共查询到20条相似文献，搜索用时 46 毫秒
1.
Two types of supernovae are considered: thermonuclear supernovae, whose explosions are due to thermonuclear energy, and core-collapse supernovae, whose explosions are due to the gravitational energy of collapsing stars released in the form of neutrinos. Numerical models of supernovae are discussed. Themain problem in devising supernova explosion mechanisms is producing the energy required to disperse the envelope. In theoretical models, it is necessary to solve multi-dimensional problems involving complex physics (3D gas dynamics, neutrino transport, large-scale convective instability, and other important physical processes). In recent years, the development of large-scale convection during supernova explosions has been reconsidered. Self-consistent problems problems in three-dimensional, gas-dynamical instability have been considered. Two-dimensional gas-dynamical calculations taking into account neutrino absorption in the envelope have been performed. The spherically symmetric collapse and neutrino transport were calculated including all reactions, leading to a new understanding of possible paths for the development of supernova theory. The main emphasis is placed on the neutrino transport and the basis for promising multidimensional models taking into account large-scale convective instability. 相似文献
2.
We present the results of simulations of Type Ia and II supernovae explosions taking into account the rotation of the initial configuration. The main idea is development of a large-scale convective instability which affects strongly the geometry of the explosion. For Type Ia supernova a jet-like structure of the ejecta was obtained. An important point here is the possibility of continuing consecutive flares, produced when the fresh thermonuclear fuel is ignited in the central part of the star. This fuel is moved to the center by convective fluxes from the outer stellar layers. For Type II supernova a large-scale convection results in a non-equilibrium neutronization of the matter. Large bubbles, moving to the surface, contain high-energy neutrinos from the central region of the proto-neutron stellar core. The following ejection of these neutrinos to the stellar envelope gives enough energy support to the bounce shock, which finally destroys the envelope producing a non-spherical explosion. 相似文献
3.
Most of the energy released in the gravitational collapse of the cores of massive stars is carried away by neutrinos. Neutrinos play a pivotal role in explaining core-collapse supernovae. In this work the multidimensional gas dynamics is used with neutrino transport in the flux-limited diffusion approximation to study the role of multi-dimensional effects. The possibility of large-scale convection is discussed, which is interesting both for explaining SNII and for setting up observations to register possible high-energy (?10 MeV) neutrinos from the supernova. In compare with the previous work describing a new multidimensional gas dynamics method with neutrino transport we investigate the role of the rotation in the convection. 相似文献
4.
Neutrino transfer via convective flow to the surface of a proto-neutron star is numerically simulated. The evolution of the neutrino distribution in a heated region rising from the center of the proto-neutron star to its surface is simulated using a kinetic equation with a Uehling-Uhlenbeck collision integral in a uniform, isotropic approximation. The composition of the matter in the region under consideration changes due to the “burning” of electrons and protons by beta processes. The simulation results enable the estimation of the characteristic time required for the rising medium to become optically thin to neutrinos and the characteristic spectrum of the neutrinos that are emitted. 相似文献
5.
I. V. Baikov V. M. Suslin V. M. Chechetkin V. Bychkov L. Stenflo 《Astronomy Reports》2007,51(4):274-281
We propose a new mechanism for type II supernova explosions. An important element of the model is large-scale convection that arises due to non-equilibrium neutronization of the matter in the central region of the proto-neutron star. Our analytical estimates and numerical simulations of the convection rate are in good mutual agreement. Large-scale convection leads to the rapid transport of neutrinos from the center of the star to the bounce shock formed during the pause in the collapse of the stellar matter in the proto-neutron star. The mean neutrino energy is 30–50 MeV. We analyze the dependence of the mean neutrino energy on the size of the convection cells—“bubbles.” Our computations of the interaction between the neutrinos and the shock show that the velocity of the shock along the rotational axis of the star exceeds the escape velocity. Thus, explosion of the envelope and a supernova with a very asymmetrical envelope structure become possible, leading to the formation of a neutron star. 相似文献
6.
