Tungsten isotope evidence from similar to 3.8-Gyr metamorphosed sediments for early meteorite bombardment of the Earth

The 'Late Heavy Bombardment' was a phase in the impact history of the Moon that occurred 3.8-4.0 Gyr ago, when the lunar basins with known dates were formed(1,2). But no record of this event has yet been reported from the few surviving rocks of this age on the Earth. Here we report tungsten isotope anomalies, based on the Hf-182-W-182 system (half-life of 9 Myr), in metamorphosed sedimentary rocks from the 3.7-3.8-Gyr-old Isua greenstone belt of West Greenland and closely related rocks from northern Labrador, Canada. As it is difficult to conceive of a mechanism by which tungsten isotope heterogeneities could have been preserved in the Earth's dynamic crust-mantle environment from a time when short-lived Hf-182 was still present, we conclude that the metamorphosed sediments contain a component derived from meteorites.

Stratigraphy, facies architecture and tectonic implications of the Upper Devonian to Lower Carboniferous Campwyn Volcanics of the northern New England Fold Belt

Upper Devonian to Lower Carboniferous strata of the Campwyn Volcanics of east central Queensland preserve a substantial sequence of first-cycle volcaniclastic sedimentary and coeval volcanic rocks that record prolonged volcanic activity along the northern New England Fold Belt. The style and scale of volcanism varied with time, producing an Upper Devonian sequence of mafic volcano-sedimentary rocks overlain by a rhyolitic ignimbrite-dominated sequence that passes upward into a Lower Carboniferous limestone-bearing sedimentary sequence. We define two facies associations for the Campwyn Volcanics. A lower facies association is dominated by mafic volcanic-derived sedimentary breccias with subordinate primary mafic volcanic rocks comprising predominantly hyaloclastite and peperite. Sedimentary breccias record episodic and high energy, subaqueous depositional events with clastic material sourced from a mafic lava-dominated terrain. Some breccias contain a high proportion of attenuated dense, glassy mafic juvenile clasts, suggesting a syn-eruptive origin. The lower facies association coarsens upwards from a lithic sand-dominated sequence through a thick interval of pebble- to boulder-grade polymict volcaniclastic breccias, culminating in facies that demonstrate subaerial exposure. The silicic upper facies association marks a significant change in eruptive style, magma composition and the nature of eruptive sources, as well as the widespread development of subaerial depositional conditions. Crystal-rich, high-grade, low- to high-silica rhyolite ignimbrites dominate the base of this facies association. Biostratigraphic age controls indicate that the ignimbrite-bearing sequences are Famennian to lower-mid Tournaisian in age. The ignimbrites represent extra-caldera facies with individual units up to 40 m thick and mostly lacking coarse lithic breccias. Thick deposits of pyroclastic material interbedded with fine-grained siliceous sandstone and mudstone (locally radiolarian-bearing) were deposited from pyroclastic flows that crossed palaeoshorelines or represent syn-eruptive, resedimented pyroclastic material. Some block-bearing lithic-pumice-crystal breccias may also reflect more proximal subaqueous silicic explosive eruptions. Crystal-lithic sandstones interbedded with, and overlying the ignimbrites, contain abundant detrital volcanic quartz and feldspar derived from the pyroclastic deposits. Limestone is common in the upper part of the upper facies association, and several beds are oolitic (cf. Rockhampton Group of the Yarrol terrane). Overall, the upper facies association fines upward and is transgressive, recording a return to shallow-marine conditions. Palaeocurrent data from all stratigraphic levels in the Campwyn Volcanics indicate that the regional sediment-dispersal direction was to the northwest, and opposed to the generally accepted notion of easterly sediment dispersal from a volcanic arc source. The silicic upper facies association correlates in age and lithology to Early Carboniferous silicic volcanism in the Drummond (Cycle 1) and Burdekin Basins, Connors Arch, and in the Yarrol terranes of eastern Queensland. The widespread development of silicic volcanism in the Early Carboniferous indicates that silicic (rift-related) magmatism was not restricted to the Drummond Basin, but was part of a more substantial silicic igneous province.

