ca2ZnSi2O7) have been measured across the normal-incommensurate phase transition for both materials. Least-squares fitting of the high temperature (normal phase) data yields expressions linear in T for the coefficients of instantaneous linear thermal expansion, $$\alpha _1 = \frac{1}{l}\frac{{dl}}{{dT}}$$ for åkermanite: $$\begin{gathered} \alpha _{[100]} = 6.901(2) \times 10^{ - 6} + 1.834(2) \times 10^{ - 8} T \hfill \\ \alpha _{[100]} = - 2.856(1) \times 10^{ - 6} + 11.280(1) \times 10^{ - 8} T \hfill \\ \end{gathered} $$ for hardystonite: $$\begin{gathered} \alpha _{[100]} = 15.562(5) \times 10^{ - 6} - 1.478(3) \times 10^{ - 8} T \hfill \\ \alpha _{[100]} = - 11.115(5) \times 10^{ - 6} + 11.326(3) \times 10^{ - 8} T \hfill \\ \end{gathered} $$ Although there is considerable strain for temperatures within 10° C of the phase transition, suggestive of a high-order phase transition, there appears to be a finite ΔV of transition, and the phase transition is classed as “weakly first order”.  相似文献   

5.
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.  相似文献   

6.
Oxygen diffusion in albite has been determined by the integrating (bulk 18O) method between 750° and 450° C, for a P H2O of 2 kb. The original material has a low dislocation density (<106 cm?2), and its lattice diffusion coefficient (D 1), given below, agrees well with previous determinations. A sample was deformed at high temperature and pressure to produce a uniform dislocation density of 5 × 109 cm?2. The diffusion coefficient (D a) for this deformed material, given below, is about 0.5 and 0.7 orders of magnitude larger than D 1 at 700° and 450° C, respectively. This enhancement is believed due to faster diffusion along the cores of dislocations. Assuming a dislocation core radius of 4 Å, the calculated pipe diffusion coefficient (D p), given below, is about 5 orders of magnitude larger than D 1. These results suggest that volume diffusion at metamorphic conditions may be only slightly enhanced by the presence of dislocations. $$\begin{gathered} D_1 = 9.8 \pm 6.9 \times 10^{ - 6} (cm^2 /\sec ) \hfill \\ {\text{ }} \cdot \exp [ - 33.4 \pm 0.6(kcal/mole)/RT] \hfill \\ \end{gathered} $$ $$\begin{gathered} D_a = 7.6 \pm 4.0 \times 10^{ - 6} (cm^2 /\sec ) \hfill \\ {\text{ }} \cdot \exp [ - 30.9 \pm 1.1(kcal/mole)/RT] \hfill \\ \end{gathered} $$ $$\begin{gathered} D_p \approx 1.2 \times 10^{ - 1} (cm^2 /\sec ) \hfill \\ {\text{ }} \cdot \exp [ - 29.8(kcal/mole)/RT]. \hfill \\ \end{gathered} $$   相似文献   

