In this short note, we review results on equilibrium shapes of minimizers to the sessile drop problem. More precisely, we study the Winterbottom problem and prove that the Winterbottom shape is indeed optimal. The arguments presented here are based on relaxation and the (anisotropic) isoperimetric inequality.

Scanning electron microscopic (SEM) examination of the quartz isolated from chert of Transvaal and Swaziland, of 2000 and 3400 million year (MY) ages, respectively, in southern Africa revealed marked differences in quartz morphology. Well-defined individual euhedral quartz crystals, with polyhedral triple-point faces, were clearly evident on freshly fractured Transvaal chert surfaces as well as with the quartz isolates from the chert. The morphology and coarseness suggest crystal growth with little, if any, metamorphism; however, the δ18O values of 23.8–24.1‰ suggest crystallization temperatures of perhaps 40–45°C. In contrast, fracture surfaces of the older, strongly metamorphosed Swaziland cherts revealed a high degree of grain intergrowth which inhibited fracture between quartz grains. Quartz isolates from these showed strongly interlocked quartz crystal clusters and elongated chips of quartz with poorly defined irregular faces. Intercalation of mineral veins in the cherts on a mm scale and the intergrown character of the quartz grain boundaries provide evidence that the latter cherts have been strongly metamorphosed and recrystallized, in keeping with 14.6–15.1‰ δ18O values, corresponding to 80°C fractionation with water. The SEM micrographs of the fine quartz (1–10 µm) isolated from the Otavi dolomite formation of the 700-MY Damara System and from the 2000-MY Transvaal Dolomite Series revealed well-defined subhedral and euhedral quartz crystals of small size which, together with the 26.9–27.8‰ and 23.8‰ δ18O values, respectively, indicate that these dolomites have been affected little, if any, by post-depositional metamorphism; their crystallization temperatures fall in the range of 25–30 and 40–45°C, respectively.

Hydroxy-carboxylic acids inhibit the crystallization of ferrihydrite in the pH range 9–11 in the order

citric > meso tartaric > L-tartaric ≫ lactic

and favor hematite formation relative to goethite in the order

L-tartaric > citric > meso tartaric > lactic.

The crystal shape of hematite can change from hexagonal plates to acicular in the presence of these acids. The influence of the acids on the crystallization rises with increasing concentration and with falling pH.

The effectiveness in suppressing crystallization depends on whether and how strongly the acid adsorbs on ferrihydrite and how strongly it complexes with Fe3+ in solution. Inhibition of crystallization of hematite is believed to be due to the di- and tricarboxylic acid linking ferrihydrite particles in an immobile network. Goethite formation is suppressed by the acid complexing with Fe in solution and hindering nucleation; strongly adsorbing acids also adsorb on the nuclei and hinder further growth. Certain acids can induce hematite formation because they contain a group which acts as a template for nucleation of hematite.

Chelating organic acids hampered the hydrolytic reactions of Al and affected the nature of the crystalline aluminum hydroxides. Chemical composition, structure, size, nature of functional groups, and concentration of each organic anion, as well as the pH of the system, controlled the rate of Al(OH)3 crystallization. The order of effectiveness of the various acids was: glutaric < succinic = phthalic < glycine < malonic < glutamic < aspartic < oxalic < salicylic = malic < citric < tartaric. An increase in the stability of complexes formed between the organic ligands and Al decreased the rate of crystallization and changed the final aluminous products from bayerite to nordstrandite and/or gibbsite and then to pseudoboehmite and/or amorphous material. In the presence of anions with a great affinity for Al, particularly at pH equal to or less than 9.0, the reaction products were commonly poorly crystalline or structurally distorted. In the range of pH 8.0 to 10.0 moderately or strongly chelating anions acted to retard or prevent olation and facilitated the formation of stable pseudoboehmite or X-ray-amorphous products. The stronger the chelating power or the higher the concentration of organic anions, the easier was the formation of pseudoboehmite or amorphous material.

A method using a finite, first-order Markov chain is presented to estimate rate constants for zeolite formation from experimental nuclear magnetic resonance (NMR) data on the abundance of different silica oligomers. An experimental design is suggested by which this method can be implemented. The method uses weighted least squares to estimate transition probabilities from aggregate NMR data. Rate constants, equilibrium constants, and free energies of elementary zeolite-forming reactions can be estimated. Hypothetical zeolite-forming reactions can also be modeled. An example of modeling, using hypothetical data, shows how zeolite formation can result from reactions involving mainly silica cyclic tetramers.