Shoemaker impact structure, Western Australia

The Shoemaker impact structure, on the southern margin of the Palaeoproterozoic Earaheedy Basin, with an outer diameter of similar to30 km, consists of two well-defined concentric ring structures surrounding a granitoid basement uplift. The concentric structures, including a ring syncline and a ring anticline, formed in sedimentary rocks of the Earaheedy Group. In addition, aeromagnetic and geological field observations suggest that Shoemaker is a deeply eroded structure. The central 12 km-diameter uplift consists of fractured Archaean basement granitoids of syenitic composition (Teague Granite). Shock-metamorphic features include shatter cones in sedimentary rocks and planar deformation features in quartz crystals of the Teague Granite. Universal-stage analysis of 51 sets of planar deformation features in 18 quartz grains indicate dominance of sets parallel to omega (10 (1) over bar3}, but absence of sets parallel to pi (10 (1) over bar2}, implying peak shock pressures in the range of 10-20 GPa for the analysed sample. Geophysical characteristics of the structure include a -100 mus(-2) gravity anomaly coincident with the central uplift and positive circular trends in both magnetic and gravity correlating with the inner ring syncline and outer ring anticline. The Teague Granite is dominated by albite-quartz-K-feldspar with subordinate amounts of alkali pyroxene. The alkali-rich syenitic composition suggests it could either represent a member of the Late Archaean plutonic suite or the product of alkali metasomatism related to impact-generated hydrothermal activity. In places, the Teague Granite exhibits partial to pervasive silicification and contains hydrothermal minerals, including amphibole, garnet, sericite and prehnite. Recent isotopic age studies of the Teague Granite suggest an older age limit of ca 1300 Ma (Ar-Ar on K-feldspar) and a younger age limit of ca 568 Ma (K-Ar on illite-smectite). The significance of the K-Ar age of 568 Ma is not clear, and it might represent either hydrothermal activity triggered by impact-related energy or a possible resetting by tectonothermal events in the region.

A new estimate for the composition of weathered young upper continental crust from alluvial sediments, Queensland, Australia

We present new major element, trace element and Nd-isotope data for 30 alluvial sediments collected from 25 rivers in Queensland, E Australia. Samples were chosen to represent drainage from the region's most important lithologies, including Tertiary intraplate volcanic rocks, a Cretaceous igneous province (and sedimentary rocks derived thereof) as well as Proterozoic blocks. In most chemical and isotopic aspects, the alluvial sediments represent binary or ternary mixing relationships, with absolute abundances implied to reflect the proportion of lithologies in the catchments. When averaged, the studied sediments differ from other proxies of upper continental crust (UCC) mainly in their relative middle rare earth element enrichment (including an elevated Sm/Nd ratio), higher relative Eu abundance and higher Nb/Ta ratio. These features are inherited from eroded Tertiary intraplate basalts, which commonly form topographic highs in the studied region. Despite the high degree of weathering strong to excellent coherence between similarly incompatible elements is found for all samples. From this coherence, we suggest revisions of the following upper crustal element ratios: Y/Ho = 26.2, Yb/Tm = 6.37, Th/W = 7.14, Th/Tl = 24 and Zr/Hf = 36.9. Lithium, Rb, Cs and Be contents do not seem depleted relative to UCC, which may reflect paucity of K-feldspar in the eroded catchments. Nickel, Cr, Pb, Cu and Zn concentrations are elevated in polluted rivers surrounding the state capital. River sediments in the Proterozoic Georgetown Inlier are elevated in Pb, Cu and Zn but this could be a natural phenomenon reflecting abundant sulphide mineralisation in the area. Except for relative Sr concentrations, which broadly anticorrelate with mean annual rainfall in catchments, there is no obvious relationship between the extent of weathering and climate types, which range from and to tropical. The most likely explanation for this observation is that the weathering profiles in many catchments are several Myr old, established during the much wetter Miocene period. The studied sediment compositions (excluding those from the Proterozoic catchments) are used to propose a new trace element normalisation termed MUQ (MUd from Queensland), which serves as an alternative to UCC proxies derived from sedimentary rocks. Copyright (C) 2005 Elsevier Ltd

Upper Devonian biostratigraphy of the Iberian Pyrite Belt, southwest Spain Part One: Miospores