7.
The standard enthalpies of formation of FeS (troilite), FeS2 (pyrite), Co0.9342S, Co3S4 (linnaeite), Co9S8 (cobalt pentlandite), CoS2 (cattierite), CuS (covellite), and Cu2S (chalcocite) have been determined by high temperature direct reaction calorimetry at temperatures between 700 K and 1021 K. The following results are reported: $$\Delta {\rm H}_{f,FeS}^{tr} = - 102.59 \pm 0.20kJ mol^{ - 1} ,$$ $$\Delta {\rm H}_{f,FeS}^{py} = - 171.64 \pm 0.93kJ mol^{ - 1} ,$$ $$\Delta {\rm H}_{f,Co_{0.934} S} = - 99.42 \pm 1.52kJ mol^{ - 1} ,$$ $$\Delta {\rm H}_{f,Co_9 S_8 }^{ptl} = - 885.66 \pm 16.83kJ mol^{ - 1} ,$$ $$\Delta {\rm H}_{f,Co_3 S_4 }^{In} = - 347.47 \pm 7.27kJ mol^{ - 1} ,$$ $$\Delta {\rm H}_{f,CoS_2 }^{ct} = - 150.94 \pm 4.85kJ mol^{ - 1} ,$$ $$\Delta {\rm H}_{f,Cu_2 S}^{cc} = - 80.21 \pm 1.51kJ mol^{ - 1} ,$$ and $$\Delta {\rm H}_{f,CuS}^{cv} = - 53.14 \pm 2.28kJ mol^{ - 1} ,$$ The enthalpy of formation of CuFeS2 (chalcopyrite) from (CuS+FeS) and from (Cu+FeS2) was determined by solution calorimetry in a liquid Ni0.60S0.40 melt at 1100 K. The results of these measurements were combined with the standard enthalpies of formation of CuS, FeS, and FeS2, to calculate the standard enthalpy of formation of CuFeS2. We found \(\Delta {\rm H}_{f,CuFeS_2 }^{ccp} = - 194.93 \pm 4.84kJ mol^{ - 1}\) . Our results are compared with earlier data given in the literature; generally the agreement is good and our values agree with previous estimates within the uncertainties present in both.  相似文献   

8.
In the system Na2O-CaO-Al2O3-SiO2 (NCAS), the equilibrium compositions of pyroxene coexisting with grossular and corundum were experimentally determined at 40 different P-T conditions (1,100–1,400° C and 20.5–38 kbar). Mixing properties of the Ca-Tschermak — Jadeite pyroxene inferred from the data are (J, K): $$\begin{gathered} G_{Px}^{xs} = X_{{\text{CaTs}}} X_{{\text{Jd}}} [14,810 - 7.15T - 5,070(X_{{\text{CaTs}}} - X_{{\text{Jd}}} ) \hfill \\ {\text{ }} - 3,350(X_{{\text{CaTs}}} - X_{{\text{Jd}}} )^2 ] \hfill \\ \end{gathered} $$ The excess entropy is consistent with a complete disorder of cations in the M2 and the T site. Compositions of coexisting pyroxene and plagioclase were obtained in 11 experiments at 1,190–1,300° C/25 kbar. The data were used to infer an entropy difference between low and high anorthite at 1,200° C, corresponding to the enthalpy difference of 9.6 kJ/mol associated with the C \(\bar 1\) =I \(\bar 1\) transition in anorthite as given by Carpenter and McConnell (1984). The resulting entropy difference of 5.0 J/ mol · K places the transition at 1,647° C. Plagioclase is modeled as ideal solutions, C \(\bar 1\) and I \(\bar 1\) , with a non-first order transition between them approximated by an empirical expression (J, bar, K): $$\Delta G_T = \Delta G_{1,473} \left[ {1 - 3X_{Ab} \tfrac{{T^4 - 1,473^4 }}{{\left( {1,920 - 0.004P} \right)^4 - 1,473^4 }}} \right],$$ where $$\Delta G_{1,473} = 9,600 - 5.0T - 0.02P$$ The derived mixing properties of the pyroxene and plagioclase solutions, combined with the thermodynamic properties of other phases, were used to calculate phase relations in the NCAS system. Equilibria involving pyroxene+plagioclase +grossular+corundum and pyroxene+plagioclase +grossular+kyani te are suitable for thermobarometry. Albite is the most stable plagioclase.  相似文献   

