Geopotential harmonics of order 15 and even degree,from changes in orbital eccentricity at resonance

When a satellite orbit decaying slowly under the action of air drag experiences 15th-order resonance with the Earth's gravitational field, so that the ground track repeats after 15 rev, the orbital eccentricity may suffer appreciable changes due to perturbations from the gravitational harmonics of order 15 and even degree (16, 18, 20…). In this paper the changes in eccentricity at resonance for six satellites in near-circular orbits at inclinations between 56 and 90° have been analysed to derive 11 pairs of equations linking the harmonic coefficients of order 15 and (even) degree l, $\text{C}{}_{\mathrm{l,15}}\text{and}\text{S}{}_{\mathrm{l,15}}$ in the usual notation. These equations (together with eight constraint equations) are solved to give:

     

782.

Geopotential harmonics of order 15 and odd degree from analysis of resonant orbits     

D.G. King-Hele  Doreen M.C. Walker  R.H. Gooding 《Planetary and Space Science》1975,23(9):1239-1256

We have analysed the variations of inclination in 13 satellite orbits as they pass slowly, under the action of air drag, through 15th-order resonance with the geopotential, when successive equatorial crossings are 24° apart and the ground track repeats after 15 rev. The size and form of the change in inclination are determined mainly by the values of the geopotential harmonics of 15th order and odd degree, $\text{C}\text{?}{}_{\mathrm{l,15}}$ and $\text{S}\text{?}{}_{\mathrm{l,15}}$ (with l = 15, 17, 19, …) in the usual notation. Our analysis gives values of these coefficients up to l = 33 as follows:

$\text{l}$	109$\text{C}{}_{\mathrm{l,15}}$	109$\text{S}{}_{\mathrm{l,15}}$
16	?13.7 ± 1.3	?18.5 ± 2.7
18	?42.3 ± 1.8	?34.7 ± 3.4
20	10.5 ± 3.1	29.8 ± 5.2
22	?8.6 ± 3.8	?20.2 ± 7.4

     

783.

Variations in the atmospheric neutral density at 145km     

J.M. Forbes  H.B. Garrett 《Planetary and Space Science》1975,23(10):1399-1404

A least-squares multiple linear regression is performed on orbital decay density data obtained from precise orbital analysis of 22 low-perigee (130–160 km) Air Force satellites. Variations related to solar activity, the semi-annual effect, geomagnetic activity, and the zenith angle of the Sun are in agreement with the model of Jacchia (1971). Density variations in longitude and latitude are also deduced and compared with recent results from other investigations within this altitude regime.     

784.

Transport and emplacement of crater and basin deposits     

Verne R. Oberbeck  Robert H. Morrison  Friedrich Hörz 《Earth, Moon, and Planets》1975,13(1-3):9-26

Material is ejected from impact craters in ballastic trajectories; it impacts first near the crater rim and then at progressively greater ranges. Ejecta from craters smaller than approximately 1 km is laid predominantly on top of the surrounding surface. With increasing crater size, however, more and more surrounding surface will be penetrated by secondary cratering action and these preexisting materials will be mixed with primary crater ejecta. Ejecta from large craters and especially basin forming events not only excavate preexisting, local materials, but also are capable of moving large amounts of material away from the crater. Thus mixing and lateral transport give rise to continuous deposits that contain materials from within and outside the primary crater. As a consequence ejecta of basins and large highland craters have eroded and mixed highland materials throughout geologic time and deposited them in depressions inside and between older crater structures.Because lunar mare surfaces contain few large craters, the mare regolith is built up by successive layers of predominantly primary ejecta. In contrast, the lunar highlands are dominated by the effects of large scale craters formed early in lunar history. These effects lead to thick fragmental deposits which are a mixture of primary crater material and local components. These deposits may also properly be named regolith though the term has been traditionally applied only to the relatively thin fine grained surficial deposit on mare and highland terranes generated during the past few billion year. We believe that the surficial highland regolith - generated over long periods of time - rests on massive fragmental units that have been produced during the early lunar history.     

785.