M. Cai 《Rock Mechanics and Rock Engineering》2010,43(2):167-184
By applying the Griffith stress criterion of brittle failure, one can find that the uniaxial compressive strength (σc) of rocks is eight times the value of the uniaxial tensile strength (σt). The Griffith strength ratio is smaller than what is normally measured for rocks, even with the consideration of crack closure.
The reason is that Griffith’s theories address only the initiation of failure. Under tensile conditions, the crack propagation
is unstable so that the tensile crack propagation stress (σcd)t and the peak tensile strength σt are almost identical to the tensile crack initiation stress (σci)t. On the other hand, the crack growth after crack initiation is stable under a predominantly compressive condition. Additional
loading is required in compression to bring the stress from the crack initiation stress σci to the peak strength σc. It is proposed to estimate the tensile strength of strong brittle rocks from the strength ratio of
R = \fracs\textc | s\textt | = 8\fracs\textc s\textci . R = {\frac{{\sigma_{\text{c}} }}{{\left| {\sigma_{\text{t}} } \right|}}} = 8{\frac{{\sigma_{\text{c}} }}{{\sigma_{\text{ci}} }}}. The term
\fracs\textc s\textci {\frac{{\sigma_{\text{c}} }}{{\sigma_{\text{ci}} }}} accounts for the difference of crack growth or propagation in tension and compression in uniaxial compression tests.
\fracsc sci {\frac{{\sigma_{c} }}{{\sigma_{ci} }}} depends on rock heterogeneity and is larger for coarse grained rocks than for fine grained rocks. σci can be obtained from volumetric strain measurement or acoustic emission (AE) monitoring. With the strength ratio R determined, the tensile strength can be indirectly obtained from
| s\textt | = \fracs\textc R = \fracs\textci 8. \left| {\sigma_{\text{t}} } \right| = {\frac{{\sigma_{\text{c}} }}{R}} = {\frac{{\sigma_{\text{ci}} }}{8}}. It is found that the predicted tensile strengths using this method are in good agreement with test data. Finally, a practical
estimate of the Hoek–Brown strength parameter m
i is presented and a bi-segmental or multi-segmental representation of the Hoek–Brown strength envelope is suggested for some
brittle rocks. In this fashion, the rock strength parameters like σt and m
i, which require specialty tests such as direct tensile (or Brazilian) and triaxial compression tests for their determination,
can be reasonably estimated from uniaxial compression tests. 相似文献
7.
8.
Gao Xuzheng 《中国地球化学学报》1986,5(3):215-225
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
9.
Stuart J. Mills Anthony R. Kampf Mati Raudsepp William D. Birch 《Mineralogy and Petrology》2010,100(3-4):249-253
Sr- and Ca-rich waylandite, $ {\left( {{\hbox{B}}{{\hbox{i}}_{0.{54}}}{\hbox{S}}{{\hbox{r}}_{0.{31}}}{\hbox{C}}{{\hbox{a}}_{0.{25}}}{{\hbox{K}}_{0.0{1}}}{\hbox{B}}{{\hbox{a}}_{0.0{1}}}} \right)_{\Sigma 1.12}}{{\hbox{H}}_{0.{18}}}{\left( {{\hbox{A}}{{\hbox{l}}_{{2}.{96}}}{\hbox{C}}{{\hbox{u}}_{0.0{2}}}} \right)_{\Sigma 2.98}}{\left[ {{{\left( {{{\hbox{P}}_{0.{97}}}{{\hbox{S}}_{0.0{3}}}{\hbox{S}}{{\hbox{i}}_{0.0{1}}}} \right)}_{\Sigma 1.00}}{{\hbox{O}}_4}} \right]_2}{\left( {\hbox{OH}} \right)_6} $ , from Wheal Remfry, Cornwall, United Kingdom has been investigated by single-crystal X-ray diffraction and electron microprobe analyses. Waylandite crystallises in space group R $ \overline 3 $ ? m, with the cell parameters: a?=?7.0059(7) Å, c?=?16.3431(12) Å and V?=?694.69(11) Å3. The crystal structure has been refined to R 1?=?3.76%. Waylandite has an alunite-type structure comprised of a rhombohedral stacking of (001) composite layers of corner-shared AlO6 octahedra and PO4 tetrahedra, with (Bi,Sr,Ca) atoms occupying icosahedrally coordinated sites between the layers. 相似文献
10.