9.
Data systematization using the constraints from the equation $$Cp = Cv + \alpha _P {}^2V_T K_T T$$ where C p, C v, α p, K T and V are respectively heat capacity at constant pressure, heat capacity at constant volume, isobaric thermal expansion, isothermal bulk modulus and molar volume, has been performed for tungsten and MgO. The data are $$K_T (W) = 1E - 5/(3.1575E - 12 + 1.6E - 16T + 3.1E - 20T^2 )$$ $$\alpha _P (W) = 9.386E - 6 + 5.51E - 9T$$ $$C_P (W) = 24.1 + 3.872E - 3T - 12.42E - 7T^2 + 63.96E - 11T^3 - 89000T^{ - 2} $$ $$K_T (MgO) = 1/(0.59506E - 6 + 0.82334E - 10T + 0.32639E - 13T^2 + 0.10179E - 17T^3 $$ $$\alpha _P (MgO) = 0.3754E - 4 + 0.7907E - 8T - 0.7836/T^2 + 0.9148/T^3 $$ $$C_P (MgO) = 43.65 + 0.54303E - 2T - 0.16692E7T^{ - 2} + 0.32903E4T^{ - 1} - 5.34791E - 8T^2 $$ For the calculation of pressure-volume-temperature relation, a high temperature form of the Birch-Murnaghan equation is proposed $$P = 3K_T (1 + 2f)^{5/2} (1 + 2\xi f)$$ Where $$K_T = 1/(b_0 + b_1 T + b_2 T^2 + b_3 T^3 )$$ $$f = (1/2)\{ [V(1,T)/V(P,T)]^{2/3} - 1\} $$ $$\xi = ({3 \mathord{\left/ {\vphantom {3 4}} \right. \kern-\nulldelimiterspace} 4})[K'_0 + K'_1 \ln ({T \mathord{\left/ {\vphantom {T {300}}} \right. \kern-\nulldelimiterspace} {300}}) - 4]$$ where in turn $$V(1,T) = V_0 [\exp (\int\limits_{300}^T {\alpha dT)]} $$ . The temperature dependence of the pressure derivative of the bulk modulus (K′1) is estimated by using the shock-wave data. For tungsten the data are K′0 = 3.5434, K′1 = 0.032; for MgO K′0 = 4.17 and K′1 = 0.1667. For calculating the Gibbs free energy of a solid at high pressure and at temperatures beyond that of melting at 1 atmosphere, it is necessary to define a high-temperature reference state for the fictive solid.  相似文献   

10.
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.  相似文献   

11.
Reversed phase equilibrium experiments in the system (Ca, Mg, Fe)2SiO4 provide four tielines at P?1 bar and 1 kbar and 800° C–1,100° C. These tielines have been used to model the solution properties of the olivine quadrilateral following the methods described by Davidson et al. (1981) for quadrilateral clinopyroxenes. The discrepancy between the calculated phase relations and the experimentally determined tielines is within the uncertainty of the experiments. The solution properties of quadrilateral olivines can be described by a non-convergent site-disorder model that allows for complete partitioning of Ca on the M2 site, highly disordered Fe-Mg cation distributions and limited miscibility between high-Ca and low-Ca olivines. The ternary data presented in this paper together with binary solution models for the joins Fo-Mo and Fa-Kst have been used to evaluate two solution parameters: $$\begin{gathered} F^0 \equiv 2(\mu _{{\rm M}o}^0 - \mu _{{\rm K}st}^0 ) + \mu _{Fa}^0 - \mu _{Fo}^0 = 12.660 (1.6) kJ, \hfill \\ \Delta G_*^0 \equiv \mu _{{\rm M}gFe}^0 + \mu _{FeMg}^0 - \mu _{Fo}^0 - \mu _{Fa}^0 = 7.030 (3.9) kJ. \hfill \\ \end{gathered} $$ . Ternary phase quilibrium data for olivines tightly constrain the value of F0, but not that for ΔG * 0 which describes nonideality in Fe-Mg mixing. From this analysis, we infer a function for the apparent standard state energy of Kst: $$\begin{gathered} \mu _{{\rm K}st}^0 = - 102.79 \pm 0.8 - (T - 298)(0.137026) \hfill \\ + (T - 298 - T1n(T/298))(0.155519) \hfill \\ + (T - 298)^2 (2.8242E - 05)/2 \hfill \\ + (T - 298)^2 (2.9665E + 03)/(2T(298)^2 ) kJ \hfill \\ \end{gathered} $$ where T is in Kelvins and the 298 K value is relative to oxides.  相似文献   