Nestling diets of coexisting salt marsh sparrows: Opportunism in a food-rich environment     

William Post  Jon S. Greenlaw 《Estuaries and Coasts》2006,29(5):765-775

The saltmarsh sharp-tailed sparrow (Ammodramus caudacutus) and the morphologically similar seaside sparrow (Ammodramus maritimus) occur together in Atlantic coast salt marshes. Over 2 yr we examined food exploitation patterns to gain an understanding of how these species coexist and to characterize the trophic conditions that allow the maintenance of different mating systems within the same habitat. In the promiscuous saltmarsh sharp-tailed sparrow, only females feed the young, while the young of the socially monogramous seaside sparrow are fed by both parents. To determine dietary patterns, we used a nonlethal method (throat constriction) to obtain food samples from nestlings. Resource states were determined by sweep-netting the vegetation and by taking cores from the marsh surface. Based on volume, the same 4 prey groups (flies, amphipods, grasshoppers, moths) composed > 80% of each species diet. The main food of both sparrows was adult and juvenile (larval and pupal) soldier flies (Stratiomyidae:Odontomyia microstomata). Measures of dietary overlap, based on resource states, indicated that nestling diets did not differ between species on a seasonal basis or over 2-wk intervals. As the season progressed, each species tracked in parallel changes in resource abundance. Diets did not diverge from what was expected if food was exploited randomly; diets frequently overlapped significantly more than expected. Interspecific resource-use patterns were congruent over 2 yr. Based on the results of this study, and on an evaluation of hypotheses based on life history information from previously published work, we conclude that food usually is not limiting for these sparrows and that resource abundance has fostered behavioral and dietary opportunism.     

786.

Na depletion in modern adakites via melt / rock reaction within the sub-arc mantle     

X.L. Xiong  B. Xia  J.F. Xu  H.C. Niu  W.S. Xiao 《Chemical Geology》2006,229(4):273-292

Interaction between slab-derived melt and mantle peridotite and the role of slab melt as a metasomatizing agent in the sub-arc mantle is being increasingly recognized. Adakite, the slab melt erupted on the surface, usually exhibits anomalously high MgO, CaO, Cr and Ni contents that indicate interaction with mantle peridotitite. Here we note that Cenozoic adakites have Na₂O contents below 5.8 wt.% with ∼95% samples lower than 5.0 wt.%, and are generally depleted in this component relative to experimental basalt partial melts (mostly beyond 5.0 wt.% and up to 9.0 wt.% Na₂O) produced under 1.5-3.0 GPa conditions that are most relevant to adakite production. We interpret the adakite Na depletion to be also a consequence of the melt / rock reaction that takes place within the hot mantle wedge. During ascent and reaction with mantle peridotite, primary adakite melts gain mantle components MgO, CaO, Cr and Ni but lose Na₂O, SiO₂ and perhaps K₂O to the mantle, leading to Na-rich mantle metasomatism. Selective assimilation of predominately mantle clinopyroxene, some spinel and minor olivine at high T/P has been considered to be an important process in producing high-Mg adakites from primary low-Mg slab melts [Killian, R., Stern, C. R., 2002. Constraints on the interaction between slab melts and the mantle wedge from adakitic glass in peridotite xenoliths. Eur. J. Mineral. 14, 25-36]. In such a process, Na depletion in the assimilated melt is the result of dilution due to the increase in melt mass. Phase relationships in the reaction system siliceous melt + peridotite and quantitative calculation suggest that assimilation of mantle clinopyroxene, olivine and spinel and fractional crystallization of sodic amphibole and orthopyroxene, under conditions of moderate T/P and increasing melt mass, is also an important process that modifies the composition of adakites and causes the Na depletion.     

787.

Mantle plumes from top to bottom   总被引：5，自引：0，他引：5  

Norman H. Sleep 《Earth》2006,77(4):231-271

Hotspots include midplate features like Hawaii and on-axis features like Iceland. Mantle plumes are a well-posed hypothesis for their formation. Starting plume heads provide an explanation of brief episodes of flood basalts, mafic intrusions, and radial dike swarms. Yet the essence of the hypothesis hides deep in the mantle. Tests independent of surface geology and geochemistry to date have been at best tantalizing. It is productive to bare the current ignorance, rather than to dump the plume hypothesis. One finds potentially fruitful lines of inquiry using simple dynamics and observations. Ancient lithospheric xenoliths may reveal heating by plumes and subsequent thermal equilibration in the past. The effect at the base of the chemical layer is modest 50-100 K for transient heating by plume heads. Thinning of nonbuoyant platform lithosphere is readily observed but not directly attributable to plumes. The plume history in Antarctica is ill constrained because of poor geological exposure. This locality provides a worst case on what is known about surface evidence of hotspots. Direct detection of plume tail conduits in the mid-mantle is now at the edge of seismic resolution. Seismology does not provide adequate resolution of the deep mantle. We do not know the extent of a chemically dense dregs layer or whether superplume regions are cooler or hotter than an adiabat in equilibrium with the asthenosphere. Overall, mid-mantle seismology is most likely to give definitive results as plume conduits are the guts of the dynamic hypothesis. Finding them would bring unresolved deep and shallow processes into place.     