Ronald E. Cohen 《Physics and Chemistry of Minerals》1986,13(3):174-182
A statistical mechanical analysis of the limiting laws for coupled solid solutions shows that the random model, in which the configurational entropy is calculated as if atoms mix randomly on each crystallographic site, is correct as a first approximation. In coupled solid solutions, since atoms of different valence substitute on the same sites, significant short-range order which reduces the entropy can be expected. A first-order correction is rigorously obtained for the entropy in dilute binary short-range ordered coupled solid solutions: $$\bar S^{{\text{XS}}} {\text{/R = }}Q\left( {{\text{e}}^{--H_{\text{A}} /{\text{R}}T} \left( {\frac{{H_{\text{A}} }}{{{\text{R}}T}} + 1} \right) - 1} \right)N_2^a N_4^b ,$$ where Q is the number of positions an associated cation pair can assume per formula unit, H A is the association energy per formula unit, and N 2 a and N 4 b are the site occupancy fractions for atoms 2 and 4 that are dilute on sites a and b. S XS is the configurational entropy minus the random model entropy. Aluminous pyroxenes on the joints diopside-jadeite and diopside-CaTs are examined as examples. A generalization for dilute multiple component solutions, including possible long-range ordering variations is given by: $$\frac{{\bar S^{{\text{XS}}} }}{{\text{R}}}{\text{ = }}\sum\limits_i {\sum\limits_j {\sum\limits_k {Q_i } } \left( {{\text{e}}^{--H_{\text{A}}^{j{\text{ }}k{\text{, }}i} /{\text{R}}T} \left( {\frac{{H_{\text{A}}^{j{\text{ }}k{\text{, }}i} }}{{{\text{R}}T}} + 1} \right) - 1} \right)N_j^l N_k^m ,} $$ where i labels each crystallographically distinct pair, j and k label atomic species, l and m label crystallographic sites, and the N's are site occupancy fractions for the solute atoms. A total association model is examined as well as the partial association and random models. Real solution behavior must lie between the total association model and the random model. Molecular models in which the ideal activity is proportional to a mole fraction, which in itself is not always unambiguously defined, do not lie in this range and furthermore have no physical justification. 相似文献
11.
Most of the energy released in the gravitational collapse of the cores of massive stars is carried away by neutrinos. Neutrinos play a pivotal role in explaining core-collape supernovae. Currently, mathematical models of the gravitational collapse are based on multi-dimensional gas dynamics and thermonuclear reactions, while neutrino transport is considered in a simplified way. Multidimensional gas dynamics is used with neutrino transport in the flux-limited diffusion approximation to study the role of multi-dimensional effects. The possibility of large-scale convection is discussed, which is interesting both for explaining SN II and for setting up observations to register possible high-energy (?10MeV) neutrinos from the supernova. A new multi-dimensional, multi-temperature gas dynamics method with neutrino transport is presented. 相似文献
12.