The Iberian Pyrite Belt (IPB), which forms part of the Variscan orogenic massif, is renowned for the magnitude and extent of its massive sulfide mineralization. The stratigraphic record of the IPB consists of Upper Palaeozoic sedimentary and igneous rocks. In ascending order, these comprise the thick Phyllite-Quartzite Group attributed to the Middle and Upper Devonian and characterized by shales and quartzites with conglomeratic and carbonate intercalations towards the top; the appreciably thinner Volcano-Sedimentary Complex, a heterogeneous uppermost Devonian-Mississippian unit embodying diverse volcanic, subvolcanic, and sedimentary rocks that host the massive sulfide deposits; and the shaly and sandy, turbiditic Culm Group (Carboniferous). This entire succession was folded and faulted during the Asturian phase of the Variscan Orogeny that gave rise to a thin-skinned type structure. The present study constitutes a detailed blostratigraphic investigation of palynologically productive samples representative of the Phyllite-Quartzite Group and the basal (anoxic) portion of the Volcano-Sedimentary Complex. These were collected from surface and mine exposures variously located in the Spanish part of the IPB; out of 282 samples processed, 117 proved to be productive palynologically. The aim of this project is to provide comprehensive palynostratigraphic data applicable to precise dating and correlation of the IPB's stratigraphic succession (i.e., of the two sampled lithostratigraphic units), which has hitherto been investigated biostratigraphically on a relatively localized basis. The results are incorporated in two successive parts. The first of these, i. e., the present paper, focuses on the systematic analysis of the terrestrial (miospore) component of the palynological assemblages. The second part, devoted to the marine, organic-walled microphytoplankton (acritarchs and prasinophytes), will evaluate the stratigraphic significance of the IPB palynofloras and their application to elucidating the geological history of the region. In the systematic-descriptive section, which occupies the bulk of this paper, 55 species of trilete miospores are described and are allocated among 34 genera, two of which (Cristicavatispora and Epigruspora) are newly instituted herein. The majority of the species are either positively identifiable or closely affiliable with previously named species. The nine newly established species are as follows: Camptozonotriletes confertus, Indotriradites diversispinosus, Cristicavatispora dispersa (type species), Epigruspora regularis (type species), Ancyrospora? implicata, Endosporites tuberosus, Rugospora explicata, Spelaeotriletes plicatus, and Teichertospora iberica.

Chemical characterization of earth's most ancient clastic metasediments from the Isua Greenstone Belt, southern West Greenland

New and published major and trace element abundances of elastic metasediments (mainly garnet-biotite-plagioclase schists) from the similar to 3.8 Ga Isua Greenstone Belt (IGB), southern West Greenland, are used in an attempt to identify the compositional characteristics of the protoliths of these sediments. Compositionally, the metasediments are heterogeneous with enrichment of LREE (La/Sm-chord = 1.1-3.9) and variable enrichment and depletion of HREE (Gd/Yb-chord = 0.8-4.3). Chondrite-normalized Eu is also variable, spanning a range from relative Eu depletion to enrichment (Eu/Eu* = 0.6-1.3). A series of geochemical and geological criteria provides conclusive evidence for a sedimentary origin, in disagreement with some previous studies that questioned the presence of genuine elastic metasediments. In particular, trace element systematics of IGB metasediments show strong resemblance to other well-documented Archaean clastic sediments, and are consistent with a provenance consisting of ultramafic, malic and felsic igneous rocks. Two schists, identified as metasomatized mafic igneous rocks from petrographic and field evidence, show distinct compositional differences to the metasediments. Major element systematics document incipient-to-moderate source weathering in the majority of metasediments, while signs of secondary K-addition are rare. Detailed inspection of Eu/Eu*, Fe2O3 and CIW (chemical index of weathering) relationships reveals that elevated iron contents (when compared to averages for continental crust) and strong relative enrichment in Eu may be due to precipitation of marine Fe-oxyhydroxides during deposition or diagenesis on the seafloor. Some of the IGB metasediments have yielded anomalous Nd-142 and W-182 isotopic compositions that were respectively interpreted in terms of early mantle differentiation processes and the presence of a meteorite component. Alternatively, W and possibly Nd isotopes could have been affected by thermal neutron capture on the Hadean surface. The latter process was tested in this study by analysis of Sm isotope compositions, which serve as an effective monitor for neutron capture effects. As no anomalous variation from terrestrial values was detected, we infer that isotope systematics (including W-182 and Nd-142) of IGB metasediments were not affected by neutron capture, but reflect decay of radioactive parent isotopes. Copyright (c) 2005 Elsevier Ltd.