788.

Influence of physiology and climate on δD of leaf wax n-alkanes from C₃ and C₄ grasses     

Francesca A. Smith  Katherine H. Freeman 《Geochimica et cosmochimica acta》2006,70(5):1172-1187

We measured hydrogen isotope compositions (δD) of high-molecular-weight n-alkanes (C₂₇-C₃₃) from grasses grown in greenhouses and collected from the US Great Plains. In both cases, n-alkanes from C₄ grasses are enriched in D by more than 20‰ relative to those from C₃ grasses. The apparent enrichment factor (ε_C29-GW) between C₂₉n-alkane and greenhouse water is −165 ± 12‰ for C₃ grasses and −140 ± 15‰ for C₄ grasses. For samples from the Great Plains, δD values of C₂₉n-alkanes range from −280 to −136‰, with values for C₄ grasses ca. 21‰ more positive than those for C₃ grasses from the same site. Differences in C₃ and C₄ grass n-alkane δD values are consistent with the shorter interveinal distance in C₄ grass leaves, and greater back-diffusion of enriched water from stomata to veins, than in C₃ grass leaves. Great Plains’ grass n-alkane isotopic ratios largely reflect precipitation δD values. However, the offset or apparent fractionation between n-alkanes and precipitation is not uniform and varies with annual precipitation and relative humidity, suggesting climatic controls on lipid δD values. The dryer sites exhibit smaller absolute apparent fractionation indicative of D-enrichment of source waters through transpiration and/or soil evaporation. To explore the relationship between climate and n-alkane δD values, we develop three models. (1) The ‘direct analog’ model estimates δD_C29 values simply by applying the apparent enrichment factors, ε_C29-GW, observed in greenhouse grasses to precipitation δD values from the Great Plains. (2) The ‘leaf-water’ model uses a Craig-Gordon model to estimate transpirational D-enrichment for both greenhouse and field sites. The transpiration-corrected enrichment factors between C₂₉ and bulk leaf-water, ε_C29-GW, calculated from the greenhouse samples (−181‰ for C₃ and −157‰ for C₄) are applied to estimate δD_C29 values relative to modeled bulk leaf-water δD values. (3) The ‘soil- and leaf-water’ model estimates the combined effects of soil evaporation, modeled by analogy with a flow-through lake, and transpiration on δD_C29 values. Predictions improve with the addition of the explicit consideration of transpiration and soil evaporation, indicating that they are both important processes in determining plant lipid δD values. D-enrichment caused by these evaporative processes is controlled by relative humidity, suggesting that important climatic information is recorded in leaf wax n-alkane δD values. Calibration studies such as this one provide a baseline for future studies of plant-water-deuterium systematics and form the foundation for interpretation of plant wax hydrogen isotope ratios as a paleo-aridity proxy.     

789.

Incorporating solid solutions in reactive transport equations using a kinetic discrete-composition approach     

Peter C. Lichtner  J. William Carey 《Geochimica et cosmochimica acta》2006,70(6):1356-1378

A new approach is proposed for incorporating solid solution reactions into mass conservation equations describing reaction paths in both closed and open systems. The method is applicable to problems involving advective, dispersive, and diffusive transport in a porous medium. By representing the continuously variable solid solution composition with a discrete set of stoichiometric solids that span composition space, combined with a kinetic formulation of their rates of reaction, a self-determining spatial and temporal evolution of the solid solution concentration and composition is obtained. It is demonstrated that equilibrium of an aqueous solution with a stoichiometric solid derived from a solid solution corresponds to equilibrium of the solid solution itself if and only if equilibrium of the stoichiometric solid is stable. One advantage of this approach is that it is unnecessary to introduce any additional compositional variables to represent the solid solution. Discretization may be over the entire range of composition space, or over some subset depending on the system. A major consequence of the kinetic discrete-composition solid solution representation is that modeling solid solutions is similar to modeling pure mineral phases with the exception of a weighting factor applied to reaction rates of stoichiometric solids corresponding to a common solid solution. With this approach, precipitation leads to a discrete zonation of the solid solution that approximates the continuous variation in composition expected for the actual solid solution. The approach is demonstrated for a hypothetical ideal and non-ideal binary solid solution A_xB_1−xC for a reaction path formulation and reactive transport involving advection and diffusion.     