J. William Carey 《Contributions to Mineralogy and Petrology》1995,119(2-3):155-165
A thermodynamic formulation of hydrous Mg-cordierite (Mg2Al4Si5O18·nH2O) has been obtained by application of calorimetric and X-ray diffraction data for hydrous cordierite to the results of hydrothermal syntheses. The data include measurements of the molar heat capacity and enthalpy of hydration and the molar volume. The synthesis data are consistent with a thermodynamic formulation in which H2O mixes ideally on a single crystallographic site in hydrous cordierite. The standard molar Gibbs free energy of hydration is-9.5±1.0 kJ/mol (an average of 61 syntheses). The standard molar entropy of hydration derived from this value is-108±3 J/mol-K. An equation providing the H2O content of cordierite as a function of temperature and fugacity of H2O is as follows (n moles of H2O per formula unit, n<1): $$\begin{gathered}n = {{f_{{\text{ H}}_{\text{2}} O}^{\text{V}} } \mathord{\left/{\vphantom {{f_{{\text{ H}}_{\text{2}} O}^{\text{V}} } {\left( {f_{{\text{ H}}_{\text{2}} O}^{\text{V}} + {\text{exp}}\left[ { - {\text{3}}{\text{.8389}} - 5025.2\left( {\frac{1}{T} - \frac{1}{{298.15}}} \right)} \right.} \right.}}} \right.\kern-\nulldelimiterspace} {\left( {f_{{\text{ H}}_{\text{2}} O}^{\text{V}} + {\text{exp}}\left[ { - {\text{3}}{\text{.8389}} - 5025.2\left( {\frac{1}{T} - \frac{1}{{298.15}}} \right)} \right.} \right.}} \hfill \\{\text{ }}\left. {\left. { - {\text{ln}}\left( {\frac{T}{{{\text{298}}{\text{.15}}}}} \right) - \left( {\frac{{298.15}}{T} - 1} \right)} \right]} \right) \hfill \\\end{gathered}$$ Application of this formulation to the breakdown reaction of Mg-cordierite to an assemblage of pyrope-sillimanite-quartz±H2O shows that cordierite is stabilized by 3 to 3.5 kbar under H2O-saturated conditions. The thermodynamic properties of H2O in cordierite are similar to those of liquid water, with a standard molar enthalpy and Gibbs free energy of hydration that are the same (within experimental uncertainty) as the enthalpy and Gibbs free energy of vaporization. By contrast, most zeolites have Gibbs free energies of hydration two to four times more negative than the corresponding value for the vaporization of water. 相似文献
13.
The Gibbs free energy and volume changes attendant upon hydration of cordierites in the system magnesian cordierite-water have been extracted from the published high pressure experimental data at \(P_{{\text{H}}_{\text{2}} {\text{O}}} \) =P total, assuming an ideal one site model for H2O in cordierite. Incorporating the dependence of ΔG and ΔV on temperature, which was found to be linear within the experimental conditions of 500°–1,000°C and 1–10,000 bars, the relation between the water content of cordierite and P, T and \(f_{{\text{H}}_{\text{2}} {\text{O}}} \) has been formulated as $$\begin{gathered} X_{{\text{H}}_{\text{2}} {\text{O}}}^{{\text{crd}}} = \hfill \\ \frac{{f_{{\text{H}}_{\text{2}} {\text{O}}}^{{\text{P, T}}} }}{{\left[ {{\text{exp}}\frac{1}{{RT}}\left\{ {64,775 - 32.26T + G_{{\text{H}}_{\text{2}} {\text{O}}}^{{\text{1, }}T} - P\left( {9 \times 10^{ - 4} T - 0.5142} \right)} \right\}} \right] + f_{{\text{H}}_{\text{2}} {\text{O}}}^{{\text{P, T}}} }} \hfill \\ \end{gathered} $$ The equation can be used to compute H2O in cordierites at \(P_{{\text{H}}_{\text{2}} {\text{O}}} \) <1. Our results at different P, T and partial pressure of water, assuming ideal mixing of H2O and CO2 in the vapour phase, are in very good agreement with the experimental data of Johannes and Schreyer (1977, 1981). Applying the formulation to determine \(X_{{\text{H}}_{\text{2}} {\text{O}}}^{{\text{crd}}} \) in the garnet-cordierite-sillimanite-plagioclase-quartz granulites of Finnish Lapland as a test case, good agreement with the gravimetrically determined water contents of cordierite was obtained. Pressure estimates, from a thermodynamic modelling of the Fe-cordierite — almandine — sillimanite — quartz equilibrium at \(P_{{\text{H}}_{\text{2}} {\text{O}}} = 0\) and \(P_{{\text{H}}_{\text{2}} {\text{O}}} \) =Ptotal, for assemblages from South India, Scottish Caledonides, Daly Bay and Hara Lake areas are compatible with those derived from the garnetplagioclase-sillimanite-quartz geobarometer. 相似文献
14.