12.
Oxygen isotope fractionation between rutile and water   总被引：1，自引：0，他引：1  
Synthetic rutile-water fractionations (1000 ln α) at 775, 675, and 575° C were found to be ?2.8, ?3.5, and ?4.8, respectively. Partial exchange experiments with natural rutile at 575° C and with synthetic rutile at 475° C failed to yield reliable fractionations. Isotopic fractionation within the range 575–775° C may be expressed as follows: 1 $$1000\ln \alpha ({\rm T}i{\rm O}_{2 } - H_2 O) = - 4.1 \frac{{10^6 }}{{T_{k^2 } }} + 0.96$$ . Combined with previously determined quartz-water fractionations, the above data permit calibration of the quartz-rutile geothermometer: 1 $$1000\ln \alpha ({\text{S}}i{\rm O}_{2 } - Ti{\rm O}_{2 } ) = 6.6 \frac{{10^6 }}{{T_{k^2 } }} - 2.9$$ . When applied to B-type eclogites from Europe, as an example, the latter equation yields a mean equilibration temperature of 565° C.  相似文献   

13.
Experimental exchanges between plagioclases (synthesized from gels) and aqueous solutions (0.5N–8N) were carried out according to the reaction $$\begin{gathered} 2NaA1Si_3 O_8 + CaC1_2 \hfill \\ \leftrightarrow CaA1_2 Si_2 O_8 + 4SiO_2 + 2NaC1. \hfill \\ \end{gathered}$$ Distribution coefficients defined by $$K_D = \frac{{X_{An} }}{{(X_{Ab} )^2 }}\frac{{(X_{NaC1} )^2 }}{{X_{CaC1_2 } }}$$ were determined at 700° C and 1 kbar. From previous studies it is known that variations in the concentration of the aqueous solutions have no influence upon K D if the fluid is a single phase. In this study, variation of K D with the concentration of the solutions is interpreted as the result of fluid unmixing to vapour and brine phases. This implies boiling of CaCl2-NaCl-H2O fluids analogous to that known for the system NaCl-H2O. Experimental data permit calculation of the compositions of vapours and estimation of those of the brines for fluids in which Ca/Na<0.5. Boiling has an effect upon the exchange between feldspars and solutions (metasomatism) and must be considered when determining the activity coefficients.  相似文献   

14.
A multisite solid solution of the type (A, B) (X, Y) has the four possible components AX, AY, BX, BY. Taking the standard state to be the pure phase at the pressure and temperature of interest, the mixing of these components is shown not to be ideal unless the condition: $$\Delta G^0 = (\mu _{AX}^0 + \mu _{BY}^0 - \mu _{AY}^0 - \mu _{BX}^0 = 0$$ applies. Even for the case in which mixing on each of the individual sublattices is ideal, ΔG 0 contributes terms of the following form to the activity coefficients of the constituent components: $$RT\ln \gamma _{AX} = - X_{B_1 } X_{Y_2 } \Delta G^0$$ (X Ji refers to the atomic fraction of J on sublattice i). The above equation, which assumes complete disorder on (A, B) sites and on (X, Y) sites is extended to the general n-component case. Methods of combining the “cross-site” or reciprocal terms with non-ideal terms for each of the individual sites are also described. The reciprocal terms appear to be significant in many geologically important solid solutions, and clinopyroxene, garnet and spinel solid solutions are all used as examples. Finally, it is shown that the assumption of complete disorder only applies under the condition: $$\Delta G^0 \ll zn_1 RT$$ where z is the number of nearest-neighbour (X, Y) sites around A and n 1 is the number of (A, B) sites in the formula unit. If ΔG 0 is relatively large, then substantial short range oder must occur and the activity coefficient is given by (ignoring individual site terms): $$\gamma _{AX} = \left( {\frac{{1 - X'_{Y_2 } }}{{1 - X_{Y_2 } }}} \right)^{zn_1 }$$ where X′Y2 is the equilibrium atomic fraction of Y atoms surrounding A atoms in the structure. The ordered model may be developed for multicomponent solutions and individual site interactions added, but numerical methods are needed to solve the simultaneous equations involved.  相似文献   