790.

Molybdenum and uranium geochemistry in continental margin sediments: Paleoproxy potential   总被引：4，自引：0，他引：4  

James McManus  William M. Berelson  Rebecca L. Poulson  Gary P. Klinkhammer 《Geochimica et cosmochimica acta》2006,70(18):4643-4662

     

[首页] « 上一页 [74] [75] [76] [77] [78] 79 [80] [81] [82] [83] [84] 下一页 » 末  页»

l	109C?l,15	109S?l,15
15	?23.5 ± 0.8	?7.7 ± 0.8
17	6.3 ± 1.5	5.6 ± 1.5
19	?25.1 ± 2.5	?7.3 ± 2.3
21	27.8 ± 3.6	?0.7 ± 3.4
23	17.1 ± 4.1	13.9 ± 4.8
25	?1.1 ± 3.0	8.5 ± 4.2
27	10.0 ± 3.3	6.7 ± 2.7
29	?9.4 ± 3.5	0.1 ± 4.7
31	10.1 ± 5.4	3.8 ± 5.6
33	1.1 ± 5.7	3.1 ± 5.8

Geopotential harmonics of order 15 and odd degree from analysis of resonant orbits

We have analysed the variations of inclination in 13 satellite orbits as they pass slowly, under the action of air drag, through 15th-order resonance with the geopotential, when successive equatorial crossings are 24° apart and the ground track repeats after 15 rev. The size and form of the change in inclination are determined mainly by the values of the geopotential harmonics of 15th order and odd degree, $\text{C}\text{?}{}_{\mathrm{l,15}}$ and $\text{S}\text{?}{}_{\mathrm{l,15}}$ (with l = 15, 17, 19, …) in the usual notation. Our analysis gives values of these coefficients up to l = 33 as follows:

Variations in the atmospheric neutral density at 145km

A least-squares multiple linear regression is performed on orbital decay density data obtained from precise orbital analysis of 22 low-perigee (130–160 km) Air Force satellites. Variations related to solar activity, the semi-annual effect, geomagnetic activity, and the zenith angle of the Sun are in agreement with the model of Jacchia (1971). Density variations in longitude and latitude are also deduced and compared with recent results from other investigations within this altitude regime.     

Transport and emplacement of crater and basin deposits

Material is ejected from impact craters in ballastic trajectories; it impacts first near the crater rim and then at progressively greater ranges. Ejecta from craters smaller than approximately 1 km is laid predominantly on top of the surrounding surface. With increasing crater size, however, more and more surrounding surface will be penetrated by secondary cratering action and these preexisting materials will be mixed with primary crater ejecta. Ejecta from large craters and especially basin forming events not only excavate preexisting, local materials, but also are capable of moving large amounts of material away from the crater. Thus mixing and lateral transport give rise to continuous deposits that contain materials from within and outside the primary crater. As a consequence ejecta of basins and large highland craters have eroded and mixed highland materials throughout geologic time and deposited them in depressions inside and between older crater structures.Because lunar mare surfaces contain few large craters, the mare regolith is built up by successive layers of predominantly primary ejecta. In contrast, the lunar highlands are dominated by the effects of large scale craters formed early in lunar history. These effects lead to thick fragmental deposits which are a mixture of primary crater material and local components. These deposits may also properly be named regolith though the term has been traditionally applied only to the relatively thin fine grained surficial deposit on mare and highland terranes generated during the past few billion year. We believe that the surficial highland regolith - generated over long periods of time - rests on massive fragmental units that have been produced during the early lunar history.     