Volcanic setting of the Bajo de la Alumbrera porphyry Cu-Au deposit, Farallon Negro Volcanics, Northwest Argentina

The late Miocene Farallon Negro volcanics, comprising basaltic to rhyodacitic volcano-sedimentary rocks, host the Bajo de la Alumbrera porphyry copper-gold deposit in northwest Argentina. Early studies of the geology of the district have underpinned the general model for porphyry ore deposits where hydrothermal alteration and mineralization develop in and around porphyritic intrusions emplaced at shallow depths (2.5-3.5 km) into stratovolcanic assemblages. The Farallon Negro succession is dominated by thick sequences of volcano-sedimentary breccias, with lavas forming a minor component volumetrically. These volcaniclastic rocks conformably overlie crystalline basement-derived sedimentary rocks deposited in a developing foreland basin southeast of the Puna-Altiplano plateau. Within the Farallon Negro volcanics, volcanogenic accumulations evolved from early mafic to intermediate and silicic compositions. The younger and more silicic rocks are demonstrably coeval and comagmatic with the earliest group of mineralized porphyritic intrusions at Bajo de la Alumbrera. Our analysis of the volcanic stratigraphy and facies architecture of the Farallon Negro volcanics indicates that volcanic eruptions evolved from effusive to mixed effusive and explosive styles, as magma compositions changed to more intermediate and silicic compositions. Air early phase of mafic to intermediate voleanism was characterized by small synsedimentary intrusions with peperitic contacts, and lesser lava units scattered widely throughout the district, and interbedded with thick and extensive successions of coarse-grained sedimentary breccias. These sedimentary breccias formed from numerous debris- and hyperconcentrated flow events. A later phase of silicic volcanism included both effusive eruptions, forming several areally restricted lavas, and explosive eruptions, producing more widely dispersed (up to 5 kin) tuff units, some tip to 30-m thickness in proximal sections. Four key features of the volcanic stratigraphy suggest that the Farallon Negro volcanics need not simply record the construction of a large steep-sided polygenetic stratovolcano: (1) sheetlike, laterally continuous debris-flow and other coarse-grained sedimentary deposits are dominant, particularly in the lower sections; (2) mafic-intermediate composition lavas are volumetrically minor; (3) peperites are present throughout the sequence; and (4) fine-grained lacustrine sandstone-siltstone sequences occur in areas previously thought to be proximal to the summit region of the stratovolcano. Instead, the nature, distribution, and geometry of volcanic and volcaniclastic facies suggest that volcanism occurred as a relatively low relief, multiple-vent volcanic complex at the eastern edge of a broad, > 200-km-wide late Miocene volcanic belt and oil ail active foreland sedimentary basin to the Puna-Altiplano. Volcanism that occurred synchronously with the earliest stages of porphyry-related mineralization at Bajo de la Alumbrera apparently developed in an alluvial to ring plain setting that was distal to larger volcanic edifices.

Geological and trace element evidence for a marine sedimentary environment of deposition and biogenicity of 3.45 Ga stromatolitic carbonates in the Pilbara Craton, and support for a reducing Archaean ocean

Bedded carbonate rocks from the 3.45 Ga Warrawoona Group, Pilbara Craton, contain structures that have been regarded either as the oldest known stromatolites or as abiotic hydrothermal deposits. We present new field and petrological observations and high-precision REE + Y data from the carbonates in order to test the origin of the deposits. Trace element geochemistry from a number of laminated stromatolitic dolomite samples of the c. 3.40 Ga Strelley Pool Chert conclusively shows that they precipitated from anoxic seawater, probably in a very shallow environment consistent with previous sedimentological observations. Edge-wise conglomerates in troughs between stromatolites and widespread cross-stratification provide additional evidence of stromatolite construction, at least partly, from layers of particulate sediment, rather than solely from rigid crusts. Accumulation of particulate sediment on steep stromatolite sides in a high-energy environment suggests organic binding of the surface. Relative and absolute REE + Y contents are exactly comparable with Late Archaean microbial carbonates of widely agreed biological origin. Ankerite from a unit of bedded ankerite–chert couplets from near the top of the stratigraphically older (3.49 Ga) Dresser Formation, which immediately underlies wrinkly stromatolites with small, broad, low-amplitude domes, also precipitated from anoxic seawater. The REE + Y data of carbonates from the Strelley Pool Chert and Dresser Formation contrast strongly with those from siderite layers in a jasper–siderite–Fe-chlorite banded iron-formation from the base of the Panorama Formation (3.45 Ga), which is clearly hydrothermal in origin. The geochemical results, together with sedimentological data, strongly support: (1) deposition of Dresser Formation and Strelley Pool Chert carbonates from Archaean seawater, in part as particulate carbonate sediment; (2) biogenicity of the stromatolitic carbonates; (3) a reducing Archaean atmosphere; (4) ongoing extensive terrestrial erosion prior to ∼3.45 Ga.