The formation of a neutrino pulse emitted during the relativistic collapse of a spherical supermassive star is considered. The free collapse of a body with uniform density in the absence of rotation and with the free escape of the emitted neutrinos can be solved analytically by quadrature. The light curve of the collapsing star and the spectrum of the emitted neutrinos at various times are calculated. 相似文献
15.
切向恢复系数是滚石碰撞回弹的重要控制参数,目前的理论公式不能完全反映其作用机制,这是滚石动力学研究的一个难点问题.为此,根据滚石不同的回弹状态,提出基于入射角度变化的切向力模型;进一步,以切向接触理论和动能定理为基础,考虑碰撞过程中切向的摩擦耗能与变形耗能,推导了切向恢复系数的理论公式;最后研究入射速度、入射角、被撞击物体的变形模量对切向恢复系数的影响.结果表明:滚动回弹的切向恢复系数主要受切向变形量的影响;滑动回弹时,入射速度对切向恢复系数的影响参数为\begin{document}$ {v}^{\frac{1}{20}} $\end{document}
16.
The crystallization of plagioclase-bearing assemblages in mantle rocks is witness of mantle exhumation at shallow depth. Previous experimental works on peridotites have found systematic compositional variations in coexisting minerals at decreasing pressure within the plagioclase stability field. In this experimental study we present new constraints on the stability of plagioclase as a function of different Na2O/CaO bulk ratios, and we present a new geobarometer for mantle rocks. Experiments have been performed in a single-stage piston cylinder at 5–10 kbar, 1050–1150?°C at nominally anhydrous conditions using seeded gels of peridotite compositions (Na2O/CaO?=?0.08–0.13; X Cr = Cr/(Cr?+?Al)?=?0.07–0.10) as starting materials. As expected, the increase of the bulk Na2O/CaO ratio extends the plagioclase stability to higher pressure; in the studied high-Na fertile lherzolite (HNa-FLZ), the plagioclase-spinel transition occurs at 1100?°C between 9 and 10 kbar; in a fertile lherzolite (FLZ) with Na2O/CaO?=?0.08, it occurs between 8 and 9 kbar at 1100?°C. This study provides, together with previous experimental results, a consistent database, covering a wide range of P–T conditions (3–9 kbar, 1000–1150?°C) and variable bulk compositions to be used to define and calibrate a geobarometer for plagioclase-bearing mantle rocks. The pressure sensitive equilibrium: has been empirically calibrated by least squares regression analysis of experimental data combined with Monte Carlo simulation. The result of the fit gives the following equation: where P is expressed in kbar and T in kelvin. K is the equilibrium constant K?=?a CaTs × a en/a an × a fo, where a CaTs, a en, a an and a fo are the activities of Ca-Tschermak in clinopyroxene, enstatite in orthopyroxene, anorthite in plagioclase and forsterite in olivine. The proposed geobarometer for plagioclase peridotites, coupled to detailed microstructural and mineral chemistry investigations, represents a valuable tool to track the exhumation of the lithospheric mantle at extensional environments.