High-resolution transmission electron microscopy (HRTEM) has shown regions of crystallites within noncrystalline matrices of three types of glass (volcanic glass, alkalic igneous glass, and synthetic, nuclear-waste-form glass) The volcanic glass fragments showed domains having 3-Å spacings. About 30% of the fragments of this glass showed localized lattice images, having spacings of 5, 7, 8, 10, 13, 14, 16, 19, and 20 Å, which also contain regular fringes having 3.3-Å separations. In the alkalic igneous glass fragments 3-Å domain structures were also noted as were localized lattice images having 7- and 12.5-Å spacings. Well-developed hollow spheres of primitive clays were present in both the volcanic and alkalic igneous glasses. Synthetic, nuclear-waste-foTm glass, fused at 1400°C and annealed at 550°C, showed locally ordered regions having 3.3-Å spacings. Low-angle X-ray powder diffraction showed major reflections at 8.5, 15–16, and 19 Å, which agree with some of the HRTEM measurements. These observations of domain structures, localized lattice images, primitive clays, and 14-Å clays in such noncrystalline glass matrices may contribute to an understanding of the growth of clay minerals. Such domains can apparently trigger the growth of clay products on the glass substrate.

To interpret the erratic conditions, rates, and extent of gibbsite crystallization from partially neutralized A1C13 solution, the following hypothesis is proposed: The initial OH-A1 polymers in the freshly prepared solutions were probably unstable and transformed into either gibbsite or stable OH-A1 polymers via two different reaction paths. In the presence of nuclei, the OH-A1 polymers dissociated into monomeric ions, which then deposited onto nuclei to form gibbsite. In the absence of nuclei, the unstable polymers slowly converted to stable polymers. The erratic stability of OH-Al solutions and gibbsite crystallization are therefore attributed to the relative magnitudes of these two reaction paths which, in turn, are attributed to two key factors: (1) the distribution of unstable vs. stable OH-Al polymers; and (2) the presence or absence of nuclei. The duration of aging of the parent solution governed the distribution of unstable vs. stable polymers. The rate of neutralization resulted in varying localized high alkalinity in OH-Al solution preparation and thus varying development of nuclei.

To provide a greater understanding of the crystallization of iron oxides under natural aqueous conditions, the combined effect of an inorganic ion (Mn2+) and a reducing organic ligand (L-cysteine) on the conversion of noncrystalline ferric hydroxide to goethite and/or hematite was investigated at pH 8.

At cysteine: Fe ratios ≥ 0.2, L-cysteine caused noncrystalline iron(III) hydroxide to transform rapidly into goethite at pH 8; in the absence of the organic ligand, hematite was the predominant reaction product. The presence of Mn (≥9 mole %) in the cysteine-ferric hydroxide system retarded crystallization and reduced the goethite-promoting effect of cysteine.

Polarographic measurements showed that the adsorption of cysteine on noncrystalline iron(III) hydroxide was immediately followed by the oxidation of cysteine to the disulfide with simultaneous reduction of a proportion of the interracial ferric ions. The partly reduced noncrystalline iron(III) hydroxide dissolved at pH 8 more rapidly than the original material, thus facilitating the formation of goethite. In Mn(II)-noncrystalline iron(III) hydroxide coprecipitates, the interfacial oxidation/reduction reaction with cysteine (and hence the partial reduction of the noncrystalline phase) was reduced, due to replacement of some interfacial Fe(III) by non-reducible Mn.

At pH 8, uptake of Mn by crystalline iron oxides was low (< 5 mole %). Mn precipitated preferentially as pure Mn phases, either rhodochrosite (in NaHCO3 buffer) or hausmannite (in NH4Cl/NH3 buffer).