15.
The data of Reed (1983) are analysed to produce the following empirical equations for the amplitude p 0 (overall fluctuation) in Pascals of the air pressure wave associated with a volcanic eruption of volume V km3 or a nuclear explosion of strength M Mt: Here s is the distance from the source in km. $$\begin{gathered} \log _{10} p_0 = 4.44 + \log _{10} V - 0.84\log _{10} s \hfill \\ {\text{ }} = 3.44 + \log _{10} M - 0.84\log _{10} s. \hfill \\ \end{gathered} $$ Garrett's (1970) theory is examined on the generation of water level fluctuations by an air pressure wave crossing a water depth discontinuity such as a continental shelf. The total amplitude of the ocean wave is determined to be where c 2 1 = gh 1, c 2 2 = gh 2, g is acceleration of gravity, h 1 and h 2 are the water depths on the ocean and shore side of the depth discontinuity, c is the speed of propagation of the air pressure wave, and ? is the water density. $$B = \left[ {\frac{{c_2^2 }}{{c^2 - c_2^2 }} + \frac{{c^2 (c_1 - c_2 )}}{{(c - c_1 )(c^2 - c_2^2 )}}} \right]\frac{{p_0 }}{{g\varrho }}$$ It is calculated that a 10 km3 eruption at Mount St. Augustine would cause a 460 Pa air pressure wave and a discernible water level fluctuation at Vancouver Island of several cm amplitude.  相似文献   

16.
The complexation between gold and silica was experimentally, confirmed and calibrated at 200 °C: $$\begin{gathered} Au^ + + H_3 SiO_4^ - \rightleftharpoons AuH_3 SiO_4^0 \hfill \\ \log K_{(200^\circ C)} = 19.26 \pm 0.4 \hfill \\ \end{gathered} $$ Thermodynamic calculations show that AuH3SiO 4 0 would be far more abundant than AuCl 2 ? under physicochemical conditions of geological interest, suggesting that silica is much more important than chloride as ligands for gold transport. In systems containing both sulfur and silica, AuH3SiO 4 0 would be increasingly more important than Au (HS) 2 ? as the proportion of SiO2 in the system increases. The dissolution of gold in aqueous SiO2 solutions can be described by the reaction: $$\begin{gathered} Au + 1/4O_2 + H_4 SiO_4^0 \rightleftharpoons AuH_3 SiO_4^0 + 1/2H_2 O \hfill \\ log K_{(200^\circ C)} = 6.23 \hfill \\ \end{gathered} $$ which indicates that SiO2 precipitation is an effective mechanism governing gold deposition, and thus explains the close association of silicification and gold mineralization.  相似文献   