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$$\mathop {{\text{M}}{{\text{g}}_{\text{2}}}{\text{Si}}{{\text{O}}_{\text{4}}}^{{\text{Ol}}}}\limits_{{\text{Forsterite}}} +\mathop {{\text{CaA}}{{\text{l}}_{\text{2}}}{\text{S}}{{\text{i}}_{\text{2}}}{{\text{O}}_{\text{8}}}^{{\text{Pl}}}}\limits_{{\text{Anorthite}}~} =\mathop {{\text{CaA}}{{\text{l}}_{\text{2}}}{\text{Si}}{{\text{O}}_{\text{6}}}^{{\text{Cpx}}}}\limits_{{\text{Ca-Tschermak}}} +{\text{ }}\mathop {{\text{M}}{{\text{g}}_{\text{2}}}{\text{S}}{{\text{i}}_{\text{2}}}{{\text{O}}_{\text{6}}}^{{\text{Opx}}}}\limits_{{\text{Enstatite}}} ,$$
$$P=7.2( \pm 2.9)+0.0078( \pm 0.0021)T{\text{ }}+0.0022( \pm 0.0001)T{\text{ }}\ln K,$$
$${R^2}=0.93,$$
17.
We report new experimental data of Cu diffusivity in granite porphyry melts with 0.01 and 3.9 wt% H2O at 0.15–1.0 GPa and 973–1523 K. A diffusion couple method was used for the nominally anhydrous granitic melt, whereas a Cu diffusion-in method using Pt95Cu5 as the source of Cu was applied to the hydrous granitic melt. The diffusion couple experiments also generate Cu diffusion-out profiles due to Cu loss to Pt capsule walls. Cu diffusivities were extracted from error function fits of the Cu concentration profiles measured by LA-ICP-MS. At 1 GPa, we obtain \({D_{{\text{Cu, dry, 1 GPa}}}}=\exp \left[ {( - {\text{13.89}} \pm {\text{0.42}}) - \frac{{{\text{12878}} \pm {\text{540}}}}{T}} \right],\) and \({D_{{\text{Cu, 3}}{\text{.9 wt\% }}{{\text{H}}_{\text{2}}}{\text{O}},{\text{ 1 GPa}}}}=\exp \left[ {( - 16.31 \pm 1.30) - \frac{{{\text{8148}} \pm {\text{1670}}}}{T}} \right],\) where D is Cu diffusivity in m2/s and T is temperature in K. The above expressions are in good agreement with a recent study on Cu diffusion in rhyolitic melt using the approach of Cu2S dissolution. The observed pressure effect over 0.15–1.0 GPa can be described by an activation volume of 5.9 cm3/mol for Cu diffusion. Comparison of Cu diffusivity to alkali diffusivity and its variation with melt composition implies fourfold-coordinated Cu+ in silicate melts. Our experimental results indicate that in the formation of porphyry Cu deposits, the diffusive transport of magmatic Cu to sulfide liquids or fluid bubbles is highly efficient. The obtained Cu diffusivity data can also be used to assess whether equilibrium Cu partitioning can be reached within certain experimental durations. 相似文献
18.
The thermodynamic calculation of dehydration reacton suggests very low activity of H2O during metamorphic peak of the Archaean granulite complex in the region studied.The αH2O values for Al-rich gneiss and hypersthene biotite gneiss-granulite in the Taipingzhai region are usually between 0.10 and 0.20,and those in the Louzishan region are 0.15-0.25.The fugacity of O2 in terms of lgf O2 in whole region ranges form-8to-14.The average coefficients of (δμH2O/δHMg^Bt)and(δμO2/δXMg^Bt)in the Taipingzhai region are-0.293 and-1.60 respectively,and those in the Louzishan region are-0.364and-1.420.The activity of H2O is very low in the whole region,but its values and other data mentioned above are considerably constant from place to place within a given region,even in rocks of dirrerent lithological characters.However,they show a certain gradient between different regions.Such characteristics are compatible with the genetic mechanism known as“carbonic metamorphism” put forward by Newton et al.,i.e.,the α H2O during the peak stage is controlled by permeation of pervasive CO2 influx of the mantle source,and shows features of external buffering. 相似文献
19.
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. 相似文献
20.
The kinetic and equilibrium behaviour of order/disorder systems and related processes are simulated using an Ising spin model in which the coupling between spins occurs via local strain in a harmonic lattice. The equilibrium states are found to be well described by a mean field Landau-type Gibbs free energy. The ordering kinetics laws follow the rate law:
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