Iron salts react readily with calcite in oxidizing calcareous environments to produce solid phase Fe-oxides. These reactions represent important processes in aqueous, geologic, and pedogenic environments. In the present investigation, Fe-oxides were precipitated from Fe(ClO4)2 solutions on undisturbed calcite grains in aqueous suspension. In this way it was possible to investigate the sequence of events in the crystallization process. Following an initial precipitation on the calcite grains, a period of slow growth of lepidocrocite was noted wherein 4-μm euhedral platelets formed with uniform orientation perpendicular to the calcite surface. The slow growth and highly crystalline nature of the Fe-oxide product may be partially due to the diffusion barrier formed by the growing oxide crystal mass which influenced rate of movement of HCO3− to the dissolved Fe phase and Fe ions and H+ towards the calcite surface. Upon continued aging, the supernate became noticeably opaque. As the suspended nuclei settled, new surfaces for crystal growth were provided which resulted in somewhat less crystalline lepidocrocite and goethite.

The effects of humic acid (HA) on the crystallization of precipitation products of Al under mildly acidic to alkaline conditions were investigated. The extent of Al precipitation substantially decreased with increasing HA concentration (0 to 75 µg/ml) in the pH range 6 to 10 during the 80-day aging period. The X-ray powder diffraction (XRD) data show that, at pH 6.0, the amount of pseudoboehmite formed in the systems decreased with the increasing concentration of HA present. The proportion of Al hydroxide polymorphs (gibbsite and bayerite) was greatly influenced by the amounts of HA present in the systems. At pH 6.0 and HA concentration of 37.5 µg/ml, all the precipitation products of Al were noncrystalline. At pH 8.0 and a HA concentration of 12.5 µg/ml, the formation of gibbsite and bayerite was completely inhibited and only pseudoboehmite was evident in the XRD patterns. Further increase in HA concentration (25–75 µg/ml HA) at pH 8.0 resulted in no precipitation of Al, and only a broad peak at ∼3.3 Å, characteristic of HA, was observed. The XRD patterns of the precipitates of Al formed in the absence of HA at pH 10.0 showed the characteristic peaks of bayerite. At pH 10.0, the precipitation products of Al formed even at the HA concentration of 2.5 µg/ml yielded no XRD peaks. Infrared absorption spectra and transmission electron micrographs of the precipitation products of Al formed in the systems studied substantiate the findings obtained by XRD. The data obtained in this study indicate that HA affects the formation of Al hydroxide polymorphs, pseudoboehmites and short-range ordered mineral colloids.

Gibbsite samples of various particle sizes (0.2–80 μm) were heated at 250°C in a series of straight-chain primary alcohols under the autogenous vapor pressure of the alcohol (alcohothermal treatment of gibbsite). The treatment in ethanol yielded pure boehmite, the morphology of which was similar to that of the boehmite obtained by hydrothermal treatment of gibbsite. In middle-range alcohols, the boehmite yields were low (50% if 80 μm gibbsite was used), and the products were contaminated by a poorly crystallized phase, having a χ-alumina-like structure. The products preserved the morphology of the originating gibbsite, this feature being similar to the thermal dehydration of gibbsite. Complete conversion to boehmite was also attained in mineral oil (a hydrocarbon mixture, which was used as a limit of higher alcohol. The morphology of the boehmite formed in this medium was identical to that of the product prepared by thermal dehydration of gibbsite in a sealed bomb without a medium. If fine particle-size gibbsite was used, the yield of boehmite decreased and the yield of the poorly crystallized phase increased in all the media.

The reaction mechanisms may be discussed in terms of the reported mechanisms for the thermal and hydrothermal formations of boehmite from gibbsite. Thus, in lower alcohols boehmite formed by a dissolution-recrystallization mechanism, whereas in middle-range or higher alcohols it formed by intra-particle hydrothermal reaction mechanism proposed by de Boer and coworkers for the thermal dehydration of gibbsite. The difference in behavior in middle-range and higher alcohols can be explained in terms of the solubility of water in the medium: In the middle-range alcohols, water molecules formed by partial dehydration of gibbsite were removed from the gibbsite particles into the medium so that dehydration proceeded in a manner similiar to that of thermal dehydration, whereas in the higher alcohols, the low solubility of water in the medium allowed the water molecules to remain on the surface of the particles, thereby promoting the complete hydrothermal formation of boehmite.