17.
The available experimental data on garnet-bearing-assemblages for synthetic chemical systems (MAS, FMAS, CMAS) have been used to calibrate consistent models for the Al-solubility in orthopyroxene coexisting with garnet, on the basis of equilibrium reaction Py(opx) ? Py(gt). The alternative reaction En(opx)+MgTs(opx) ? Py(gt) is discarded as it yields larger a-posteriori uncertainties. To provide a reliable equation, directly applicable to natural garnet lherzolites, each successive synthetic-system calibration is tested against Mori and Green's (1978) natural-system reequilibration data. For the MAS system, an ideal solution model with constant ΔH°, ΔV° and ΔS° based on 12-oxygen structural formulae for aluminous pyroxenes yields the best fit (GPa, K), $${\text{25,134 + 9,941 }}P - 23.177{\text{ }}T{\text{ + }}RT{\text{ ln (}}X_{{\text{Al}}}^{TB'} {\text{) = 0}}$$ . The MAS synthetic-system calibration can be directly applied to the FMAS system by adding an empirical correction term (20,835 [X Fe gt ]2) independent of either pressure and temperature. However, this correction term is not important because of the limited Fe content of mantle peridotites. When calcium is added to the MAS system, the equilibrium constant is calculated as: $$K_{{\text{CMAS}}} = {{[(1 - X_{{\text{Ca}}}^{M2} )^2 (X_{{\text{Al}}}^{TB'} )]} \mathord{\left/ {\vphantom {{[(1 - X_{{\text{Ca}}}^{M2} )^2 (X_{{\text{Al}}}^{TB'} )]} {[(1 - X_{{\text{Ca}}}^X )^3 (X_{{\text{Al}}}^Y )^2 ]}}} \right. \kern-\nulldelimiterspace} {[(1 - X_{{\text{Ca}}}^X )^3 (X_{{\text{Al}}}^Y )^2 ]}}$$ where M2 and TB′ are pyroxene sites and X and Y are garnet sites. Up to 5 GPa, X Ca X ～ and the CMAS experimental data agree well with the MAS model, but for Yamada and Takahashi's (1983) higher pressure experiments (up to 10 GPa), this no longer holds. Indeed, the garnet solid solution does not behave ideally and an asymmetric regular solution model is needed for application to the deepest natural samples available (>7GPa). Calibration based on new high pressure data yields, $$\begin{gathered} \Delta G_{{\text{CMAS}}}^{XS} = (X_{{\text{Ca}}}^X )(1 - X_{{\text{Ca}}}^X )(0.147 - X_{{\text{Ca}}}^X ) \hfill \\ {\text{ }} \cdot {\text{(6,440,535 - 1,490,654 }}P{\text{)}} \hfill \\ \end{gathered}$$ . According to tests of the inferred solution model, the CFMAS system is a good analogue of natural systems in the pressure, temperature and composition ranges covered by the natural-system reequilibration data (up to 1,500° C and 4 GPa). Simultaneous application of this thermobarometer and of the two-pyroxene mutual solubility thermometer (Bertrand and Mercier 1985) to the phases of the garnet-peridotite xenoliths from Thaba Putsoa, Lesotho, yields a refined paleogeotherm for southern Africa strongly contrasting with previous results. The “granular” nodules yield a thermal gradient of about 8 K/km characteristic of a lithospheric-type environment, whereas the “sheared” ones show a lower gradient of about 1 K/km. This is a typical geotherm expected for a steady thermal state with an inflexion point at the depth of about 160 km corresponding to the lithosphere/asthenosphere boundary.  相似文献   

18.
An empirically derived Redlich-Kwong type of equation of state (ERK) is proposed for H2O, expressing a, the term related to the attraction between the molecules, as a pressure-independent function of temperature, and b, the covolume, as a temperature-independent function of pressure. The coefficients of a(T) and b(P) were derived by least squares non-linear regression, using P-V-T data given by Burnham et al. (1969b) and Rice and Walsh (1957) in conjunction with more precise recent data obtained by Tanishita et al. (1976), Hilbert (1979) and Schmidt (1979): $$a(T) = 1.616 x 10^8 - 4.989 x 10^4 T - 7.358 x 10^9 T^{ - 1} $$ and $$ = \frac{{1 + 3.4505x 10^{--- 4} P + 3.8980x 10^{--- 9} P^2 - 2.7756x 10^{--- 15} P^3 }}{{6.3944x 10^{--- 2} + 2.3776x 10^{--- 5} + 4.5717x 10^{--- 10} P^2 }}$$ , where T is expressed in Kelvin and P in bars. The ERK works very well at upper mantle conditions, at least up to 200 kbar and 1,000 °C. At subcritical conditions and those somewhat above the critical point, it still reproduces the molar Gibbs energy, \(\tilde G_{{\text{H}}_{\text{2}} {\text{O}}} \) , with a maximum deviation of 400 joules. Thus, for the purpose of calculation of geologically interesting heterogeneous equilibria, it predicts the thermodynamic properties of H2O well enough. The values of molar volume, \(\tilde V_{{\text{H}}_{\text{2}} {\text{O}}} \) , and \(\tilde G_{{\text{H}}_{\text{2}} {\text{O}}} \) are tabulated in the appendix over a considerable P-T range. A FORTRAN program generating these functions as well as a FORTRAN subroutine for calculating the fugacity values, \(f_{{\text{H}}_{\text{2}} {\text{O}}} \) for incorporation into existing programs, are available upon request.  相似文献   