Nestling diets of coexisting salt marsh sparrows: Opportunism in a food-rich environment

The saltmarsh sharp-tailed sparrow (Ammodramus caudacutus) and the morphologically similar seaside sparrow (Ammodramus maritimus) occur together in Atlantic coast salt marshes. Over 2 yr we examined food exploitation patterns to gain an understanding of how these species coexist and to characterize the trophic conditions that allow the maintenance of different mating systems within the same habitat. In the promiscuous saltmarsh sharp-tailed sparrow, only females feed the young, while the young of the socially monogramous seaside sparrow are fed by both parents. To determine dietary patterns, we used a nonlethal method (throat constriction) to obtain food samples from nestlings. Resource states were determined by sweep-netting the vegetation and by taking cores from the marsh surface. Based on volume, the same 4 prey groups (flies, amphipods, grasshoppers, moths) composed > 80% of each species diet. The main food of both sparrows was adult and juvenile (larval and pupal) soldier flies (Stratiomyidae:Odontomyia microstomata). Measures of dietary overlap, based on resource states, indicated that nestling diets did not differ between species on a seasonal basis or over 2-wk intervals. As the season progressed, each species tracked in parallel changes in resource abundance. Diets did not diverge from what was expected if food was exploited randomly; diets frequently overlapped significantly more than expected. Interspecific resource-use patterns were congruent over 2 yr. Based on the results of this study, and on an evaluation of hypotheses based on life history information from previously published work, we conclude that food usually is not limiting for these sparrows and that resource abundance has fostered behavioral and dietary opportunism.     

Na depletion in modern adakites via melt / rock reaction within the sub-arc mantle

Interaction between slab-derived melt and mantle peridotite and the role of slab melt as a metasomatizing agent in the sub-arc mantle is being increasingly recognized. Adakite, the slab melt erupted on the surface, usually exhibits anomalously high MgO, CaO, Cr and Ni contents that indicate interaction with mantle peridotitite. Here we note that Cenozoic adakites have Na₂O contents below 5.8 wt.% with ∼95% samples lower than 5.0 wt.%, and are generally depleted in this component relative to experimental basalt partial melts (mostly beyond 5.0 wt.% and up to 9.0 wt.% Na₂O) produced under 1.5-3.0 GPa conditions that are most relevant to adakite production. We interpret the adakite Na depletion to be also a consequence of the melt / rock reaction that takes place within the hot mantle wedge. During ascent and reaction with mantle peridotite, primary adakite melts gain mantle components MgO, CaO, Cr and Ni but lose Na₂O, SiO₂ and perhaps K₂O to the mantle, leading to Na-rich mantle metasomatism. Selective assimilation of predominately mantle clinopyroxene, some spinel and minor olivine at high T/P has been considered to be an important process in producing high-Mg adakites from primary low-Mg slab melts [Killian, R., Stern, C. R., 2002. Constraints on the interaction between slab melts and the mantle wedge from adakitic glass in peridotite xenoliths. Eur. J. Mineral. 14, 25-36]. In such a process, Na depletion in the assimilated melt is the result of dilution due to the increase in melt mass. Phase relationships in the reaction system siliceous melt + peridotite and quantitative calculation suggest that assimilation of mantle clinopyroxene, olivine and spinel and fractional crystallization of sodic amphibole and orthopyroxene, under conditions of moderate T/P and increasing melt mass, is also an important process that modifies the composition of adakites and causes the Na depletion.     

Mantle plumes from top to bottom

Hotspots include midplate features like Hawaii and on-axis features like Iceland. Mantle plumes are a well-posed hypothesis for their formation. Starting plume heads provide an explanation of brief episodes of flood basalts, mafic intrusions, and radial dike swarms. Yet the essence of the hypothesis hides deep in the mantle. Tests independent of surface geology and geochemistry to date have been at best tantalizing. It is productive to bare the current ignorance, rather than to dump the plume hypothesis. One finds potentially fruitful lines of inquiry using simple dynamics and observations. Ancient lithospheric xenoliths may reveal heating by plumes and subsequent thermal equilibration in the past. The effect at the base of the chemical layer is modest 50-100 K for transient heating by plume heads. Thinning of nonbuoyant platform lithosphere is readily observed but not directly attributable to plumes. The plume history in Antarctica is ill constrained because of poor geological exposure. This locality provides a worst case on what is known about surface evidence of hotspots. Direct detection of plume tail conduits in the mid-mantle is now at the edge of seismic resolution. Seismology does not provide adequate resolution of the deep mantle. We do not know the extent of a chemically dense dregs layer or whether superplume regions are cooler or hotter than an adiabat in equilibrium with the asthenosphere. Overall, mid-mantle seismology is most likely to give definitive results as plume conduits are the guts of the dynamic hypothesis. Finding them would bring unresolved deep and shallow processes into place.     