The clay mineral textures, assemblages, formation mechanisms, and controlling geological parameters relating to alteration of silicic volcanic rocks by hydrothermal solutions, in core samples from the Broadlands-Ohaaki hydrothermal system, New Zealand, were investigated using X-ray diffraction (XRD), scanning electron microscopy (SEM), and transmission and analytical electron microscopy (TEM/AEM). Mineralogical and textural relations of this active hydrothermal system, for which temperatures and fluid relations are well known, are equivalent to those in the Golden Cross hydrothermal gold deposit as described in Part 1.

XRD data show a sequence of clay minerals from smectite to a range of interstratified I-S to mica with increasing depth and temperature, on average. TEM observations are in general agreement with XRD data, especially with respect to relative proportions of illite (I)- and smectite (S)- like layers. TEM data also show that: (1) Smectite packets contain no discrete illite-like layers in samples identified as (Reichweite, R = 0) I-S by XRD. They coexist with separate packets of (R = 1) I-S. (2) A continuous range in I-S occurs from (R = 1) I-S with increasing proportion of illite-like layers, but at high illite-like layer contents there is a gap between I-S and illite. (3) 1M and 2M1 polytypes of mica coexist in separate packets, but the rare 1M polytype has a larger VIMg content.

The data imply that clay minerals formed by dissolution and neocrystallization directly from volcanic phases, although multiple reaction events can not be ruled out. Such “episodic” alteration produces a sequence of clay minerals identical to those of prograde diagenesis of pelitic sediments. This result implies that the presence of a continuous sequence is not definitive proof of continuous sequences of transformation as a function of time and continuous burial. Reaction progress of the clay-mineral sequence is in general accord with the known temperature gradient, but with significant and common exceptions. High porosity and permeability, both inherent in rock texture and local structure, are inferred to foster local reaction progress, as consistent with metastability of phases and the Ostwald step rule.

We studied the influence of time ageing (up to 120 d at 50°C or 30d at 95°C) on the mineralogical and chemical composition of hydrolytic species of mixed aluminum and iron samples formed at pH 5.0 and initial Fe/Al molar ratio (Ri) ranging from 0.1 to 10. The partitioning distribution of Fe and Al in soluble or solid phases of different sizes (<0.01, 0.2–0.01, >0.2 μm) depended on Ri and time. The ratio of Fe to Al of the <0.2 μm Fe-Al species of the samples at Ri ≤ 4 slowly increased with time. Usually the higher Ri the higher the amount of Fe + Al present in soluble or very fine solids (<0.2 μm). With time, high percentages of Fe were found mainly in the <0.01 μm while the Al increase in the >0.2 μm sizes. Gibbsite, without the presence of well-crystallized Fe-oxides was formed in the samples at Ri ≤ 0.5 after 7–120 d at 50°C. In the samples at Ri ≥ 1 low-crystalline ferrihydrite was observed after ≥60 d. Only after 120 d did gibbsite or hematite start to form in the samples at Ri = 1–10. However, even after prolonged ageing at 95°C, low-crystalline ferrihydrite was still present at Ri ≤ 4.

The Fe-Al samples at Ri ≥ 1 aged 32 d at 50°C dissolved almost completely by acid ammonium-oxalate (82–93%), but the samples at Ri ≤ 0.5 were only partially solubilized (13–60%). After further 30 d at 95°C, the percentages of Fe + Al solubilized by oxalate from the samples at R ≥ 0.5 was still relatively high (22–39%).

A comparative study is reported in which kaolinite has been hydrothermally synthesized at several pH conditions. The syntheses were carried out at 220 °C for 3 to 10 d with distilled water or acidic solutions using a mixture of silica-gel derived from alkoxide and gibbsite with a Si/Al ratio of 1:1 as the starting material. Use of acidic solution for the synthesis promotes the dissolution of the starting materials and leads to kaolinitization at an earlier stage of the reaction. However, the rate of kaolinitization is found to be rather slow, in comparison to the reaction with distilled water. The synthetic kaolinite was characterized by X-ray powder diffraction pattern. Kaolinite synthesized with distilled water was poorly grown for direction of the stacking. For example, crystallite size along the c*-axis = 155 Å, whereas kaolinite synthesized with acidic solution gave a higher crystallite size along the c*-axis, such as 253 Å in the case of the synthesis with 0.1 N HCl. Hinckley index of the synthetic kaolinite was varied from 0.35 to 0.80 by the acidity of the reaction. Different kaolinitization processes are implied by differences observed in the rate of kaolinitization, which has an influence on the nature of the stacking faults of the kaolinite.