19.
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.  相似文献   

20.
The enthalpy of formation of andradite (Ca3Fe2Si3O12) has been estimated as-5,769.700 (±5) kJ/mol from a consideration of the calorimetric data on entropy (316.4 J/mol K) and of the experimental phaseequilibrium data on the reactions: 1 $$\begin{gathered} 9/2 CaFeSi_2 O_6 + O_2 = 3/2 Ca_3 Fe_2 Si_3 O_{12} + 1/2 Fe_3 O_4 + 9/2 SiO_2 (a) \hfill \\ Hedenbergite andradite magnetite quartz \hfill \\ \end{gathered} $$ 1 $$\begin{gathered} 4 CaFeSi_2 O_6 + 2 CaSiO_3 + O_2 = 2 Ca_3 Fe_2 Si_3 O_{12} + 4 SiO_2 (b) \hfill \\ Hedenbergite wollastonite andradite quartz \hfill \\ \end{gathered} $$ 1 $$\begin{gathered} 18 CaSiO_3 + 4 Fe_3 O_4 + O_2 = 6Ca_3 Fe_2 Si_3 O_{12} (c) \hfill \\ Wollastonite magnetite andradite \hfill \\ \end{gathered} $$ 1 $$\begin{gathered} Ca_3 Fe_2 Si_3 O_{12} = 3 CaSiO_3 + Fe_2 O_3 . (d) \hfill \\ Andradite pseudowollastonite hematite \hfill \\ \end{gathered} $$ and $$log f_{O_2 } = E + A + B/T + D(P - 1)/T + C log f_{O_2 } .$$ Oxygen-barometric scales are presented as follows: $$\begin{gathered} E = 12.51; D = 0.078; \hfill \\ A = 3 log X_{Ad} - 4.5 log X_{Hd} ; C = 0; \hfill \\ B = - 27,576 - 1,007(1 - X_{Ad} )^2 - 1,476(1 - X_{Hd} )^2 . \hfill \\ \end{gathered} $$ For the assemblage andradite (Ad)-hedenbergite (Hd)-magnetite-quartz: $$\begin{gathered} E = 13.98; D = 0.0081; \hfill \\ A = 4 log(X_{Ad} / X_{Hd} ); C = 0; \hfill \\ B = - 29,161 - 1,342.8(1 - X_{Ad} )^2 - 1,312(1 - X_{Hd} )^2 . \hfill \\ \end{gathered} $$ For the assemblage andradite-hedenbergite-wollastonite-quartz: 1 $$\begin{gathered} E = 13.98;{\text{ }}D = 0.0081; \hfill \\ A = 4\log (X_{Ad} /X_{Hd} );{\text{ C = 0;}} \hfill \\ B = - 29,161 - 1,342.8(1 - X_{Ad} )^2 - 1,312(1 - X_{Hd} )^2 . \hfill \\ \end{gathered} $$ For the assemblage andradite-hedenbergite-calcitequartz: 1 $$\begin{gathered} E = - 1.69;{\text{ }}D = - 0.199; \hfill \\ A = 4\log (X_{Ad} /X_{Hd} );{\text{ C = 2;}} \hfill \\ B = - 20,441 - 1,342.8(1 - X_{Ad} )^2 - 1,312(1 - X_{Hd} )^2 . \hfill \\ \end{gathered} $$ For the assemblage andradite-hedenbergite-wollastonite-calcite: 1 $$\begin{gathered} E = - 17.36;{\text{ }}D = - 0.403; \hfill \\ A = 4\log (X_{Ad} /X_{Hd} );{\text{ C = 4;}} \hfill \\ B = - 11,720 - 1,342.8(1 - X_{Ad} )^2 - 1,312(1 - X_{Hd} )^2 \hfill \\ \end{gathered} $$ The oxygen fugacity of formation of those skarns where andradite and hedenbergite assemblage is typical can be calculated by using the above equations. The oxygen fugacity of formation of this kind of skarn ranges between carbon dioxide/graphite and hematite/magnetite buffers. It increases from the inside zones to the outside zones, and appears to decrease with the ore-types in the order Cu, Pb?Zn, Fe, Mo, W(Sn) ore deposits.  相似文献   

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