Rare earth element fractionation in authigenic illite–smectite from Late Permian clastic rocks, Bowen Basin, Australia: implications for physico-chemical environments of fluids during illitization

REE analyses were performed on authigenic illitic clay. minerals from Late Permian mudrocks, sandstones and bentonites from the Bowen Basin (Australia). The mixed-layer illite-smectite exhibit REE patterns with an obvious fractionation of the HREE from the LREE and MREE, which is an apparent function of degree of illitization reaction. The highly illitic (R greater than or equal to 3) illite-smectite from the northern Bowen Basin show a depletion of LREE relative to the less illitic (R=0 and 1) clays. In contrast, an enrichment of HREE for the illite-rich clays relative to less. illitic clays is evident for the southern Bowen Basin samples. The North American Shale Composite-normalized (La/Lu)(sn) ratios show negative correlations with the illite content in illite-smectite and positive correlations with the delta(18)O values of the clays for both the northern and southern Bowen Basin samples. These correlations indicate that the increasing depletion of LREE in hydrothermal fluids is a function of increasing water/rock ratios in the northern Bowen Basin. Good negative correlations between (La/Lu)(sn) ratios and illite content in illite-smectite from the southern Bowen Basin suggest the involvement of fluids with higher alkalinity and higher pH in low water/ rock ratio conditions. Increasing HREE enrichment with delta(18)O decrease indicates the effect of increasing temperature at low water/rock ratios in the southern Bowen Basin. Results of the present study confirm the conclusions of some earlier studies suggesting that REE in illitic clay minerals are mobile and fractionated during illitization and that this fact should be considered in studies of sedimentary processes and in identifying provenance. Moreover, our results show that REE systematic of illitic clay minerals can be applied as an useful technique to gain information about physico-chemical conditions during thermal and fluid flow events in certain sedimentary basins. (C) 2003 Elsevier Science B.V. All rights reserved.

Finite element modeling of fluid-rock interaction problems in pore-fluid saturated hydrothermal/sedimentary basins

In order to use the finite element method for solving fluid-rock interaction problems in pore-fluid saturated hydrothermal/sedimentary basins effectively and efficiently, we have presented, in this paper, the new concept and numerical algorithms to deal with the fundamental issues associated with the fluid-rock interaction problems. These fundamental issues are often overlooked by some purely numerical modelers. (1) Since the fluid-rock interaction problem involves heterogeneous chemical reactions between reactive aqueous chemical species in the pore-fluid and solid minerals in the rock masses, it is necessary to develop the new concept of the generalized concentration of a solid mineral, so that two types of reactive mass transport equations, namely, the conventional mass transport equation for the aqueous chemical species in the pore-fluid and the degenerated mass transport equation for the solid minerals in the rock mass, can be solved simultaneously in computation. (2) Since the reaction area between the pore-fluid and mineral surfaces is basically a function of the generalized concentration of the solid mineral, there is a definite need to appropriately consider the dependence of the dissolution rate of a dissolving mineral on its generalized concentration in the numerical analysis. (3) Considering the direct consequence of the porosity evolution with time in the transient analysis of fluid-rock interaction problems; we have proposed the term splitting algorithm and the concept of the equivalent source/sink terms in mass transport equations so that the problem of variable mesh Peclet number and Courant number has been successfully converted into the problem of constant mesh Peclet and Courant numbers. The numerical results from an application example have demonstrated the usefulness of the proposed concepts and the robustness of the proposed numerical algorithms in dealing with fluid-rock interaction problems in pore-fluid saturated hydrothermal/sedimentary basins. (C) 2001 Elsevier Science B.V. All rights reserved.