The crystallization kinetics of goethite were studied colorimetrically under highly alkaline conditions (pH 10.1–12.2) at temperatures from 40° to 85°C. Color changes during crystallization from fresh precipitates, plotted on a*-b* colorimetric diagrams, were used to discriminate between pure goethite and mixtures of goethite and hematite. Only the b* value increased as goethite crystallization proceeded, and even a minor increase in the a* value revealed the existence of hematite. The rate of goethite crystallization, estimated from the b* value, could be modeled by a pseudo-first-order rate law. This rate depended both on pH and on temperature. Apparent activation energies for the reactions of 56.1 kJ/mol at pH 11.7 and 48.2 kJ/mol at pH 12.2 were estimated from Arrhenius plots.

Color variations from brown to yellow of synthesized goethite have been studied colorimetrically and spectroscopically. Goethite with various colors was synthesized at pH 13 and 40°C by varying the incubation time. Colorimetry revealed that the b* value (yellowish chroma) in L*a*b* color space was a quantitative indicator of color variations of the diluted samples. From UV-VIS-NIR spectra, the increase in the b* value was found to be caused by the increase in crystal field absorptions due to goethite formation around 500 nm. The b* value was a good indicator of the relative proportion of goethite in the precipitates including ferrihydrite. X-ray diffraction patterns and infrared spectra revealed that crystallization of goethite was associated with loss of water from the proto-ferrihydrite.

The influence of tartaric acid and pH on chemical composition, morphology, surface area, and porosity of short-range ordered Al precipitation products was studied. Samples were prepared (1) at pH 8.0 and at the tartaric acid/Al molar ratios (R) ranging from 0 to 0.25 and (2) at R = 0.1 and in the pH range of 4.7 to 10.0. In Al precipitation products formed at pH 8.0, the organic C content increased from 8 g/kg (R = 0.01) to 93 g/kg (R = 0.25), whereas the Al content decreased from 363 g/kg (R = 0.01) to 271 g/kg (R = 0.25). The specific surface of the materials was particularly high (>400 m2/g) when samples were prepared at R < 0.1, but drastically decreased when samples were prepared at R > 0.1 (e.g., 78.6 m2/g at R = 0.25). When the C content was relatively high (>45 g/kg), aggregation between the particles was promoted, and the specific surface, thus, decreased. Electron optical observations showed that such samples were strongly aggregated. In the materials prepared at R = 0.1, but at different initial pH values, the C content decreased from 90 g/kg (pH = 4.7) to 25 g/kg (pH = 10.0). As a consequence, the lower the initial pH, the lower was the specific surface of the Al precipitation products. Tartaric acid plays an important role in both Pertubation of crystallization of Al hydroxides and promotion of aggregation of the reaction products. The two processes counteract in influencing the specific surface and pore volume of Al hydroxides.

Heating treatments greatly affected the specific surface and porosity of Al precipitation products. The specific surface and porosity of the samples generally increased by increasing the temperature up to 400°C and then decreased. Small amounts of C still remained after heating some samples for 12 hr at 600°C.

We investigated the crystallization of ferrihydrite prepared by hydrolysis of Fe(NO3)3 solutions containing phosphate. Crystallization was studied at different pH (3–9), temperatures (298, 323, and 373 K), and initial P/Fe atomic ratios for periods to 730 d. Generally, crystallization was inhibited or only poorly crystallized lepidocrocite was formed at P/Fe > 2.5%. Phosphate favored the formation of hematite over goethite at all temperatures for most of the pH and P/Fe ranges investigated. This result is consistent with a model in which phosphate acts as a template for hematite formation, in analogy with other anions, such as oxalate. However, goethite was preferentially formed at alkaline pH and P/Fe > 1%, probably because high phosphate concentration resulted in a large increase in the negative charge of the ferrihydrite particles. This resulted in turn in less aggregation, a process that is known to precede dehydration to hematite. Phosphate greatly influenced the morphology of hematite and goethite. Hematite was often ellipsoidal or spindle-shaped. Twinned goethite crystals with a hematite core were formed at alkaline pH at P/Fe > 1%. Both hematite and goethite particles incorporated phosphate in an occluded form not desorbable by repeated alkali treatments.