Influence of physiology and climate on δD of leaf wax n-alkanes from C3 and C4 grasses

We measured hydrogen isotope compositions (δD) of high-molecular-weight n-alkanes (C₂₇-C₃₃) from grasses grown in greenhouses and collected from the US Great Plains. In both cases, n-alkanes from C₄ grasses are enriched in D by more than 20‰ relative to those from C₃ grasses. The apparent enrichment factor (ε_C29-GW) between C₂₉n-alkane and greenhouse water is −165 ± 12‰ for C₃ grasses and −140 ± 15‰ for C₄ grasses. For samples from the Great Plains, δD values of C₂₉n-alkanes range from −280 to −136‰, with values for C₄ grasses ca. 21‰ more positive than those for C₃ grasses from the same site. Differences in C₃ and C₄ grass n-alkane δD values are consistent with the shorter interveinal distance in C₄ grass leaves, and greater back-diffusion of enriched water from stomata to veins, than in C₃ grass leaves. Great Plains’ grass n-alkane isotopic ratios largely reflect precipitation δD values. However, the offset or apparent fractionation between n-alkanes and precipitation is not uniform and varies with annual precipitation and relative humidity, suggesting climatic controls on lipid δD values. The dryer sites exhibit smaller absolute apparent fractionation indicative of D-enrichment of source waters through transpiration and/or soil evaporation. To explore the relationship between climate and n-alkane δD values, we develop three models. (1) The ‘direct analog’ model estimates δD_C29 values simply by applying the apparent enrichment factors, ε_C29-GW, observed in greenhouse grasses to precipitation δD values from the Great Plains. (2) The ‘leaf-water’ model uses a Craig-Gordon model to estimate transpirational D-enrichment for both greenhouse and field sites. The transpiration-corrected enrichment factors between C₂₉ and bulk leaf-water, ε_C29-GW, calculated from the greenhouse samples (−181‰ for C₃ and −157‰ for C₄) are applied to estimate δD_C29 values relative to modeled bulk leaf-water δD values. (3) The ‘soil- and leaf-water’ model estimates the combined effects of soil evaporation, modeled by analogy with a flow-through lake, and transpiration on δD_C29 values. Predictions improve with the addition of the explicit consideration of transpiration and soil evaporation, indicating that they are both important processes in determining plant lipid δD values. D-enrichment caused by these evaporative processes is controlled by relative humidity, suggesting that important climatic information is recorded in leaf wax n-alkane δD values. Calibration studies such as this one provide a baseline for future studies of plant-water-deuterium systematics and form the foundation for interpretation of plant wax hydrogen isotope ratios as a paleo-aridity proxy.     

Incorporating solid solutions in reactive transport equations using a kinetic discrete-composition approach

A new approach is proposed for incorporating solid solution reactions into mass conservation equations describing reaction paths in both closed and open systems. The method is applicable to problems involving advective, dispersive, and diffusive transport in a porous medium. By representing the continuously variable solid solution composition with a discrete set of stoichiometric solids that span composition space, combined with a kinetic formulation of their rates of reaction, a self-determining spatial and temporal evolution of the solid solution concentration and composition is obtained. It is demonstrated that equilibrium of an aqueous solution with a stoichiometric solid derived from a solid solution corresponds to equilibrium of the solid solution itself if and only if equilibrium of the stoichiometric solid is stable. One advantage of this approach is that it is unnecessary to introduce any additional compositional variables to represent the solid solution. Discretization may be over the entire range of composition space, or over some subset depending on the system. A major consequence of the kinetic discrete-composition solid solution representation is that modeling solid solutions is similar to modeling pure mineral phases with the exception of a weighting factor applied to reaction rates of stoichiometric solids corresponding to a common solid solution. With this approach, precipitation leads to a discrete zonation of the solid solution that approximates the continuous variation in composition expected for the actual solid solution. The approach is demonstrated for a hypothetical ideal and non-ideal binary solid solution A_xB_1−xC for a reaction path formulation and reactive transport involving advection and diffusion.