Finite element modelling of reactive fluids mixing and mineralization in pore-fluid saturated hydrothermal/sedimentary basins

We present the finite element simulations of reactive mineral carrying fluids mixing and mineralization in pore-fluid saturated hydrothermal/sedimentary basins. In particular we explore the mixing of reactive sulfide and sulfate fluids and the relevant patterns of mineralization for Load, zinc and iron minerals in the regime of temperature-gradient-driven convective flow. Since the mineralization and ore body formation may last quite a long period of time in a hydrothermal basin, it is commonly assumed that, in the geochemistry, the solutions of minerals are in an equilibrium state or near an equilibrium state. Therefore, the mineralization rate of a particular kind of mineral can be expressed as the product of the pore-fluid velocity and the equilibrium concentration of this particular kind of mineral Using the present mineralization rate of a mineral, the potential of the modern mineralization theory is illustrated by means of finite element studies related to reactive mineral-carrying fluids mixing problems in materially homogeneous and inhomogeneous porous rock basins.

Effects of hot intrusions on pore-fluid flow and heat transfer in fluid-saturated rocks

We use the finite element method to solve coupled problems between pore-fluid flow and heat transfer in fluid-saturated porous rocks. In particular, we investigate the effects of both the hot pluton intrusion and topographically driven horizontal flow on the distributions of the pore-flow velocity and temperature in large-scale hydrothermal systems. Since general mineralization patterns are strongly dependent on distributions of both the pore-fluid velocity and temperature fields, the modern mineralization theory has been used to predict the general mineralization patterns in several realistic hydrothermal systems. The related numerical results have demonstrated that: (1) The existence of a hot intrusion can cause an increase in the maximum value of the pore-fluid velocity in the hydrothermal system. (2) The permeability of an intruded pluton is one of the sensitive parameters to control the pore-fluid flow, heat transfer and ore body formation in hydrothermal systems. (3) The maximum value of the pore-fluid velocity increases when the bottom temperature of the hydrothermal system is increased. (4) The topographically driven flow has significant effects on the pore-fluid flow, temperature distribution and precipitation pattern of minerals in hydrothermal systems. (5) The size of the computational domain may have some effects on the pore-fluid flow and heat transfer, indicating that the size of a hydrothermal system may affect the pore-fluid flow and heat transfer within the system. (C) 2003 Elsevier Science B.V. All rights reserved.

An equivalent algorithm for simulating thermal effects of magma intrusion problems in porous rocks

An equivalent algorithm is proposed to simulate thermal effects of the magma intrusion in geological systems, which are composed of porous rocks. Based on the physical and mathematical equivalence, the original magma solidification problem with a moving boundary between the rock and intruded magma is transformed into a new problem without the moving boundary but with a physically equivalent heat source. From the analysis of an ideal solidification model, the physically equivalent heat source has been determined in this paper. The major advantage in using the proposed equivalent algorithm is that the fixed finite element mesh with a variable integration time step can be employed to simulate the thermal effect of the intruded magma solidification using the conventional finite element method. The related numerical results have demonstrated the correctness and usefulness of the proposed equivalent algorithm for simulating the thermal effect of the intruded magma solidification in geological systems. (C) 2003 Elsevier B.V. All rights reserved.

Numerical modelling of chemical effects of magma solidification problems in porous rocks

The solidification of intruded magma in porous rocks can result in the following two consequences: (1) the heat release due to the solidification of the interface between the rock and intruded magma and (2) the mass release of the volatile fluids in the region where the intruded magma is solidified into the rock. Traditionally, the intruded magma solidification problem is treated as a moving interface (i.e. the solidification interface between the rock and intruded magma) problem to consider these consequences in conventional numerical methods. This paper presents an alternative new approach to simulate thermal and chemical consequences/effects of magma intrusion in geological systems, which are composed of porous rocks. In the proposed new approach and algorithm, the original magma solidification problem with a moving boundary between the rock and intruded magma is transformed into a new problem without the moving boundary but with the proposed mass source and physically equivalent heat source. The major advantage in using the proposed equivalent algorithm is that a fixed mesh of finite elements with a variable integration time-step can be employed to simulate the consequences and effects of the intruded magma solidification using the conventional finite element method. The correctness and usefulness of the proposed equivalent algorithm have been demonstrated by a benchmark magma solidification problem. Copyright (c) 2005 John Wiley & Sons, Ltd.